'COTTAP-2,Rev 1,Theory & Input Description Manual.' · in buildings where compartments are...
Transcript of 'COTTAP-2,Rev 1,Theory & Input Description Manual.' · in buildings where compartments are...
COTTAP-2, REV. 1
THEORY AND INPUT DESCRIPTION MANUAL
Prepared by.
N. A. Chaiko
and
H. J. Murphy
'5 (<
NOVEMBER 5, 1990
9103260165 910319PDR ADOCK 05000337P PDR
PAL Form 2454 i10/83)Cat, s973401 $E -B- N A -04 6 R- .0
1'ept.
Date It- I> 19 ~~Designed by
Approved by
PENNSYLVANIAPOWER & LIGHTCOMPANY - ER No.CALCULATIONSHEET
PROJECT
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 withoutMass Transfer Between CompartmentsBalance Equations with MassTransfer Between Compartments
2.1.2 Slab Heat Transfer Equations 12
2.1.2.1 Conduction Equation and BoundaryConditions
2.1.2.2 Film Coefficients2.1.2.3 Initial Temperature Profiles
131723
2.1.3 Spdcial Purpose Models
2.1.3.12.1.3.22.1.3.32.1.3.42.1.3.52.1.3.62.1.3.72.1.3.82.1.3.92.1.3.10
Pipe Break ModelCompartment Leakage ModelCondensation ModelRainout ModelRoom Cooler ModelHot Piping ModelComponent Cool-Down ModelNatural Circulation ModelTime-Dependent Compartment ModelThin Slab Model
24252833343539414343
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
54555960
rrPE 1. Form 2lSl (rar831Ckr, l973401 $E -B- N A-0 4 6 Rev.0 l''
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~Lof
PENNSYLVANIAPOWER & LIGHTCOMPANY .ER No.CALCULATIONSHEET
3.5
3.63.73.83.93.103.11
3.123.133.143.153.163.173.183. 193.203.213.223.233.243.253.263.27
Error Tolerance for Compartment Ventilation-Flow Mass BalanceEdit Control DataEdit Dimension DataSelection of Room EditsSelection of Thick-Slab EditsSelection of Thin-Slab EditsReference Temperature and Pressure forVentilation FlowsStandard Room DataVentilation Flow DataLeakage Flow DataCirculation Flow DataAir-Flow Trip DataHeat. Load DataHot Piping DataHeat-Load Trip DataPipe Break DataThick Slab Data (Card 1 of 3)Thick Slab Data (Card 2 of 3)Thick Slab Data (Card 3 of 3)Thin Slab Data (Card 1 of 2)Thin Slab Data (Card 2 of 2)Time-Dependent Room Data (Card 1 of 2)Time-Dependent Room Data (Card 2 of 2)
616162636364
6465666768697071737475787980818284
4. SAMPLE PROBLEMS 85
4.1
4.2
4.3
4 4
4.5
4.6
Comparison of COTTAP Results with Analytical Solutionfor Conduction through a Thick Slab (Sample Problem 1)Comparison of COTTAP Results with Analytical Solutionfor Compartment Heat-Up due to Tripped Heat Loads(Sample Problem 2)
COTTAP Results for Compartment Cooling by NaturalCirculation (Sample Problem 3)COTTAP Results for Compartment Heat-Up Resulting froma High-Energy Pipe Break (Sample Problem 4)COTTAP Results for Compartment Heat-Up from a Hot-PipeHeat Load (Sample Problem 5)Comparison of COTTAP Results with Analytical Solutionfor Compartment Depressurization due to Leakage (SampleProblem 6)
85
96
98
103
112
117
: ~
PPLL Form 2l54 l1$S3)
C4t. e9Q401
F -B- N A.-04 6 Rev.0
1'ept.
Date 19
Designed by
Approved by
PROJECT~ ~ ~
Sht. No. ~ofPENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET
5 . REFERENCES
APPENDZX A THERMODYNAMZC AND TRANSPORT PROPERTZES OFAZR AND WATER
122
126
l
PPKL Form 2I54 (1083)Cat. t9%401
$F -B- N A =04 6 Rev.ap
Dept.
Date 19
DesIgned by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.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.
PPdL Form 2i54 (10/83)Cat. S9D401 (F B fq A-Q4 5 Rev. Q
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
CALCULATIONSHEET
The scale of this problem is rather large in that a model of the Unit 1I
and Unit 2 secondary containments consists of approximately 120S
compartments and 800 slabs. In addition to the large size of the problem,
the temperature behavior is to be simulated over a long period of time,
typically one hundred days. Zt is therefore necessary to develop a code
that can not only handle a large volume of data, but can also perform the
required calculations with a reasonable amount of computer time.
Zn addition to large scale problems COTTAP is capable of modeling room
heatup due to breaks in hot piping and cooldown due to condensation and
rainout. It also contains a natural circulation model to simulate
inter-compartment flow.
The purpose of this calculation is to demonstrate the validity of this
computer code with regard to the types of analyses described above. This
validation process is carried out in support of the computer code
documentation package PCC-SE-006.
pphL Form 2454 lror83rCar, e97&or
S< -B- N A-0 4 6 gee O ~.
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. of8
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.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 thissection. 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 the1
mass-tracking parameter MASSTR (see problem description data cards in
section 3.2).
2.1.1.1 Balance E ations without Mass Transfer between Com artments
If MASSTR 0, the compartment mass balance equations are neglected and the
total mass in each compartment is held constant'throughout the
calculation. This option can be used if there is no air flow between
compartments or if air flow is due to ventilation flow only '(i.e., there
are no leakage or circulation flow paths) . In COTTAP, ventilation flow
PPhl. Fofrft 2454 1fof83)Cat. ff973lol
SE -B- N A-046 Rev.0];
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. fff of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
rates are held constant at their initial values> thus, if the net flow out
of each compartment is zero initially, then there is no need for a
compartment mass balance because the mass of air in each compartment
remains constant.
Zn this mode of calculation, the moisture content of the air (as specified
by the value of compartment relative humidity on the room data cards, see
section 3.12 ) is only used to calculate the film heat transfer
coefficients for thick slabs; the effect of moisture content on the heat
capacity and density of air is neglected. The compartment energy balance
used in COTTAP for the case of MASSTR=O is
P C VdT =Q +0 +0 +Qa va —r light Qpanel motor cooler Qwall misc pipingdt
N+ P W . (T . +a) C (T .)
j=1 vj vj o pa vj
where T ~ compartment (room) temperature ( F),0Z
t ~ time (hr),
p density of air within compartment (ibm/ft ),3a
C constant-volume specific heat of air (Btu/ibm F),0va
3V ~ compartment volume (ft ),
(2-1)
Qli h compart ent lighting heat lead (Btu/hr).light
panel
Q otor
= compartment electrical panel heat load (Btu/hr),
= compartment. motor heat load (Btu/hr),
PP9t. Form 2454 t>583)Cat, e913%1
SE -B- N A-046 Rev0g:
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHT COMPANY. 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 compartmentai r (Btu/hr),
misc
Nv
miscellaneous compartment heat loads (Btu/hr),
number of ventilation flow paths connected to thecompartment,
WVjT
VjC (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),0v3
a = 459.67 F.0
Ventilation flow rates are positive for flow into the compartment and
negative for flow out of the compartment.
Compartment lighting, panel, motor and miscellaneous loads, which are
input to the code, remain at initial values throughout the transient
unless acted on by a trip. Heat loads may be tripped on, off, or
exponentially decayed at any time during the transient. Use of the heat
load trip is discussed in Section 3.19, and the exponential decay
approximation is discussed in Section 2.1.3.7.
The compartment room cooler load is a heat sink and is input as a negative
value. The code automatically adjusts this load for changes in room
ppd,L Form 2454 n0/831Cat. «97340I
SE -~- N A -0 4 6 Rev.Q P
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. 4 of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
Itemperature. 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 istaken for compartment heat rejection to a pipe when compartment
temperature exceeds pipe temperature. When this situation occurs, the
piping heat load is set to zero and remains there unless compartment
temperature decreases below pipe temperature. If this should occur a
positive piping heat load would be computed in the usual'anner. Piping
heat loads as well as room cooler loads may be tripped on, off, or
exponentially decayed. See Section 2.1.3.6 for a detailed description ofthe piping heat load calculation.
The rate of heat transfer from walls to compartment air is calculated from
N
E h.A.(T . - T),wwall . j j surfj r
'~1
(2-2)
whereN ~ the number of'walls (slabs) surrounding the room,w
h . = film heat transfer coefficient (Btu/hr ft F),2 0j
PP5L Form 2L54 (la(83)Cat. %7340l
SE -8- N A -0 4 6 Rev.Q
y'ept.
Date 19
Designed by
Approved by
'ROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
A. = surface area of wall (ft ),2
and
T . = wall surface temperature ( F).0surf j
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 inorder to maintain constant pressure. In this situation a model which
accounts for mass exchange between compartments is recpxired. Use of
MASSTR=.O, where applicable, is highly desirable especially for problems
with many compartments and slabs because large savings in computation time
can be realized. The more general case of MASSTR=1 is described below.
2.1.1.2 Balance E ations with Mass Transfer Between Com artments
When the mass-tracking option of COTTAP is selected (MASSTR~1), special
purpose models are available for describing air and water-vapor leakage
between compartments, circulation flows between compartments, and the
effect of pipe breaks upon compartment temperature and relative humidity.
ppat. Form P«5«<1$ 83t
C«t. «973«01 S~ -B" N A -G 4 6 Rev.Q ]
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.CALCULATIONSHEET
and
A. ~ surface area of wall (ft ),2
j
T . ~ wall surface temperature ( F).0surfj
Use of MASSTR~O is only valid for the case where compartment temperatures
undergo small or moderate variations. For these situations, maintaining
constant mass inventory in each compartment i.s a fairly good approximation
since density changes are small. If large temperature changes occur,
compartment mass inventories will undergo significant fluctuations in
order to maintain constant pressure. In this situation a model which
accounts for mass exchange between compartments is required. Use of
MASSTR=O, where applicable, is. highly desirable especially for problems
with many compartments and slabs because large savings, in computation time
can be realised. The more general case of MASSTR~1 is described below.
2.1.1.2 Balance E ations with Mass Transfer Between Com artments
When the mass-tracking option of COTTAP is selected (MASSTR~1), special
purpose models are available for describing ai.r and water-vapor leakage
between compartments, circulation flows between compartments, and the
effect of pipe breaks upon compartment, temperature and relative humidity.
pplLL Form 2«si n0183)C«t. «913401
SE -B- N A-046 RevQp
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
The air and vapor mass balance erpxations that are solved by COTTAP for the
case of MASSTR~1 are
NVdP ~P W.Y—a . vj vjdt j~l
Nl+ E W . Y
3««1 3 3
N+ Z (W ~ Y ~ ~
- W ~ Y ~ l«cj,in cj,in cj,out cj,outjul(2-3)
NVdP ~ P W . (1 Y .)
dt j~l
Nl+ g W . (1-Y .)
13 13
N+ Z [W .. (1-Y .. ) - W . (1-Yc
cj,in cj,in cj,out cj,out
+W -W -Wbs cond ro'2-4)
where p ~ compartment air density (ibm/ft ),3a
3p compartment water vapor density (ibm/ft ),vN number of ventillation flow paths connected to thev
compartment,
ppct. Form 2454 nOI83iCol, I873401
Ix—SE -B- N A -0 4 6 Rev,p g>
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~O of
PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.CALCULATIONSHEET
N ~ number of leakage paths connected to the1
compartment,
N ~ number of circulation paths connected toc
the compartment,
W . ~ total mass flow through leakage path j (ibm/hr),ljW . . = total inlet mass flow through circulationcj,in
path j (ibm/hr),
W . = total outlet mass flow through circulationcj,outpath j (ibm/hr),
l
Y . ~ air mass fraction for ventilation path j,vjY . ~ air mass fraction for leakage path j,lj
Y . . ~ air mass fraction of inlet flow forcj,incirculation path j,
Y . = air mass fraction of outlet flow forcj,outcirculation path j,
Wb 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 1 is
Vf(T +a )p dC (T ) + p C (T ) + p dh (T )r o a~a r a pa r v~ rr r
«
PP«L Form 2«54 nOr83)C«r. «9'«Oi
SE -B- N A -0 4 6 Rev.0
1'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET
- p R - p R ] dT ~ -V(T + a )C (T )dpvv a a —r r o pa r —adt dt- Vh (T )dp + (T+a )(R dP + R dP )Vv dv o Zp a ddt
+Q.+Q+0+Q + Qlight panel Qmotor cooler piping+ 0 + 0 . + Q + W hmall misc break bs v, break- W h (T ) — W h (T )
N+ E 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) Ij=l lj lj lj o pa 1 j lj v ljN
+Z W .. [Y .. (T .. +a )C (T .. )
j 1cj,in cj,in cj,in o pa cj,in
+ (1-Y .. )h (T . ) ]cj,in v cj,inNc
W . [Y . (T+a)C (T)cj,out cj,out r o pa rj««1
+(1Y . )h (T)],cj,out v r (2-5)
where h saturated water vapor enthalpy (Btu/ibm),
h = enthalpy of steam exiting break (Btu/ibm)v,breakh (P ) if pipe contains liquid,v rh (P ) if pipe contains steam,v p
P ~ compartment pressure (psia),rP = pressure of fluid within pipe (psia),
P
ppB,L Foim 2i54 n(v83)Cat. e973401
SE -B- N A -0 4 6 Rev.P
y'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. I~ of
PENNSYLVANIAPOWER & LIGHT COMPANY - ER No.CALCULATIONSHEET
R ~ ideal gas constant for steam (0.1104 Btu/ibm R)v
R ~ ideal gas constant for air (0.0690 Btu/ibm R),0
Q heat transferred to air and water vapor frombreak
liquid exiting break as it cools to compartment
temperature (Btu/hr),C
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 Transfer B ations
The slab model in COTTAP describes the transient behavior of relativelythick slabs which have a significant thermal capacitance. Eor each thickslab, the one-dimensional unsteady heat conduction equation is solved to , ~
PP41, Form 2454 (10/831
Col. 4973401
SE -B- N A -0 4 6 Rey 0 >
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER & 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 tax2 2s s (2-6)
subject to the following boundary and initial conditions:
3TBx X~BT3x X~L
- h [T (t) - T (o,t)],—1 rlk s
-h [T (Lt) - T (t)J,—2 sk z2
(2-7)
(2-8)
where
T (x,o) ax+ b,s
T (x,t) = slab temperature ( F),0s I
t ~ time (hr),
(2-9)
PP&L Form 245'0r&3)Col, 0970401
SE -B- N A -0 4 6 R~v 0
1'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
x ~ spatial coordinate (ft),~ thermal diffusivity of slab m k/(p C ) (ft /hr),2
s ps~ thermal conductivity (Btu/hr ft F),
p ~ slab density (ibm/ft ),3
C m specific heat of slab material (Btu/ibm F)ps 1
h ~ film coefficient for heat transfer between thy slab1and the room on side 1 of the slab (Btu/hr ft F),
h = film coefficient for heat transfer between thy slab2 and the room on side 2 of the slab (Btu/hr ft F),T 1(t) Temperature of room on side 1 of slab ( F),rlT 2(t) = Temperature of room on side 2 of slab ( F).r2
The slab and room arrangement described by these equations is shown inFigure 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 isgiven by
q (t) h A[T (o,t) «T (t) ], (2-10)
PP&L Form 2«&d (l0(83)Cat. «913«Of
SE -B- N A -0 4 6 Rev () y
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~8 of
PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.CALCULATIONSHEET
al (t) ~ SS(t)
Room on side 1 of slabat temperature T.l(t)r'1
SlabTemp «
T (x,t)s
Room on side 2 of slabat temperature T (t)r2
Side l of slabFilm coefficient hlHeat Transfer Area, A
~Side 2 of slabFil coefficient. h2Heat Transfer Area, A
X=O X=L
Figure 2.1 Thick slab and adjacent rooms
PPtLL Forrtt 2454 (10I83)C91, 991340t
N A-046 Rev.0g:
Dept.Date 19
Designed by
Approved by
PROJECT Sht. No. ~&of
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.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)J, (2-11)
where A is the surface area of one side of the slab.
A slab can also be in contact with outside ground. Calculation of the
heat loss from a slab to outside ground would involve modeling of
multi«dimensional unsteady conduction which would greatly complicate the
analysis. As a simplifying approximation, heat transfer from below grade
slabs to the outside ground is neglected by setting the film coefficient
equal to zero at the outer surface of every slab in contact with the
outside ground. This is a conservative approximation in the sense that
the heat loss from the building will be underpredicted giving rise to
slightly higher than actual room temperatures. The governing equations
for a below grade slab with side 2 in contact with ground are (2-6)
through (2-9) but with h set equal to zero. If side 1 of the slab is in2
contact with ground then hl is set to zero.
ppAL Form 245'$ 83)C4t. l873i01
N A 0 4 6 Rey Q )
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~7of
PENNSYLVANIAPOWER 5 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
throughout the entire calculation. Natural-convection film coefficients
are, however, temperature dependent, and values representative of the
average conditions during the transient should be used.
Suggested values of natural convection film coefficients for interior
walls and forced convection coefficients for walls in contact with outside
air are given in ref. 11, p. 23.3; note that the radiative heat transfer I
l
component is already included in these coefficients. l
PPEL Form 2454 noI83)CSt. 4973S01
SE -B- N A-04 6 Rev.a
y'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
.PENNSYLVANIAPOWER & LIGHT COMPANY ER No.CALCULATIONSHEET
Correlations are also available in COTTAP for calculation of naturalconvection film coefficients. Coefficients for vertical slabs are
calculated from (ref. 8 p.442)
h = kclC
0.825 + 0.387 Ra
[1+(0 492/P )9/16)8/27(2-12)
wher e h1
= natural convection film.coefficient for verticalclslab (Btu/hr ft F),2 0
k ~ thermal conductivity of air (Btu/hr ft F),
C ~ characteristic length of slab (slab height in ft) .
The Rayleigh and Prantl numbers are given by
Ra ~ g8(3600) (T -T )C /@(x) P
2 3surf r L (2-13)
Pr ~ AC /k,P (2-14)
where g ~ acceleration due to gravity (32.2 ft/sec ),2
0 -1g coefficient of thermal expansion for air ( R ),g ~ kinematic viscosity of air (ft /hr),2
PPiLL FOrm 2i54 tttt183tCat. tt913401
SE -8- N A-046 RevQP
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET
a = thermal diffusivity of air (ft /hr),2
"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 isalso 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 Ra1/5
c2L
(2-15)
and for the case of upward heat, flow the correlations are (ref. 8, p.445)
h ~ 0.54 k Ra1/4c3
L
(Ra<10 )7 (2-16)
h 0.15 k Ra1/3
c3C
(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) .
PPdL Form 2l54 nOI831CaL l973401
J.
SE -B- N A -0 4 6 R ".0
y'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. 40 of
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.CALCULATIONSHEET
The effect of radiative heat transfer between slabs and compartment air isalso 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 theradiation coefficient:
h ~ (6 +1) (4+a+b-c) e QTn<a 3
w,av av2
(2-18)
where o
Tav
TZ
Stetan-Boltzman constant (0.1712x10 Btu/hr ft R ),-8
[ [(T +a ) +(T +a ) ]/2) ( R)4 4 1/4 or o surf o
~ compartment air temperature ( F),T ~ slab surface temperature ( F),0surf
sC 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 inequation (2-18) because gases such as N and 0 .are transparent to thermal2 2'
I
II
PP&L Form 2454 n0r&3)Col. @910401
SE -8- N A -0 4 6 Rev 0
>'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATIONSHEET
radiation (ref. 11, p.3.11), and the effect due to CO is negligible2
because of its small concentration (0.03% by volume, ref. 12, p.F-206) .
The emissivity of water vapor is a function of the partial pressure ofwater vapor, the mean beam length, the gas temperature, and the totalpressure (ref. 13, pp.10-57, 10-58) .
The Cess-Lian equations (ref. 21), which give an analytical approximationto the emissivity charts of Hottel and Egbert (ref. 22), are used tocompute the water vapor emissivity. These euqations are given by
6 (TP,P,P L ) =A [1 exp(AX )]1/2w a w'wm o 1 (2-19)
X(T,P iP,P L ) ~ P LI 300 ta'' m w m L T 3
P + [5(300/T) + 0.5] Pa 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 forpurposes of this work, they are represented by the following polynomial
expressions:
pp&L Form 245« (lorLr'rCar. «sncor
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-5 -9 2
0 (2-21)
A (T) = 1.0914 + 1.432x10 T + 3.964x10 T (2-22)
where 273K < T < 600K. Tabular values of A and A over the widero 1
temperature range 300K < T < 1500K are available (ref. 21). Zn equation
(2-18), 8 has the value 0.45, and a and C are defined by
I)in[a (TP «P «P L ) ]a w ''' m
Bln(P L )w m
(2-23)
and
3ln[e (T,P,P,P L ) ]w ''' m
r)ln (T)
(2-24)
n,Values of a and b are obtained through differentiation of the Cess-Lian
equations. The average mean beam length L for a compartment ism
calculated from
L R 3.5V/Am
(2-25)
Which is suggested for gas volumes of arbitrary shape (ref. 19) . Zn
(2-25) V is the compartment volume and A is the bounding surface area.
PP&1. Form 245l n0r831Cat. e973401
SE. -B- N A -0 4 6 Rev.0 y
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,O)/dx = 0,2 2=s (2-26)
dT (x,O)dx
-h [T (0) - T'0,0) ] g
0 kl rl s(2-27)
dT (x,o)dx
-2 s '2-h [T (LrO) - T (0) ].x=L
(2-28)
The solution is
T (xO) =ax+b,s
where
(2-29)
h [T (0) T (0) ]
k+hL+kh/h(2-30)
b ~ T (0) + k h [T (0) - T (0) l ~
h [k + h L + k h /h ]1 2 2 1
(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.
ppBL Form 2454 n$83)Ca<. s9rm>
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
2.1.3 S ecial Pu ose Models
2.1.3.1 Pi e Break Model
Pipe breaks can be modeled in any COTTAP standard compartment. Lines may
contain steam or saturated water as indicated by the Fluid State flag,ZBFLG, on the Pipe Break input data cards (see Section 3.20) . Zf the pipe
contains water, the following energy balance is solved simultaneously
with the continuity equation to determine the flowrate of steam exitingthe break:
W h (P ) ~W h (P ) + [W -W ]h (P ),bt f p bs v r bs f r (2-32)
where W total mass flow existing the break (ibm/sec.),
Wb steam flow exiting break (ibm/sec.),bs
h ~ enthalpy of saturated liquid (Btu/ibm),fh ~ enthalpy of saturated vapor (Btu/ibm),vP ~ fluid pressure within pipe (psia),
P
P ~ compartment pressure (psia).r
IAs a conservative approximation, the liquid exiting the break is cooled to
room temperature and the sensible heat given off is deposited in the
ppd 1. Form 2l54 nord3lCat, t973l01
SF -B- N A -0 4 6 Rev.0
1'ept.
Date 19
DesIgned by
Approved by
PROJECT Sht. No. 4~ 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 frombreak
Q = lW -Wb] [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.
Zn the case where the pipe contains high-pressure steam, all of the mass
and energy exiting the break is deposited directly into the air space of
the compartment. This is a reasonable approximation for steam line
pressures of interest in boiling water reactors.
2.1.3.2 Com artment Leakage Model
Znter-compartment leakage paths such as doorways and ventilation ducts can
be modeled using the leakage path model in COTTAP. Leakage paths are
specified on leakage path data cards (Section 3.14) by inputting the
leakage path ZD number, flow area, pressure loss coefficient, ZD numbers
of rooms connected by the leakage path, and the allowed directions for
PP&t. Form 2c54 ttor&3)Cat, rr97340t
SE -B" N A -0 4 6 Rev.0 >
Dept.
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 proportionalcontrol model:
W m C (A /A ) 'Pl pl l max (2-34)
where W = leakage flow rate (ibm/hr),
plAl
proportionality constant (ibm-in /hr-lbf),2
leakage path flow area (ft ),2
A = max flow area for all leakage paths (ft ),2
rIIP pressure differential between compartments (psia) .
The constant C is specified on the input data cards (Section 3.2). The
model given by (2-34) is used primarily to maintain constant pressure incompartments 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 tocompartment heat up.
PP&L Form 2c54 nor83iCol. @973401
SE -B- N A -0 4 6 Rev.Q
g'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~4 of
PENNSYLVANIAPOWER & 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. Zn this case the leakage rate is computed
by balancing the intercompartment pressure differential with an
irreversible pressure loss:
1 li li (3600) ~ hP
2g P 1A1 (144)2
(2-35)
where K = 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 leakage1
flow (ibm/ft ),3
BP = pressure difference between compartments associated with
leakage path (psia) .
A maximum leakage flow rate for each path is calculated from
Wl p min (V iV ) C1 tmax 1' p2'2-36)
PP4l Form 2454 (10/83)C4t. rr973401
SE -B- N A -Q 4 6 Rev.Q
g'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~4of. PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET
where Vl and V are the vo1umes ( ft ) of the compartments connected by3
3the leakage path, p (ibm/ft ) is the average of the gas density-1for the two compartments, and C
2(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 thesat, vpartial pressure of vapor within the compartment. T f is the slabsurfsurface temperature.
pp&L Form 2l54 n0/83)Cat. e973401
SE -B- N A-0 4 6 Rev,0 f
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.CALCULATIONSHEET
Zn order to avoid numerical instabilities caused by rapid fluctuation
between natural convection and condensation heat transfer modes, the
condensation coefficient is linearly increased to its full value over a 2
minute period. Similarly, the condensation coefficient is decreased over
a 2 minute period if condensation is switched off. Modulating the
transitions between the two heat transfer modes allows use of much larger
time steps than would otherwise be possible. The condensation heat
transfer coefficient is calculated from the experimentally determined
Uchida correlation which includes the diffusional resistance effect of
non-condensible gases on the steam condensation rate (ref. 16 p. 65, ref.
20) .
Values of the Uchida heat transfer coefficient, as a function of the
compartment air/steam mass ratio, are given in Table 2.3. COTTAP uses
linear interpolation to obtain the condensation coefficient at the desired
conditions.
PPa 1. Form tfa5l (10/831
Cat. ffgrm1'1
SE -B- N A -0 4 6 Rev,0 1
Dept.
Date 19
Designed by
Approved by
PROJECT Sht, No.
aloofPENNSYLVANIAPOWER & LIGHT COMPANY ER No.CALCULATIONSHEET
Table 2.3 Uchida Heat Tranfer Coefficient*
Mass Ratio(Air/Steam)
, Heat Transfer Coefficient(Btu/hr-ft - P)
(0.100.500.801.301.802.303.004.005.007.00
10.0014.0018.0020.00
>50.00
280.25140.1398.1863;1046.0037.0129.0823.9720.9717.0114.0110.019.018.002.01
*Values from ref. 16, p. 65
PP&L Form 2I54 (>0183)
Cat. %13401SE -B- N A -0 4 6 Rev.0
>'ept.
Date 19
DesIgned by
Approved by
PROJECT Sht. No. ~ I 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. Zn
addition, radiation heat transfer between the vapor and walls also occurs
during condensation. Under conditions where condensation occurs, the rate
of heat transfer to a wall is calculated from
a =-h A (T — Tu 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 0u
A = wall surface area (ft ),2w
oT ~ compartment air temperature ( F),r
T ~ wall surface temperature ( F).0surf
PPAL Form 2454 I>0/80)Cat. 40%401
~ )
SE -8- N A -0 4 6 Rev.Q gl
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATIONSHEET
The corresponding condensation rate at the wall surface is calculated from
W = (h -h)A (T - Tcond u w r surfh
(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 0c
-2 0h = thermal radiation coefficient (Btu/hr-ft - F).r
Equation (2-39) accounts for the fact that during condensation a
significant fraction of the total heat transfer rate to the slab surface
is in the form of sensible heat. In computing the sensible heat fraction,it is assumed that the condensate temperature is approximately equal to
the slab surface temperature, i.e., the major resistance to condensation'I
heat transfer is associated with the diffusion layer rather than the
condensate film.
PP6L Form 2l54 nOI83lCol. @913403
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
2.1.3.4 Rain Out Model
Rain out phenomena is important in compartments containing pipe breaks.
The model used in COTTAP is a simple proportional control model that
maintains compartment relative humidity at or below 100%. Zt is activated
when the relative humidity reaches 99%. The rain out of vapor is
calculated from
and
W = (200.0 RH — 198.0) max(W ., C ) (RH > 0.99),ro vap,in'l (2-40)
W ~ 0.0ro (RH < 0.99), (2-41)
where
W ~ rate of vapor rainout (ibm/hr),roC user specified constant (see section 3.2),rl
W . net vapor mass flow into the compartment (ibm/hr),vap,in
RH = relative humidity.
PPAL. Form 2454 n0/83lCjt, 097340l
'SE -B- N A -0 4 6 R-v.o y:
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),cool c,avg r (2-42)
where QcoolC
Tc, avg
and
~ cooler load (Btu/hr),0- T ),Btu/hr F,Qcool initial c,avg initial r initial
0= average coolant temperature ( F),
(T . + T )/2c,in c,out
oT = compartment temperature ( F).r
The inlet cooling water temperature, T i , is supplied as input, and thec,in'utlet
cooling water temperature, T , is calculated from the coolingcgoutwater energy balance,
Q =C(T - T) ~W C (T - T ),cool c,avg r cool pw c,in c,outwhere
(2-43)
W ~ cooling water flow rate (ibm/hr),cool
pphL Form 2454 nar83)car. rr973401
S~ -8- N A-046 Rev.0>
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET
C = specific heat of water (1 Btu/ibm F).0pw
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 ing Model
In COTTAP, the entire piping heat load is deposited directly into the
surrounding air. This is a conservative modeling approach because in
reality a substantial amount of the heat given off by the piping is
transferred directly to the walls of the compartment by radiative means.
If film coefficients accounting for radiative heat transfer between
compartment air and walls are used in compartments containing large piping
heat loads some of this conservatism may be removed.
The piping heat load term in Equations (2-1) and (2-5) is calculated from
Q .. = VIED (T T )ipiping f r '2-45)
PPlkL Form 2c54 tlor83>CaL tr013401
SF- "B- N A "0 4 6 Rev.O lt
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
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 insulate'd
pipes, the overall heat transfer coefficient is calculated from
U ~ D. ln(D /D ) + 1
2k H +Hc r
(2-46)
where D ~ Insulation outside diameter (ft),iD ~ Pipe outside diameter (ft),
P0k ~ Insulation thermal conductivity (Btu/hr ft F),
2 0H ~ Convective heat transfer coefficient (Btu/hr ft F),c
H ~ Radiation heat transfer coefficient (Btu/hr ft F).2 0r
pp2L Form 2454 n0/821Cht. rr973401
SE "B- N A -0 4 6 Rev.Q
y'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~3of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER, No.CALCULATIONSHEET
For uninsulated pipes,
U~H +Hc r (2-47)
The convective heat transfer coefficient, H , is calculated from thec~
'ollowingcorrelation for a horizontal cylinder (ref. 8, p. 447):
H = (k. /D)c air o0.60 + 0.387 Ra
9/16 8/27[1+(0.559/Pr) )
(2-48)
where k . = thermal conductivity of air (Btu/hr-ft- F),0air
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)r
H ~ CG(T — T )/(T -T ) I4 4
r r surf r s(2-49)
where e ~ pipe surface emissivity,
PP41. Form 2454 110I831
Ca1. rr9 73401
SE -8- N A-046 Rcv.Qy
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~S of
.PENNSYLVANIAPOWER & LIGHTCOMPAN f ER No.CALCULATIONSHEET
-8 2o4a m Stephan Boltzman constant (0.1712xl0 Btu/hr-ft - R ),0
T ~ compartment ambient temperature ( R),r
0T = pipe surface temperature ( R) for uninsulated pipessurf
0insulation surface temperature ( R) for insulated pipes.
The Rayleigh number is given by:
R ~ (3600) g (T -T )D2 3
a surf r o (2-50)
where g ~ 32.2 ft/sec 2
g ~ volumetric thermal expansion coefficient (1/ R),0
2v ~ kinematic viscosity (ft /hr),a ~ thermal diffusivity (ft /hr),2
0T ~ pipe surface temperature ( F) for uninsulated pipe,surf
0~ insulation surface temperature ( F) for insulated pipe,0
T ~ compartment ambient temperature ( F),r
D ~ pipe outside diameter (ft) for uninsulated pipe,0
~ insulation outside diameter (ft) for insulated pipe.
The Prandtl number is calculated from
Pr ~ C I1/k,P
(2-51)
PPAL Form 2954 (10/83)Cat, rt923401
SE -B- N A -0 4 6 Re..0 >
Dept.Date 19
Designed by
Approved by
PROJECT Sht. No. ~9 of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
where C = specific heat (Btu/ibm F),0P
I2 = viscosity (ibm/ft hr),
k = thermal conductivity (Btu/hr ft F) .0
2.1.3a7 Com onent Cool-Down Model
Zn COTTAP, the cooling down process of a component such as a pipe filledwith 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) m T0 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 roomrtemperature, and t is the time at which the component starts to cool
0
down.
PPd L Form 2«5« (10)83)ca~. «9yuoi
SE -8- N A -0 4 6 Rev.0
1'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~> of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
Since most of the rooms in the secondary containment are rather large, itis reasonable to assume that the component temperature changes much faster
than the room temperature> that is, T (t) is fairly constant during thercooldown process of the component. With this assumption, T (t) can berreplaced with T (t ) in equation (2-52) to obtainr o
VPC d UA[T-T (t ) I = -UA[T(t)-T (t ) I.UA dt r 0 r 0, (2-54)
Rewriting (2-45) in terms of the heat loss from the component, Q, gives
+d= -Q(t),
Ydt (2-55)
Y ~ pC V/UA.P
where Y is the thermal time constant of the component and is given by
(2-56)
The solution to (2-46) is
Q(t) ~ Q(t ) exp[-(t-t )/Y].0 0 (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, t .0
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 he calculated hy the code. Pot pipes filled with liquid, the~ ~
PPI,(. Form 2454 (l0/83IC4(. 4973401
SE -B- N A "0 4 6 Rev.Q P
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER & LIGHT COMPANY. ER No.
CALCULATIONSHEET
volume average density and the mass average specific heat of the licgxid
and metal are used in the calculation of Y. For pipes initially filledwith 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 = total internal energy of the fluid (Btu),fT the initial fluid temperature "( F),foT = the initial room temperature ( F),0
zo
M = mass of metal (ibm),m
M mass of fluid (ibm),f
C = specific heat of the metal (Btu/ibm F) .0
pm
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 iscalculated by balancing the pressure differential, due to the difference
in air density between compartments, against local pressure losses within
the circulation path;
pphL Form 2a5a rr0'83tCat, rr9734m
N A "0 4 6 Rev.Q y'.
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER 8 LIGHT COMPANY 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 circulational a2
path (p > p ), ibm/ft ,3
E,Eu
K,Ku
~ elevations of lower and upper flow paths respectively (ft),a
m pressure-loss coefficients for lower and upper flow paths
respectively,
A ,A ~ flow areas of lower and upper flow paths respectively1'
(ft )a
g m acceleration due to gravity (32.2 ft/sec ) .
A leakage path (see Section 2.1.3.2) is included in the circulation path
model in order to maintain the same pressure in both compartments. Thus,
the flow rate calculated from eq. (2-59) is adjusted to account for this
leakage.
rrrr6r. Form 2r54 l10r86)Car„rr97>0>
SE -B- N A -0 4 6 Rev.0
y'ept.
Date 19
Designed by
Approved by
PROJECT Shr. No. ~80f
.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.
Zn this model, transient environmental conditions are supplied as input
data. The data is supplied in tabular form by entering up to 500 data
points for each time-dependent room, with each data point consisting of a
value of time, room temperature, relative humidity, and pressure.
A method is also available in COTTAP to describe periodic tsinusoidal)
temperature variations within a room. In using this option, the amplitude
and frequency of the temperature oscillation and the initial room
temperature are supplied in place of a data table.
2.1.3.10 Thin Slab Model
Zt is not necessary to use the detailed slab model discussed in section
2.1.2 to describe heat flow through thin slabs with little thermalI
capacitance. Slabs of this type have nearly linear temperature profiles,I
and thus, the heat flow through the slab can be calculated by using anI
overall heat transfer coefficient. The rate of heat transfer through a
thin slab is obtained from
PP8,1. Form 2a541101821
C91. rr9 13401
SE -B- N A -0 4 6 Rev.P g:
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. 9+ of
PENNSYLVANIAPOWER & LIGHT COMPANY. ER No.CALCULATIONSHEET
q =UA[T (t) - T (t)J, (2«60)
where q = rate of heat transfer from the room on side 1 of the slab to
the room on side 2 (Btu/hr),
U = overall heat transfer coefficient'for the thin slab
(Btu/hr 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 the1
thin slabs and the values are. held constant throughout the calculation.
For thin slabs that model floors or ceilings, two values of U must be
supplied; one for upward heat flow and the other for downward heat flow.
For thin slabs that are vertical walls only one value of U can be
supplied. Up to 1200 thin slabs can be modeled with COTTAP.
2.2 Numerical Solution Methods
The governing equations to be solved consist of 3N + N ordinarysr tdrdifferential equations and N partial differential equations, where N is
s sr I
the number of standard rooms, N is the number of time-dependent rooms,tdr
ppht. aorn 2a5a ttor83tCat. e973401
S~ -8- IN A -0 4 6 Rev.0 gI
Dept.
Date 19
Designed bye
Approved by
PROJECT Sht. No. ~~ of
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.CALCULATIONSHEET
and N is the number of thick slabs. An energy balance and two masss
balances are solved for each of the standard rooms to determine air
temperature, air mass, and vapor mass. In addition, the one-dimensional
heat conduction equation is solved for each of the thick slabs. Ordinary
differential equations are also generated for the time-dependent rooms;
these equations are used only for time step control and will be discussed
later in this section.
The initial value ordinary differential equation solver, LSODES (Livermore
Solver for Ordinary Differential Equations with General Sparse Jacobian
Matrices), developed by A.C. Hindmarsh and A.H. Sherman is used within
COTTAP to solve the differential equations which describe the problem.
LSODES is a variable-time-step solver with automatic error control. This
solver is contained within the DSS/2 software package which was purchased
from Lehigh University (refe 2).
Before LSODES can be applied to the solution of the governing equations in
COTTAP, the N partial differential equations describing heat flow throughs I
Ithick slabs must be replaced with a set of ordinary differential III
equations. This is accomplished through application of the Numerical
Method of Lines (NMOL) (ref. 3). In the NMOL, a finite difference
approximation is applied only to the spatial derivative in equation (2-6),
PP8 t. Form 2454 rror83>
Car, rr9 7340 ISE -B- At A-04 6 "; .01
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.CALCULATIONSHEET
thus approximating the partial differential equation with N coupled
ordinary differential equations of the form
dT . = T ., i~1,2,...rN,~3. sxxi (2-61)
where N is the number of equally spaced grid points within the slab, TS3.
is the temperature at grid point i, and T . is the finite-differenceSXX1
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 subroutineSXX3.
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 TSXXi
T . ~ 1 [- T . + 16 T . — 30 T . + 16 T . - T . ]SXX3. —2 Si-2126 Si 1 S3. si+1 si+2
+O(~ )i (2-62)
where i = 3,4,...,N-2, and f5 is the spacing between grid points. A
six-point slopping difference formula is used to approximate T . at iSXX1
equal to 2 and N-lr
PPSt, Form 2954 |10/831
Cat. 9973aot
SE -B- N A -0 4 6 Rev.o ]
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.CALCULATIONSHEET
T ~ 1 [10 T - 15 T - 4 T + 14 T — 6 T + T ]sxx2 —2 s1 s2 s3 s4 s5 s6
and
+ 0(~ )a (2-63)
T 1 [10 T - 15 T - 4 T + 14 T — 6 T + T ]sxxN-1 —2126 sN sN-1 sN-2 sN-3 sN-4 sN-5
+ O(6 ). (2-64)
The finite difference approximations at the end points are formulated in
terms of the spatial derivative of the slab temperature at the boundaries
rather than the temperature, in order to incorporate the convective
boundary conditions (2-7) and (2-8) . The formulas are
T = 1 [-415 T + 96 T — 36 T + 32 Tsxxl —2 ~ sl126 6s2 s3 — s4
3
4-3 T — 506T ] + 0(h ),2
(2-65)
and
T ~ 1 [-415 T + 96 T - 36 T + 32 TsxxN —2 —sN126 6sN-1 sN-2 — sN-33.
-3T +506T ] +O(b ),2
(2-66)
where T and T are given bysxl sxN
T1
h [T (t) T (t) ]k
(2-67)
PP3,r Form 2«54 (19r83)Cat. «973401
'
SE -B- N A -0 4 6 Rev.p
i'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER 8 LIGHT COMPANY .ER No.
CALCULATIONSHEET
and
T = -h2 tT (t) — T (t) ].k
(2-68)
The total number of ordinary differential equations, N, to be solved is«q«now given by
NN =3N +N + N
eq sr tdr .~gj'~1
(2«69)
where N , is the number of grid points for slab j. Note that at least six
grid points must be specified for each slab.
Zt was previously mentioned that equations are generated for each
time-dependent room and are used for purposes of influencing the automatic
time step control of LSODES. The equation generated for each time
dependent room is
dT ~ g(t), (2-70)
where T is the time-dependent room temperature and g(t) is the timetdrderivative of the room temperature at time t. For rooms where temperature
versus time tables are supplied, g(t) is estimated by using a three-point
LaGrange interpolation polynomial. For rooms with sinusoidal temperature
pp&L Form 2a&a (10r&31
Cat, e913401SE -B- N A-04 6 novo 1
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & 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
k2
Y =E a.y .-hE B.F3 3 ~
0 3 3(2-71)
where h is the step size, and the constants a., and 8 . are given inj'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 ~o(2-73)
pp6L Form 9«5« n0'83)Cat, «973«0i
SE -8- N A-046 Rev,Q
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. $ 0 of
PENNSYLVANIAPOWER & LIGHT COMPANY. 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 . If1 2
k ~1, eq. (2-62) corresponds to Adam's method, and if k =0 it reduces to1 2
Gear's method. In both cases, the constant 8 is non-zero.0
Since 8 go, the finite-difference equations comprise an implicit algebraic0
system for the solution.y . In LSODES, the difference equations aren
solved by either functional iteration or by a variation of Newton's
method. If the functional iteration procedure is chosen, an explicitmethod is used to estimate a value of y; the predicted value is then
n'ubstitutedinto 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), byn
iteration, until convergence is attained. MP~10 corresponds to Adam'
method with functional iteration, and MP=20 corresponds to Gear's method
with functional iteration.
Unfortunately, the functional iteration scheme generally requires small
time steps in order to converge. The method can, however, be useful for
rapid transients of short duration.
The time step limitations associated with the functional iteration
procedure can be overcome, at least to some degree, by using Newton's
PPAL Form 2954 t tarot)Cat. 9913lol
SE -8- N A-046 Rev.P~
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~S of
PENNSYLVANIAPOWER & LIGHT COMPANY 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 to2
the Adam's method equations.
The conventional form of Newton's iteration scheme applied to Gear's
difference equations is described by
7
[s+1] ~ [s] ' [s] -1 ~ [s]
37
k— Za. y" ~ "hB F(t y ))1 [s]i n-i o n'ni=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-hB BF/By]. For large systems of equations this procedure is very time0
consuming.
In LSODES, the Jacobian is evaluated and the subsequent inversion of
[I-h 8 BF/By] is carried out only when convergence of the finite difference0
I
equations becomes slow. This technique is called chord iteration (ref. 5)
PP8,L Eorm 24' >0>83>
Ca<„e9uco>SE -B- N A -0 4 6 Re..0
g'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & 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 2«A <1583)Gal, «91340l
SF- -B- N A -0 4 6 Rev.Q g
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER 5 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 firstventillation flow data card but not within the room data cards and not
within the ventillation flow data cards.
The first line in the input data set is the title card. This card is
printed at the beginning of the COTTAP output. A listing of all the input
data cards following the title card is given below. The words that must
appear on each card are listed in order: Wl is word 1, W2 is word 2, etc.
The letters I and R indicate whether the item is to be entered in integer
or real format.
ppaL Form 2a5a nor83)Car„a9rwo>
~E -8- N A -0 4 6 Rev 0
)'ept.
Date
Designed by
Approved by
19
PROJECT Sht. No. ~G 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).
ppsL Form 2454 nsallCa4 N97340l
SE -B- N A-046 P "0~
Dept.
Date 19
Designed by
Approved by
PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.CALCULATIONSHEET
C
PROJECT Sht. No. ~of
W8-I NPIPE ~ Number of hot pipes (maximum value is 750).
W9-I NBRK ~ Number of pipe breaks (maximum is 20) .
W10-I NLEAK = Number of leakage paths (maximum is 500) .
Wll-I NCIRC ~ Number of circulation paths (maximum value is 500) .
W12-I NEC = Number of edit control cards. (At least one card must be
supplied, and a maximum of 10 cards may be supplied).
3.2 Problem Descri tion Data (Card 2 of 3)
Wl-I NFTRIP ~ Number of flow trips (maximum value is 300) . Flow tripscan act on ventilation flows, leakage flows, and
circulation flows.
W2-I MASSTR ~ Mass-tracking flag.
0~> Mass tracking is off. In this case, compartment
mass balances are not solvedr the total mass in each
compartment is held constant. In cases where thisoption can be used, it results in large savings in
ppLL Form 245'01s3)Cat, «973401
SE -B- N A -0 4 6 Rev.0
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~~ of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
computer time. In order to use this option, the
following input variables must be specified as:
NBRK=NLEAK=NCIRC=NFTRIP=O
=1=> Mass tracking is on; mass balances are solved foreach compartment.
W3-I MF Numerical solution flag. MF=222 should only be used ifMASSTR~O. If MASSTR~1, the recommended methods are MF=13
and MF 23. MF=10 and MF 20 use functional iteration
methods to solve the finite difference equations and
generally require smaller time steps and larger
computation times than MF~13 and MF=23.
~10~> Implicit Adam's method. Difference equations
solved by functional iteration (predictor-corrector
scheme) .
~13~> Implicit Adam's method. Difference equations
solved by Newton's method with chord iteration. An
II
PP4L Form 245'or83lCar. «973401
SE -B- N A -0 4 6 Rev.Q $
'ept.
PENNSYLVANIAPOWER 8r LIGHTCOMPANYCALCULATIONSHEET
Designed by PROJECT
Approved by
ER No.
Sht. No. ~Sof
internally generated diagonal approximation to the
Jacobian matrix is used.
=20~> Zmplicit method based on backward differentiation
formulas (Gear's method) . Difference equations are
solved by functional iteration; Jacobian matrix is
not used.
=23=> Zmplicit method based on backward differentiation
formulas. Difference equations are solved by
Newton's method with chord iteration. An
internally-generated diagonal approximation to the
Jacobian matrix is used.
~222~> Zmplicit method based on backward differentiation
formulas. Difference equations are solved by
Newton's method with chord iteration. An
internally-generated sparse Jacobian matrix is
used. The sparsity-structure of the Jacobian is
determined by the code.
ppdL Form 2«5«n0I83)Cw, «973401
'
8E -B- N A-0 4 6 Rev.Q ]
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~~of
.PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
W4-R CP1 Parameter used in calculation of leakage flows.
Xncreasing CP1 increases the leakage flow rate for a
given pressure difference. The recommended value of CPl4is lx10 . Larger values of CPl can be used if
compartment pressures increase above atmospheric pressure
during rapid temperature transients.
W5-R CP2 ~ Parameter used in calculating maximum allowed values forleakage flows. The recommended value of CP2 is 150.
Increasing CP2 increases the maximum leakage flow rates.
W6-R CR1 Parameter used in rain out calculation. Increasing thisparameter increases the rain out rate when rain out isinitiated. The recommended value of CR1 is 10.
W7-I XNPUTF ~ Flag controlling the printing of input data.
~0~> Summary of input data will not be printed.
=1««> Summary of input data will be printed.
pphL Form 2454 n0/83)Cat. 4973401
SE -8- N A -0 4 6 Rev.O
y'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~Eof
PENNSYLVANIAPOWER & LIGHT COMPANY- ER No.CALCULATIONSHEET
W8-I IFPRT = Ventilation-flow edit flag.
=0=> Ventilation-flow edits will not be printed.
=1=> Ventilation-flow edits will be printed.
W9-R RTOL = Error control parameter. RTOL is the maximum relativeerror in the solution. The recommended value of RTOL islxlo
3.3 Problem Descri tion Data (Card 3 of 3)
W1-I NSH = Number of time steps between re-evaluation of slab heat
transfer coefficients. If a pipe break is being
modelled, this parameter must be set to zero. If there
are no pipe breaks included in the model, NSH may have a
value as large as 10 without introducing significant
errors into the solution. For problems involving a large
number of slabs (but no pipe breaks), a value of 10 isrecommended.
PPAt. Form 2454 t1$83)Cat, 197340I
SE, -B- N A "0 4 6 Rev.0
y'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. 4O of
PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.CALCULATIONSHEET
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-5calculation. A recommended value for TFC is 10
-5Specifying 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 tripset point plus or minus TRPTOL.
W4-R TRPEND ~ The maximum time step size is limited to TRPTOL until the
problem time exceeds TRPEND (hr). Note that a large
value of TRPEND and a small value of TRPTOL will lead to
excessively large computation times.
PPCL Form 2454 n0'83)Col. 4973401
SE -B- N A -0 4 6 I'".. 0 y
Dept.
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 0.
Wl-R DELFLO m The maximum allowable compartment ventilation flowimbalance (cfm), i.e., the following condition must be
satisfied for each" compartments
Net Ventilation Flow (cfm)
into Compartment < DELFLO.
The recommended value of DELFLO is lx10 . It is-5
particularly important to ensure that there are no
ventilation flow imbalances when the mass-tracking optionis not used (MASSTRm0) because in this case the code
assumes that the mass inventory in each compartment
remains constant throughout the transient.
3.6 Edit Control Data
NEC edit control data cards must be supplied2 on each card the followingthree items must be specified.
PP0(. Form 245'0t03)Cht. N972l0(
S
SF- -8- N A -0 4 6 Rev.O
>'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No.. CW of
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.CALCULATIONSHEET
W1-I IDEC ~ ID number of the edit control parameter set. The ID
numbers must start with 1 and they must be sequential,
i.e., IDEC 1,2,3,...,NEC.
W2-R TLAST ~ Time (hr) up to which the edit parameters apply. When
time exceeds TLAST, the next set of edit control
parameters will control printout of the calculation
results.
W3-R TPRNT Print interval for calculation results (hr), i.e.,results will be printed every TPRNT hours.
3.7 Edit Dimension Data
Wl-I NRED ~ Total number of rooms for which the calculation results
will be printed. This includes both, standard rooms and
time-dependent rooms.
W2-I NS1ED ~ Number of thick slabs which will be edited. Associated
heat transfer coefficients are edited along with the slab
temperature profiles.
'
PPE,L FOcm 2454 IIO/83)Cat, s97340I
SE -B- N A -0 4 6 Rev.0 1I
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~~ of
PENNSYLVANIAPOWER & LIGHT COMPANY 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 fiton one line, additional lines may be used as necessary. The temperature
profile that is printed for each thick slab consists of seven temperatures
at equally spaced points throughout the slab. In general, these
temperatures are determined by quadratic interpolation since in most cases
ppLL Form 2454 (10/83)Cal. N973401
SE -~- N A -0 4 6 Rev.Q
>'ept.
Date t9Designed by
Approved by
PROJECT Sht. No. ~~of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
the locations do not correspond to grid points. Omit this card ifNS1EDmO.
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 willbe printed in the order that they are listed here. For each thin slab
specified, the heat flow through the slab and the direction of heat flow
will be printed. Omit this card if NS2ED=O.
3.11 Reference Tem erature and Pressure for Ventilation Flows
Omit this card if NFLOWmO.
Wl-R TREF = Temperature ( F) used by code to calculate a reference0
air density. The reference density is used by the code
to convert ventilation flows from CFM to ibm/hr.
W2-R PREP Pressure (psia) used to calculate the reference density
ppht. Form 2a54 n0i83>C4I. N913l01
SE -B- N A -0 4 6 R..V.O
1'ept.
Date
Designed by
Approved by
19
PROJECT Sht. No. 4~ of
PENNSYLVANIAPOWER 8 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.
W2-R VOL = Room volume (ft ) . In order to maintain constant3
properties in a compartment throughout the calculation,15enter a large value for VOL (e.g. 1xlO ) .
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.
pphL Form 2454 nOI83lCat. %13401
~ -B- N A-04 6 Rev.Q p
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.CALCULATIONSHEET
3.13 Ventilation Flow Data
Omit this card(s) if NFLOW 0.
Wl-I ZDFLOW = ZD number of the ventilation flow path. Values must
start with 1 and be sequential.
W2»I IFROM ID number of room that supplies ventilation flow. This
can be a standard room or a time-dependent. room.
W3-Z ZTO = ID number of room that receives flow. This can be a
standard room or a time-dependent room.
W4»R VFLOW = Ventilation flow rate (ft /min). This volumetric flow is3
converted to a mass flow rate using TREF and PREF
supplied above. The mass flow rate is held constant
throughout the calculation unless the flow is acted upon
by a trip.
PP4L Form 2ISl n0r83)Cat. 99%401
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~7ofPENNSYLVANIAPOWER & LIGHT COMPANY 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 ).
W3-R AKLEAK = pressure loss coefficient for leakage path based on flow
area ARLEAK. Specify a -1 for AKLEAK if the simple,
proportional control model is desired, see
Section 2. 1.3.2.
W4-I LRM1 ID number of room to which leakage path is connected.
This can be a standard room or a time-dependent room.
W5- I LRM2 - ID number of the other room to which the leakage path is
connected. This can be a standard room or a time-
dependent room.
e
W6-I LDIRN Allowed direction for leakage flow.
PPtLt. Form 2c5c n0/83)Cat. tr073401
SE "B" N A-046 Rev.O>:
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~4of
PENNSYLVANIAPOWER & LIGHT COMPANY 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 NCZRC~O.
Wl-I ZDCIRC ID number of circulation flow path. Values must start
with 1 and must be sequential.
W2-I KRM1 ~ ID number of room to which circulation path is connected.
This can be a standard room or a time-dependent room.
W3-I KRM2 ~ ZD number of other room to which the circulation path is
connected. This can be a standard room "or a
time-dependent room.
W4-R ELVL ~ Elevation of the lower flow path (ft).
a
WS-R ELVU ~ Elevation of the upper flow path (ft) .
pp6L Form 296a nar831Cal. 9976401
SE -B- N A -0 4 6 Rev.0
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~4of
PENNSYLVANIAPOWER & LIGHTCOMPANY'R 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
ARU.
3.16 Air-Flow Tri Data
Omit this card(s) if NFTRIP=O.
Wl-I IDFTRP Trip ID number. The 1D numbers must start with 1 and
must be sec(uential.
W2-I KFTYP1 Type of flow path.
~ 1 ~> Ventilation
2 > Leakage
3 > -Circulation
PP«,L Farm 2«5«{10/831Cat. «913«01
It
SE -B- N A -0 4 6 Rev.Q P
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~Oof
PENNSYLVANIAPOWER & 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
Omit this card(s) if NHEAT=O.
Wl-I IDHEAT ~ Heat load ID number. ID numbers must start with 1 and
must be secpxential.
W2-I NUMR ~ ID number of room containing heat load.
W3-I ITYP Type of heat load.
~ 1 ~> Lighting
~ 2 => Electrical panela
PPdL Fontt 2954 n$83)Cat. e91340l
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~l of
PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.CALCULATIONSHEET
= 3 => Motor
= 4 => Room Cooler
= 5 => Hot piping
= 8 => MiscellaneousI
~ ~
t
W4-R QDOT = Magnitude of heat load (Btu/hr). If this is a piping
heat load ( ITYP=5) enter 0.0 for this parameter; the
value of QDOT will be calculated by the code. If ITYP=4,
QDOT should be negative.
W5-R TC = Temperature ( F) of cooling water entering cooler ifITYP-4. If ITYP is not equal to 4 enter a value of -1".
W6-R WC - Cooling water flow rate (ibm/hr) if ITYP=4. If ITYP is
not equal to 4 enter a value of 0.
3. 18 Hot Pi in Data
Omit this card(s) if NPIPE=O.
Wl- I IDPIPE - ID number of pipe. The ID numbers must start with 1 and
must be sequential'
PPdL Form 24M ttiattCat, tt973lO I
N A-046 RevP):
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.CALCULATIONSHEET
W2-I ZPREF ID number of associated heat load.
W3-R POD ~ Outside diameter of pipe (in).
W4-R PZD ~ Inside diameter of pipe (in).
W5-R AZNOD ~ Outside diameter of pipe insulation (in) . If the pipe isnot insulated set AZNOD equal to POD.
W6-R PLEN Length of pipe (ft).
W7-R PEM Emissivity of pipe surface.I
W8-R AINK ~ Thermal conductivity of pipe insulation (Btu/hr ft F).
Zf the pipe is not insulated set AZNK~O.O.
W9-R PTEMP ~ Temperature ( F) of fluid contained in pipe.0
W10-I ZPHASE ~ 1 if pipe is filled with steam.
2 if pipe is filled with liquid.
pp&L Form 24M nSN>Cht. 4973401 SE -B- N A-0 4 6 Rev.0 ]l
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET
3.19 Heat Load Tri Data
Omit this card(s) if NTRZP 0.
Wl-I ZDTRIP = Trip ZD number. ZDTRIP must start with 1 and all values
must be sequential.
W2«Z ZHREF = ZD number of heat load that is to be tripped.
W3-I ITMD ~ Type of trip.~1~> Heat load is initially on and will be tripped off.m2~> Heat load is initially off and will be tripped on.
W3-R TSET ~ Time (hr) at which trip is activated.
W4-R TCON ~ Time constant for heat load trip. The following options
are available if ITMD~1:
~ Zf TCON~O.O, the entire heat load is tripped off at
ppKL Form 2c54 nOI831Cat. 4973401
a
SE -S- N A -0 4 6., Rev.Q g
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATIONSHEET
~ Zf the heat load is a piping heat load (ITYP~5), TCON
can be set to -1 and a time constant will be
calculated by the code. This time constant will then
be used to exponentially decay the heat load when itis tripped off.
~ A time constant can be supplied by setting TCON equal
to the desired time constant (hr).'hen the heat load
is tripped off, it will exponentially decay with the
user-supplied time constant. This option can be used
with any heat loads it is not restricted to just
piping heat loads.
0.0 if ITMD~2.
3.20 Pi e Break Data
Omit this card(s) if NBRK~O.
Wl-I , ZDBK ~ ID number of break. ZDBK must start with 1 and allvalues must be sequential.
PPSL Form 2454 (1SN)C4l. N973l01
SE -B- N A-046 Rev.0$
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~S of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
W2-I ZBRM = ID number of room in which pipe break occurs.
W3-R BFLPR = Fluid pressure within pipe (psia).
W4-I ZBFLG Fluid State flag.= 1 ~> fluid in pipe is steam
= 2 => fluid in pipe is licpxid water
W5-R BDOT = Total mass flow exiting the break (1bm/hr) .
W6-R TRZPON Time at which break occurs (hr).
W7-R TRZPOF = Time at which break flow is turned off (hr).
W8-R RAMP ~ Time period (hr) over which the break develops. The
total mass exiting the break increases linearly from a
value of zero at tMRZPON to a value of BDOT at
t-ZRIPON+RAMP.
3.21 Thick Slab Data (card 1 of 3)
Omit this card(s) if NSLB1 0.
PPAt. Fotm 2454 (tDt83)Cat. tt97340 I
SE -8- N A -0 4 6 Rev.0 >t
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET
W1-I IDSLBl = Slab ZD number. IDSLB1 must start with 1 and all values
must be sequential.
W2-I ZRM1 = ZD number of room on side 1 of slab. A standard room or
a time-dependent room can be specified. If side 1 of the
slab is in contact with ground enter a value of zero.
W3-I ZRM2 ID number of room on side 2 of slab. A standard room or
a" time-dependent zoom can be specified. Zf side 2 of the
slab is in contact with ground enter a value of zero.
W4-I ZTYPE ~ Type of slab.
= 1 if slab is a vertical wall
= 2 if slab is a floor with respect to room ZRM1.
= 3 if slab is a ceiling with respect to room ZRM1.
W5-I NGRIDF = Number of grid points per foot used in the
finite-difference solution of the unsteady heat
conduction equation. A minimum of 6 grid points per slab
is used by the code, and the maximum number of grid
points used per slab is 100. Zf the specified value of tNGRZDF causes the total number of grid points for the
I
ppdL Form 2454 n$83)Ca1, t973401
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. 17 of
I
PENNSYLVANIAPOWER 8 LIGHT COMPANY 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.
pp&L Form 2454 no/MrC4t. I@13401
SE -B- N A-0 4 6 Rev.a
>'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHTCOMPANY 'R No.CALCULATIONSHEET
Allow the code to calculate film coefficients for slab surfaces in contact
with ground.
W7-R CHARL m characteristic length of the slab (ft) .
= height of the slab if ITYPEml.
= the heat transfer area divided by the perimeter ifITYPEm2 or 3.
If the value of CHARL is set to 0.0, the code willcalculate a value for the characteristic length. In this ecase, the code assumes that the slab is in the shape of a
sguare.
3.22 Thick Slab Data (Card 2 of 3)
Omit this card(s) if NSLB1=0.
Wl-I IDSLB1 = Slab ID number.
W2-R ALS ~ Thickness of slab (ft) .
pp« t. Form 2«5«n0/83)C«l, «97340't I
SE -B- N A -0 4 6 Rev.o g
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ oi
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
W3-R AREAS1 = Slab heat, transfer area (ft ) . This is the surface area2
of one side of the slab.
W4-R AKS = Thermal conductivity of slab (Btu/hr ft F).0
W5-R ROS = Density of slab (ibm/ft ) .3
W6-R , CPS = Slab specific heat (Btu/ibm- F) .0
W7-R EMZSS = Slab emissivity
3.23 Thick Slab Data (Card 3 of 3)
Zf ZHFLAG=O for a slab, then do not supply a card in this section for that
particular slab. If IHFLAG 1 or 2, only supply the required data; leave
the other entries blank. Zf ZHFLAG=12, supply all the heat transfer
coefficient data for that slab. Omit this card(s) if NSLB1 0.
Wl-I ZDSLB1 = Slab ID number.
W2-R HTC1(1) Heat transfer coefficient for side 1 of slab if ITYPE=1
(Btu/hr-ft — F).2 0
pphL Form 2«5a n0/80)Cat. «973«01 SE -B- N A-046
Rev,Pg'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~O of
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.CALCULATIONSHEET
= Heat transfer coefficient for upward flow of heat between
slab and room IRM1 if ITYPE~2 or 3 (Btu/hr-ft — F).2 0
W3-R HTC2(1) ~ Heat transfer coefficient for side 2 of slab if ITYPE=1
(Btu/hr-ft — F).2 0
= Heat transfer coefficient for upward flow of heat between
slab and room IRH2 .if ITYPE~2 or 3 (Btu/hr-ft - F) .2 o
W4-R HTCl(2) ~ Heat transfer coefficient for downward flow of heat
between slab and room IRM1 if ITYPE~2 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 flow of heat
between slab and room IRH2 if ITYPE~2 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.
ppaL Fotttt 2454 nDt83tCat. tt97340t SE -B- N -A -0 4 6 Rev.p
g'ept.
Date t9Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
Wl-I ZDSLB2 = Slab ZD number. ZDSLB2 must start with 1 and all values
must be sequential.
W2-I JRM1 = ZD number of room on side 1 of slab. A standard room or
a time-dependent room can be specified. A thin slab
cannot be in contact with g'round, i.e., do not specify
JRM1 or JRM2 equal to zero.
W3-I JRM2 = ID number of room on side 2 of slab. A standard room or
a time-dependent room can b'e specified.
W4-I JTYPE = 1 if slab is a vertical wall.
= 2 if slab is a floor with respect to room JRM1.
= 3 if slab is a ceiling with respect to "room JRM1.
W5-R AREAS2 ~ Slab heat transfer area (ft ) . This is the surface area2
of one side of the slab.
3.25 Thin Slab Data (Card 2 of 2)
Omit this card(s) if NSLB2~0.
pprLL Form 2«5«norN)C«r. «973401
\
SE -B- N A -0 4 6 Rev.O
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET
Wl-I IDSLB2 Slab ID number.
W2-R UHT(1) Overall heat transfer coefficient for slab is JTYPE=1
(Btu/hr»ft - F) .2 0
~ Overall heat transfer coefficient for upward flow of heat'I
through slab if JTYPEm2 or 3 (Btu/hr-ft - F).2 0
W3-R UHT(2) = Overall heat transfer coefficient for downward flow of
heat through slab if JTYPEm2 or 3 (Btu/hr-ft - F). Do2 0
not supply a value of JTYPEml.
3,.26 Time-De endent Room Data (Card 1 of 2)
Omit this card(s) if NTDR~O.
Wl-I IDTDR ID number of time-dependent room. IDTDR must start with
-1 and proceed secgxentially (i.e.,IDTDR~ 1 «2 «3 « ~ ~ ~ «NTDR)
W2-I IRMFLG ~ 1 if temperature, pressure, and relative humidity data
will be supplied.
pplL Form 2454 n0rajjCat. l97340I
SE, -B- N A-046 Rev.Qy
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.CALCULATIONSHEET
= 2 if a sinusoidal temperature variation will be used for
this room. Zf this option is chosen there cannot be any
flow to or from this room.
W3-I NPTS ~ Number of data points that will be supplied if ZRMFLG=1.
Each data point consists of a value of time, temperature,
pressure, and relative humidity. NPTS must be less than
or equal to 500. Since output is determined by
interpolation, time-dependent-room data must be supplied
at least one time step beyond the problem end time.
~ 0 if ZRMFLG~2.
W4-R TDRTO ~ Initial room temperature ( F) if IRMFLG=2.0
~ 0.0 if ZRMFLG~1
W5-R AMPLTD Amplitude ( F) of temperature oscillation if IRMFLG=2.0
~ 0.0 if ZRMFLG=1.
W6-R FREQ ~ Frequency (rad/hr) of temperature oscillation ifZRMFLG 2.
~ 0.0 if ZRMFLGm1.
PPKL Form 2«5«n0IMIC«t, «91340l
SE -B- N A -0 4 6 Rev.0
y'ept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER & LIGHT COMPANY 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
ZRMFLG=l. Omit this card(s) if NTDR=O.
Wl-Z ZDTDR ZD number of time-dependent room
W2-R TTZME ~ Time (hr).
W3-R TTEMP ~ Temperature ( F) .0
W4-R TRHUM ~ Relative humidity (decimal fraction) .
WS»R TPRES ~ Pressure (psia).
Repeat words 2 through 5 until NPTS data points are supplied. Then
start a new card for the next time-dependent room.
t ~
pp&L Form 2i54 nOIN)Cat. l973401
SE -B- N,A=04 6 Rev.O.O
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. S~ of
PENNSYLVANIAPOWER & LIGHT COMPANY 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 Q. There are no heat loads or coolers within the standard
roomy heat is only transferred to or from the room by'onduction through
the slab.
The equations describing this problem are
aT /at = a8 T /ax,2 2s s (4-1)
3Ts3x x=0
- h [T (t) - T (Opt)]g-1 rlk s(4-2)
-h [T (L,t) - T (0) — A sin(W) ],-2 sk r2 0(4-3)
T (x 0)sax+ b, (4-4)
P 1C 1 Vl dT Ah [T (0 g t) T (t) ]dt
(4-5)
PPSL Form 24'10r83)Cat. rr973c0>
SE -B- N A -0 4 6 Rev 0 I!
Dept.
Date 19
Designed by
Approved by
PENNSYLVANIAPOWER & LIGHT COMPANYCALCULATIONSHEET
PROJECT
ER No.
Sht. No. +6 of
Room 1Standard Room
Room 2
Time-Dependent Room
Room temp, T (t)rlVolume, VlAir density, p
Specific heat, C1vl ~
Initial pressure, P
Film coefficient, hl
SlabTelllP r
T (x,t)s
"'Room temp,
T 2(t) -T 2(0)+A sin(00t)r2 r2 0
Film coefficient, h
Side 1 of slab Side 2 of slab
X=O X=L
eFigure 4.1 Description of Sample Problem 1
ppct. Form 2l5i n183)Cst. l973l01
$f -8- N A -04 6 Rev.00
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.CALCULATIONSHEET
where a and b are given by equations (2-30) and (2-31) ~ It is assumed
that both rooms have been at their initial temperatures long enough for
the slab to attain an initial steady-state temperature profile.
The general solution to this problem is rather complicated, but the
solution takes a much simplier form for large values of t.
This problem was also solved with COTTAP. Values for the input parameters
used in the calculation are given in Table 4.1 and a copy of the COTTAP
input data file is given in Table 4.2.
The slab temperature profiles at 900 and 2000 hours, calculated with
COTTAP, are compared with the asymptotic form of the analytical solution
in Figures 4.2 and 4.3. The results show good agreement. The COTTAP
results for the temperature in room 1 are compared with the analytical
solution in Figure 4.4r again, the results show good agreement.
PPdL Form 24$ 4 {10/N)Cat. NQ73401
SE -B- A A -04 6 Rev.pg
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ of
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.CALCULATIONSHEET
Table 4.1 Values of Parameters used in Sample Problem 1
Parameters Value
T 0)rlT (0)
A0
h
h
V
A
80 F
200 F
100 F
0.5 rad/hr
1.46 Btu/hr ft F
6.00 Btu/hr ft F2 0
0.0325 ft /hr2
1.0 Btu/hr ft F
800 ft300 ft2 ft
1014.7 psia
TSO FOREGROUND HARDCOPY 0 ~ ~ ~ PRINTED 89284.1100JSNAME=EAMAC.COTTAP.SAMPLI.DATAMOL=DSK533
COTTAP SAMPLE PROBLEM I -" RUN It1 ~ ~ 1 ~ 1 ~ ~ 0 ~ ~ ~ ~ 10 ~ ~ ~ ~ ~ ~ 011 ~ ~ 00 ~ 11 ~ ~ ~ 0040000000
PROBLEM DESCRIPTION DATA ( CARD I OF 3 )
NROOM NSLAB'I NSLAB2 NFLOW NHEAT NTDR NTRIPI I 0 0 0 I 0
~ 1 ~ 1 ~ 0 ~ 0 0 4 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 CPI CP2 CRI0 0 222 2. D4 2. 0 10.
~ 41 ~ ~ 10 ~ ~ ~ ~ 4 ~ ~ ~ 0 ~ ~ ~ ~ ~ 0 ~ ~ ~ ~ ~ 1 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 00 ~ 00 ~ ~
PROBLEM DESCRIPTION DATA ( CARD 3 OF4
~ NSH TFC0 1.0-5
4 ~ 0 ~ ~ 0 ~ ~ ~ ~ ~ ~ 0 ~ ~ 11 ~ ~ ~ 1 ~ 1 ~ ~ ~ ~ ~ ~ ~ 0 ~ ~ ~ 0 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~
PROBLEM TIME AND TR IP TOLERANCE
0 0 4 0 0 0 4 0 0 4 1 4 1 4 1 1 0 4 0 4 1 0 0 4 0 ~ ~
NP I PE NBRK NLEAK NC I RC NEC0 0 0 0 I
0 4 0 1 4 ~ 4 4 4 4 0 1 0 4 4 4 4 1 0 ~ 1 1 ~ 0 4 0 0
RTOLI.D-5
I NPUTF I F PRTI I
'1 0 ~ ~ 1 0 0 ~ 1 ~ ~ ~ ~ ~ ~ ~ ~ 0 0 ~ ~ 0 ~ ~ ~ ~ ~
000 ~ ~ 1 ~ 010 ~ ~ ~ 0100 ~ 1 ~ ~ ~ 4 ~ ~ ~ 1
DATA
+41 ~
T TEND TRPTOL TRPEND.0 2000.0 10.00 0.004 ~ ~ ~ ~ ~ ~ ~ ~ ~ 4 0 1 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 0 0 0 0 0 0 0 ~ ~ 0 0 0 ~ ~ ~ 0 ~ ~ ~ ~ ~ 4 0 ~ 0 0 ~ 0 ~ 0 ~ 0 0 ~ 1 ~
TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE( OMIT THIS CARD IF NFLOW = 0 )
44110
DELFLOI.D-5~ 0 ~ ~ 1 ~ 4 4 4 ~ ~ ~ 1 ~ 0 4 ~ ~ ~ 0 ~ ~ ~ ~ ~ 0 ~ ~ 0 ~ 0 0 ~ 0 0 ~ 0 ~ 0 0 ~ ~ 0 0 1 0 0 ~ ~ ~ 1 ~ 0 0 ~ 0 1 0 0 ~ 0 1 ~ ~ 0 0 ~ 0
EDIT CONTROL DATA CARDS
IOEC TLAST TPRNTI 2000. 100.
4 ~ 0 4 1 0 ~ 1 1 4 4 ~ 0 ~ ~ ~ ~ ~ 1 ~ 0 ~ ~ 0 ~ ~ 0 ~ ~ 0 ~ ~ 0 0 ~ 0 10 ~ 0 0 0 0 ~ ~ 0 ~ 1 ~ 1 0 ~ 0 ~ 0 4 0 0 1 1 4 ~ ~ 0 0 0 1 ~ 0
EDIT DIMENSION CARD
1 44
NREO NS LEO NS2ED2 I 0
1 4 ~ ~ ~ ~ ~ 0 ~ ~ 1 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 I~ ~ ~ ~ ~ 0 ~ 1 1 ~ I~ 0 1 1 ~ 1 ~ 1 I~ 1 1 1 0 0 4 1 4 4 ~ 1 1 1 4 ~ ~ 0 I~ 4 4 ~
ROOM EDIT DATA CARO(S)
I -I~ 44444440 ~ 1 ~ ~ ~ 1000 ~ ~ 0 ~ 01 ~ ~ ~ ~ 00 ~ 0010 ~ I~ 0 ~ 440444040440440004444404000000444
EDIT CARD(S) FOR THICK SLABS
444444440 ~ 0 4 0 1 ~ 1 ~ ~ 1 0 ~ ~ 0 1 ~ ~ ~ ~ ~ ~ 0 ~ 0 ~ ~ ~ ~ ~ 0 ~ 4 ~ ~ 0 0 ~ 1 4 0 0 ~ ~ 0 1 4 1 1 1 ~ 4 0 4 1 4 1 1 1 ~ 0 1 ~ 1
EOI T CARDS FOR THIN SLABS
4 4 44044444 1 ~ 1 ~ 000 ~ 40 ~ ~ 1 ~ 0 ~ 10 ~ 0 ~ ~ ~ ~ ~ 00 ~ ~ ~ ~ 1 ~ 1 ~
'REFERENCE PRESSURE FOR AIR F(OMIT THIS CARD IF NFLOW=O
0 0 1 1 0 1 4 1 1 4 4 4 4 4 0 4 4 1 0 1 4 4 0 1 1 4 1
LOWS
TREF100.
~ 1 ~ ~ 1 1 ~ ~ ~ ~
PREF14. 7
~ ~ ~ ~ 1 ~ ~ 4 ~ ~ ~ ~ ~ ~ ~ ~ 1 ~ ~ ~ ~ 1 ~ 1 ~ 14 ~ 111 ~ ~ 01ROOM DATA CARDS
(DO NOT INCLUDE TIME-DEPENDENT ROO
1 ~ 0 0 0 1 1 ~ 1 ~ 0 1 4 1 4 1 1 1 ~ 1 4 ~ 1 ~ 4 ~ 1
MS)
~ IUROOMI
~ 444 444444
VOL PRES TR RELHUM RM HT800. 14.7 80.0 0.5 10.01 ~ 11 ~ ~ 1 ~ 111 ~ ~ ~ ~ ~ 411 ~ ~ ~ 10 ~ ~ 4' ~ 1 ~ ~ 410
AIR FLOW DATA CARDS( OMIT THIS CARO IF NFLOW = 0 )
0001 ~ ~ 11 ~ 1 ~ 1414 ~ 141 ~ ~ ~ 11 ~ 11
I IIF I AW I FROM I TO VFLOW
s 4 4 ~ 4 ~ 0 ~ 0 ~ ~ ~ ~ ~ 4 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 ~ 0 0 ~ ~ ~ ~ ~ ~ ~ 4 0 ~ ~ 4 4 ~ 0 0 ~ ~ 0 4 ~ ~ ~ 4 4 4 0 ~ 4 4 ~ 4 4 4 \ 4 4 0 0 0 0
LEAKAGE PATH DATA( OMIT THIS CARD IF NLEAK = 0 )
JRM2
IDLEAK ARLEAK AKLEAK LRMI LRM2 LDIRN
~ ~ ~ 4 ~ ~ ~ ~ ~ ~ ~ ~ ~ 4 ~ ~ ~ ~ ~ ~ 4 ~ 0 0 0 ~ 4 ~ ~ ~ ~ ~ 0 0 0 ~ 0 0 ~ 0 ~ ~ 0 ~ ~ 4 4 4 4 ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 ~ 4 ~ ~ 0 0 4 4 4 4
AIR FLOW TRIP DATA
IDFTRP KFTYPI KFTYP2 FTSET IDFP
~ 444 ~ 0 ~ ~ ~ 00 ~ ~ 0 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ 00 ~ ~ ~ ~ 0 ~ ~ 0 ~ ~ 00 ~ 0 ~ ~ ~ ~ ~ ~ 4 ~ ~ 00 ~ 0 ~ 00 ~ ~ 0 ~ ~ ~ 00 ~ 0 ~ ~
HEAT LOAD DATA CARDS
~ IDHEAT NUMR ITYP QOOT TC WCOOL
~ 4 4 0 0 ~ 0 0 ~ ~ 0 ~ 0 ~ ~ 4 ~ ~ 0 ~ 0 0 ~ ~ ~ 0 ~ ~ ~ 0 0 0 0 ~ 0 0 ~ ~ 0 ~ ~ 0 0 ~ ~ ~ ~ ~ ~ 0 ~ ~ ~ ~ 0 ~ ~ 0 ~ 4 4 4 4 4 4 4 4 4 4
PIPING DATA CARDSr
~ IDPIPE IPREF POO PID AIODN PLEN PEM AINK PTEMP IPHASE
4444 ~ 4400 ~ ~ 4 ~ ~ 4 ~ ~ 4 ~ ~ ~ ~ 4 ~ ~ 4 ~ ~ ~ 0000 ~ ~ 04 ~ 00000 ~ ~ 0 ~ 000 ~ 4 ~ 04 ~ ~ 404 F 4'4444HEAT LOAD TRIP CARDS
IOTRIP IHREF ITMO TSET TCON
~ ~ ~ 4 4 ~ ~ ~ ~ ~ ~ ~ ~ 4 ~ 4 ~ ~ ~ ~ 0 4 0 ~ ~ ~ 0 ~ 0 0 0 ~ 0 0 ~ 0 ~ 0 ~ 0 0 0 0 ~ 0 ~ ~ 0 ~ 0 0 ~ ~ ~ ~ ~ ~ ~ ~ 4 ~ ~ 4 ~ 4 4 0 ~ ~
STEAM LINE BREAK DATA CARDS4
~ IDBRK IBRM BFLPR IBFLG BOOT TRIPDN TRIPOF RAMP4
~ 4 4 4 ~ 4 4 ~ 4 ~ ~ 4 0 4 4 ~ ~ 4 4 ~ ~ 0 ~ ~ 4 ~ 0 4 0 0 0 ~ 0 0 ~ 0 0 ~ 0 0 0 0 0 0 0 0 ~ 0 0 0 0 ~ 0 ~ 0 ~ 0 0 0 0 0 ~ 4 4 4 4 4 ~ 0
THICK SLAB DATA CARO (CARD I OF 3)4
ID SLB I I RM I I RLI2 I TYPE NGR I 0 IHFLAG CHARLI I -I I 'I 5 12 10.
~ 4 4 4 ~ 4 ~ 0 ~ 4 ~ 4 ~ ~ 4 ~ 0 ~ 4 ~ 4 4 0 0 0 0 4 0 0 0 ~ 0 0 0 0 ~ 0 ~ 4 ~ ~ 0 0 4 4 0 ~ ~ ~ ~ ~ ~ ~ 4 4 4 0 ~ ~ 0 0 ~ 4 4 0 0 4 4 4
THICK SLAB DATA CARD (CARO 2 OF 3)0
I OSLB I ALS AREAS I AKS ROS CPS EMISI 2.0 300. I . 00 140. 0.22 0.8
~ 4 ~ 4 ~ ~ ~ 404 ~ 4 ~ ~ ~ 0004 ~ ~ ~ ~ ~ 000 ~ 40040 ~ 0000 ~ 00 ~ 00004 ~ 4 ~ ~ ~ ~ ~ 00 ~ 044 ~ ~ 000 ~ 0 ~ 4
THICK SLAB DATA CARD (CARD 3 OF 3)~ IDSLBI HTCI(1) HTC2(l) HTCI(2) HTC2(2)
I 1.46 6.00~ 4 4 4 4 4 ~ 0 ~ 4 ~ 0 ~ ~ 440 ~ 0 ~ ~ ~ 0 ~ ~ 00 ~ ~ ~ ~ 00000444 ~ 0 ~ ~ ~ 04444 ~ ~ 44 ~ ~ ~ 4 ~ 044444 ~ 440 ~
THIN SLAB DATA CARO (CARD I OF 2)4
IDSLB2 JRMI JTYPE AREAS24
~ 4 ~ 0 4 0 4 0 0 0 0 0 0 0 0 0 ~ 0 ~ 0 ~ 0 0 ~ 0 ~ 0 ~ 4 0 0 0 0 4 0 0 ~ 4 0 0 4 0 0 0 0 0 0 0 ~ 0 0 4 0 4 4 0 4 4 0 0 0 4 4 0 4 0 4 0 0
THIN SLAB DATA CARO (CARO 2 OF 2)4
IDSL82 UHT(l) UHT(2)4
44 ~ 044 ~ ~ ~ 04 ~ ~ ~ ~ ~ 040 ~ 00 ~ ~ ~ ~ ~ 0 ~ 00 ~ ~ 0 ~ ~ 04004 ~ 4 ~ 004 ~ 000440 F 4'44044444404 TIME-DEPENDENT ROOM DATA
IDTOR IRMFLG NPTS TDRTO AMPLTO FREQ-I 2 0 200.0 100.0 0.50
~ 44 ~ 44 ~ ~ ~ ~ ~ ~ 4 ~ ~ ~ ~ ~ ~ ~ 44 ~ ~ ~ ~ ~ 4 ~ ~ 04 ~ 440 ~ ~ 4 ~ ~ 4 ~ ~ 0 ~ 4 ~ ~ ~ ~ 004 ~ 4 ~ ~ 44 ~ 4440 ~ 44 ~
TIME VERSUS TEMPERATURE DATA
~ I l)TDR TTCME TTEMP TT IME TTEMP TTIME TTEMP
~ t ~ 4 ~ 4 4 4 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 4 ~ ~ 4 4 ~ ~ 4 4 ~ ~ ~ 4 4 4 4 4 4 ~ ~ 4 4 ~ 4 4 ~ 4 4 ~ ~ ~ 4 ~ 4 ~ ~ ~ 4 4 4 ~ 4 0 ~ 4 4 4 4 4 4 4
~ ~ 4 4 ~ ~ ~ ~ ~ ~ 4 4 ~ ~ ~ ~ ~ ~ ~ 4 4 ~ 4 4 ~ 4 ~ ~ ~ 4 4 4 4 4 4 ~ 4 4 0 4 ~ 4 ~ ~ 4 ~ 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 ~ ~ 4 4 ~ ~
4 ~ 4
044
4 ~ ~
404
044
044
0 ~ 0
040
44 ~
444
444444
TSO FOREGROUND HAROCOPY ~ ~ ~ 0 PRINTED 89284.1045SNAME=EAMAC.COTTAP.SAMPLI.DATADL=DSK533
( OTTAP SAMPLE PROBLEM I -- RUN 2o 0 0 0 0 0 ~ ~ ~ 0 ~ 1 0 0 0 0 0 ~ 0 ~ 1 ~ ~ ~ ~ ~ ~ 0 0 ~ ~ ~ 0 0 ~ 0 0 ~ 0 ~ 0 ~ 0 ~ ~ ~ 1 0 0 0 0 0 0 1 0 1 ~ ~ ~ ~ ~ ~ 0 ~ ~ ~ ~ 0 1 0 ~
PROBLEM DESCRIPTION DATA ( CARD I OF 3 )
NROOM NSLAB'I NSLA82 NFLOW NHEAT NTOR NTR I P NPIPE NBRK NLEAK NCIRC NECI I 0 0 0 I 0 0 0 0 0 2
~ 0 1 ~ 0 ~ 0 0 0 0 0 0 0 0 ~ 0 0 ~ 0 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 1 0 ~ 0 0 1 0 0 0 0 0 ~ ~ ~ 1 1 ~ ~ 0 0 ~ ~ ~ ~ 0 ~ ~ 0 0 ~ ~ 0 0 0 ~ 0 ~ 0
PROBLEM DESCRIPTION DATA ( CARO 2 OF 3 )
NFTRIP MASSTR MF CP I CP2 CRI INPUTF IFPRT RTOL0 0 222 2.04 2.0 10. I I I .D-5
~ 0 1 0 ~ ~ ~ ~ 0 ~ 0 0 ~ 0 0 0 ~ ~ ~ 0 0 ~ ~ 0 ~ 0 0 0 ~ 0 ~ ~ ~ ~ ~ 1 ~ ~ 0 0 0 0 1 0 ~ ~ 0 ~ ~ 0 ~ 1 ~ 0 0 ~ 0 1 0 0 0 0 0 ~ 0 1 ~ 0 0 ~ 0
PROBLEM DESCRIPTION DATA ( CARD 3 OF 3 )
NSH TFC0 I . D-5
~ 1 0 1 ~ 0 ~ I~ 0 ~ 0 ~ 0 I~ ~ ~ 0 ~ ~ ~ ~ 0 ~ ~ 0 ~ ~ ~ ~ ~ 0 ~ 0 0 0 0 0 0 0 0 0 1 0 0 0 ~ 0 0 0 ~ 0 ~ 1 0 0 1 ~ 0 ~ 0 0 0 1 1 0 0 0 0 1 0 ~
PROBLEM TIME AND TRIP TOLERANCE DATA
T TEND TRPTOL TRPENO0.0 1520.0 IO.DO 0.00
1 ~ ~ 0 ~ 0 ~ ~ 1 ~ 11 ~ ~ ~ 00 ~ ~ ~ 0 ~ ~ 0 ~ ~ ~ ~ ~ 0 ~ ~ ~ ~ ~ ~ 0 ~ ~ ~ 0 ~ ~ ~ 01 ~ ~ 1
TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BA( OMIT THIS CARD IF NFLOW = 0 )
~ ~ ~ 0 ~ ~ ~ 00000 ~ 0 ~ ~ 00011 0
LANCE
DELFLO1.0-5
~ 00100 ~ 0 ~ 1 ~ ~ 10 ~ ~ ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 ~ ~ ~ 0 ~ ~ ~ 00 ~ 0 ~ ~ 0 ~ 0 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ 1 ~ 1 ~ ~ ~ 1 ~ ~ ~ ~ 00001EDIT CONTROL DATA CARDS
IDECI
t ~ ~ 110 ~ 00
TLAST TPRNT1500. 1500.1520. I.
0 ~ ~ ~ ~ ~ ~ 00 ~ ~ 1 ~ 0 ~ ~ ~ ~ ~ ~ 11 ~ 00000 ~ 0000 ~ ~ ~ ~ ~ ~ ~
EOI T DIMENSION CARD~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 ~ ~ 0 1 ~ ~ ~ ~ 1 ~
NREO2
~ a0 ~ 10 ~ 011 ~ ~ ~ ~
NS
00 ~ 0 ~ 10 ~ 0
ROOM
I ED NS2EDI 00 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 0 0 0 0 0 1 1
EDIT DATA CARD(S)
000-I
~ 00 ~ ~ ~ 1 ~ 00111 ~ ~ ~ ~ ~ ~ ~
EDIT~ 0 ~ ~ ~ ~ 0 ~ 0 0 0 0 0 ~ ~ ~ ~ ~ 1 ~ 0 1 0 0 ~ ~ ~ ~ 0 ~ ~ 0 1 ~ ~ 0 0 ~ ~ 0 0 0 0 0 0 00 0 0
CARO(S) FOR THICK SLABS
~ 0 ~ ~ 0 ~ 0 ~ 000000 ~ 1 ~ ~ 0 0 ~ ~ ~ ~ ~ 0 1 ~ 1 ~ 0 ~ 1 0 0 1 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 ~ ~ 1 0 0 0 1 0 0 1 0 0 ~ 0 1 0 1 1 1 1
EDIT CARDS FOR THIN SLABS
~ 1 ~ 10000 ~ 0 ~ ~ 11 1 ~ ~ ~ ~ 1 0 ~ 1 ~ 0 ~ ~ ~ 0 0 0 ~ 0 0 0 0 0 0 1 0 0 ~ ~ 0 ~ 0 ~ 1 0 1 0 ~ ~ ~ ~ 1 0 0 ~ ~ 0 0 0 0 0 0 ~ 0 0 0 0 ~
REFERENCE PRESSURE FOR AIR FLOWS(OMIT THIS CARD IF NFLOW=O)
TREF1(10.
~ 00101000 ~ ~ ~ ~
(00
PREF14. 7
10 ~ 0001 ~ ~
RNOT I NCL
~ ~ ~ ~ 1 ~ 0 0 ~ 0 ~ 0 ~ 0 ~ 0 0 0 0 ~ 0 ~ ~ ~ ~ ~ ~ ~ 1 ~ ~ ~ ~ ~ 0 1 ~ ~ ~ 0 1 1 1 1 0 0 1 1 0
OOM DATA CARDSUDE TIME-DEPENDENT ROOMS)
I (>ROOMI
VOL800.
~ ~ 0 \ 0 01 10 1 110 ~
PRES TR RELHUM RM HT14.7 80.0 0.5 10.0
0 ~ 110 ~ ~ 0 ~ ~ ~ ~ 0 ~ ~ 1 ~ ~ ~ 0 ~ 1001 ~ 01 ~ 10 ~ ~ 0 ~ 0
AIR FLOW DATA CARDSOMIT THIS CARD IF NFLOW = 0 )
~ ~ 00 ~ ~ ~ ~ 10 ~ 1 ~ ~ ~ 1 ~ 11001
TSET
JRM2
e ~ I ~ I ~ ~ ~ ~ ~ ~ 0011 ~ ~ I ~ ~ ~ 0 ~ ~ ~ ~ ~ ~ ~ I ~ 11 ~ ~ I ~ ~ ~ 010011 ~ I ~ ~ ~ ~
LEAKAGE PATH DATA( OMIT THIS CARO IF NLEAK -" 0 )
IOLEAK ARLEAK AKLEAK LRM1 LRM2 LOI
~ I I I I ~ ~ I ~ ~ I ~ ~ ~ ~ I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ I II ~ ~ I I I II I ~ I ~ I I I II I I ~ I ~ ~
AIR FLOW TRIP DATA
~ IDFTRP KFTYP1 KFTYP2 FTSET IOFP
~ ~ I ~ ~ ~ ~ I ~ I ~ I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 10 ~ 00 ~ 10 ~ ~ ~ ~ ~ ~ III~ I ~ 0000 ~
HEAT LOAD DATA CARDS
~ IDHEAT NUMR ITYP QOOT TC WCOOL
~ t ~ 11 ~ I ~ ~ 01 ~ ~ ~ ~ ~ ~ I ~ ~ I ~ I ~ ~ I ~ ~ ~ ~ ~ ~ ~ ~ I ~ ~ I ~ ~ ~ I ~ ~ ~ I ~ I ~ I ~
PIPING DATA CARDS
~ IDPIPE IPREF POD PIO AIOON PLEN PEM A
t I I I I ~ ~ I ~ I I ~ ~ ~ ~ ~ I I I ~ ~ I I I ~ I ~ I ~ ~ ~ I ~ ~ ~ I ~ II ~ I I I II I I I II IHEAT LOAD TRIP CARDS
IOTRIP IHREF ITMD TCON
t ~ ~ ~ ~ ~ 010 ~ ~ ~ I ~ I ~ 00 ~ ~ ~ ~ I ~ ~ ~ ~ I ~ ~ I ~ ~ 00 ~ ~ ~ 01 ~ I ~ 0000 ~ ~ ~ ~
t STEAM LINE BREAK DATA CARDS
~ IDBRK IBRM BFLPR IBFLG
~ ~ I I I ~ I I ~ ~ I ~ ~ ~ ~ I I ~ ~ ~ ~ 0 ~ ~ ~ 0 ~ I I I I ~ I I I I ~ ~ ~ ~ I ~ II I I I ~ 0 ~ ITHICK SLAB DATA CARO (CARO 1 OF 3)
IDSJ Bl IRMl I RM2 I TYPE NGRIDI 1 -1 I 15
~ I ~ tt ~ ~ ~ 11 ~ ~ I ~ I ~ ~ ~ ~ ~ ~ ~ ~ 01 ~ ~ 10011 ~ ~ I ~ ~ ~ I ~ 000 ~ ~ ~ ~ 00 ~ ~
THICK SLAB DATA CARD (CARO 2 OF
I DSLB 1 ALS AREAS) AKS ROS1 2.0 300. 1.00 140.
~ t ~ ~ I ~ 01 ~ ~ ~ ~ ~ ~ ~ I ~ 1001 ~ ~ I ~ ~ ~ ~ ~ ~ 10 ~ 10 ~ ~ ~ ~ ~ ~ ~ ~ 100 ~ 01 ~ ~
THICK SLAB DATA CARO (CARO 3 OF 3t
IIJSL81 HTC1(1) HTC2(1) HTC 1 (2) HTC21 1.46 6.00
~ t ~ ~ ~ ~ ~ ~ ~ t ~ ~ ~ I ~ I ~ ~ ~ ~ ~ ~ I ~ ~ ~ I ~ ~ 00 ~ ~ ~ ~ ~ ~ ~ I ~ ~ 10100 ~ ~ ~ ~ ~
t THIN SLAB DATA CARD (CARO 1 OF 2)t~ I OSL82 JRM1 JTYPE AREAS2t~ I I I ~ ~ ~ ~ I I I I ~ I ~ I I I ~ ~ ~ I ~ ~ I I I I I ~ ~ ~ I I I ~ ~ ~ I ~ ~ ~ I I ~ I I I I I I
THIN SLAB DATA CARO (CARO 2 OFt~ IDSL82 UHT( 1 ) UHT(2)
~ ~ t t ~ IIII~ I ~ ~ ~ ~ 00 ~ ~ ~ ~ ~ ~ I ~ ~ ~ I ~ ~ 001 ~ ~ I ~ I ~ 011111000 ~ I ~
TIME-DEPENDENT ROOM DATA
~ ~ I ~ 01111111100 ~ I ~ ~ ~ I
RN
I ~ 010000000001 ~ ~ ~ ~ ~ I ~
I ~ ~ ~ 0000 ~ 00 ~ ~ 00100 ~ I ~
~ ~ ~ ~ ~ ~ ~ I I ~ I ~ ~ ~ ~ I ~ ~ ~ I ~
INK PTEMP I PHASE
IIII I IIIII I I I I I ~ ~ I I I I
~ I ~ 1110 ~ 1001 ~ 01 ~ I ~ 111
F RAMP
I ~ 01 ~ ~ I ~ I ~ ~ 0101 ~ 10 ~ I ~
IHFLAG CHARL12 10.
00 ~ ~ I ~ ~ I ~ I ~ I ~ ~ I ~ 100 ~ I3)CPS EMI S0.22 0.8
~ ~ ~ ~ ~ ~ 11101 ~ I ~ ~ I ~ ~ ~
)
(2)I ~ ~ I ~ 1111 ~ 100 ~ ~ ~ I ~ ~ I ~
~ I ~ I ~ 111111 ~ 01 ~ 00 ~ 1002)
I I I I I I I I I I I ~ ~ I I I ~ ~ ~ I I
1010R IRMFLG NPTS TORTO AMPLTD-1 2 - 0 200.0 100.0
~ ~ tt ~ ~ I ~ ~ ~ ~ ~ ~ ~ ~ I ~ I ~ I ~ ~ ~ ~ I ~ ~ ~ tt ~ ~ ~ ~ ~ ~ ~ ~ I ~ 11 ~ 11 ~ I ~ 111TIME VERSUS TEMPERATURE DATA
~ IDTDR TTIME TTEMP TTIME TTEMPt~ 1tt ~ ~ ~ ~ ~ I ~ ~ ~ ~ ~ ~ ~ ~ 01 ~ ~ ~ I ~ I ~ 101 ~ I ~ ~ ~ I ~ I ~ 1101 ~ 11 ~ ~ ~ ~ ~
~ t ~ 11 ~ ~ I ~ ~ ~ ~ ~ ~ ~ ~ ~ I ~ ~ ~ ~ ~ ~ ~ 1111 ~ 11 ~ ~ ~ I ~ ~ I ~ 000 ~ ~ 111
TTIME TTEMP
10 ~ 1101 ~ 11 ~ I ~ I I ~ I ~
I ~ ~ 11 ~ ~ ~ I ~ ~ ~ 11t~ I ~~ ~ I
FREQ0.50
~ ~ ~ 11 ~ I ~ ~ ttt ~ I ~ ~ ~ ~ I ~ ~
g I
RGURE 4.2 COMPARISON OF COTTAP CALCULATED TEMPERATUREPROFILE WITH ANALYTICALSOLUTION (t=900 hr)
FOR SAMPLE PROBLEM t
220
210
QlQ)
200
I~
190
180
LegendANALYIICAL
4 COTTAP
1700.5
x (tt)1.5 o
(C
C)
FIGURE 4.3 COMPARISON OF COTTAP CALCULATEDTEMPERATUREPROFILE WITH ANALYTICALSOLUllON (t—2000 hr)
FOR SAMPLE PROBLEM 1
250
240
Q)230
220l~50- 210
200
Legend~WALVT|CAL
~ COTTAP
190
1800.5
x (tt)1.5 ' IO Cg
CD
FIGURE 4.4 COMPARISON OF COTlAP CALCULATED TEMPERATUREOSCILLATION WITH ANALYTICALSOLUTION
FOR SAMPLE PROBLEM 1
IM4O
LJCIMKO
OO
O4JCL
I-!L
4JI—
200.6
200A
200.2
200
199.8
199.6
199A150 1505 1510
TIME (hr)
LegendANALYTICAL
~ COTTAP
1515 1520
cC)
PP8 L Form 24S4 (!N83)Cat. l973401
V SE -B- N A -04 6 Rev.ag
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~9of
PENNSYLVANIAPOWER & LIGHT COMPANY 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) g the temperature in the other compartment is calculated by
the code. The compartment for which the temperature is calculated
contains 4 heat loads and 5 associated heat load trips. The timing of
these trips matches the plot in figure 4.5.
The analytical solution for the room temperature is
T (t) =T (0)e +T (1-e )r r con
t-tB/a~
yB/a( )
0 a(4-6)
where the constants a and B are defined in Appendix B, T is thecon
compartment temperature on the opposite side of the thin wall, and Q is
the function shown in Figure 4.5.
Q>o o
kW <0 0 0III Ol
X7 QIO( 2
a aO O'C
A '0~ 'D
@ry 0o 3
AI
P
~ 30QQ
S
~aOoo
+ /Oo&
/o
i~L
O~—>a~> L a x Ti:p o~
HPC,+ l I0ag L Tb P O~
O gpu+ J ~aQ Q. TiI)P O~~
O Hca k Lo~d t3 Tv p—g ~~/ L<c.d g &p DCCC
~
/g 20
T>~g (Hrs)
0mO
CA
Z0
0
mXXCOC
In~rZo>C 0I 0~mOmZ gyIIIrm~xm-l~
A=0D
'X
m37
Z0'ICD
CCD
PPKL Form 2iSl (1$N)Cat. t970401
L
$F 9 lq A.-04 6 Rev Qi
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER 8c 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 is5
initially cooled by forced ventilation flow drawn from outside air
(outside conditions are represented by time»dependent compartment, -1).
Ventilation flow is tripped off at t ~ 1 hr. Since the'compartment is not
airtight, air leakage between the compartment and the environment occurs
which maintains the compartment at atmospheric pressure. This air
transfer process is modeled by means of a leakage path. No air flow to
the compartment occurs from t ~ 1 hr to t ~ 2 hr (except for leakage
flow)r at t ~ 2 hr, two vents at different elevations are opened allowing
natural circulation flow through the compartment. In order to simulate
this, a natural circulation flow path is tripped on at t = 2 hr, and at
the same time, the leakage flow is tripped off because the circulation
flow model already allows for air leakage.
~ ~ 4 TSO FOREGROUND HAROCOPY 111 ~ PRINTED 89284. 14 12SNAME=EAMAC.COTTAP~ SAMPL2.DATA ~
OL=OSK534
COTTAP SAMPLE PROBLEM 241 ~ ~ 1 ~ ~ 4444141I11 ~ 4 ~ ~ 4 ~ ~ ~ I ~ ~ 4 ~ ~ 4 ~ ~ 4 ~ ~ ~ 1 ~ 1 ~ 44I4 ~ ~ ~ 44I ~ ~ 4411 ~ ~ ~ 4 ~ ~ ~ ~ 1 ~ 44 1 ~ 44 ~
PROBLEM DESCRIPTION DATA ( CARD 1 OF 3 )
NROOM NSLA81 NSLA82 NFLOW NHEAT NTDR NTRIP NPIPE NBR1 0 1 0 4 1 5 0 0
1 4 4 ~ 1 1 4 4 ~ ~ 4 ~ ~ I4 ~ 4 ~ ~ ~ 4 ~ 4 ~ ~ ~ ~ ~ ~ I~ 1 4 4 4 4 ~ 1 4 ~ ~ 4 I4 4 ~ 4 1 4 4 4 I~ ~ ~ ~ 4
PROBLEM DESCRIPTION DATA ( CARD 2 OF 3 )
K NLEAK NC I RC NEC0 0 1
4 ~ ~ ~ 14 ~ 4 ~ 4 ~ 44444 ~ ~
NFTRIP MASSTR MF CP1 CP2 CR1 INPUTF IFPRT RTOL0 0 222 2.04 2.0 10. I 1 1. 0-5
1 4 ~ ~ 4 ~ ~ ~ ~ 4 4 4 4 ~ 4 4 ~ ~ 1 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 4 ~ 4 ~ 4 4 ~ ~ ~ ~ 4 1 4 4 4 4 ~ 4 4 1 ~ ~ 4 4 1 ~ 4 ~ ~ ~ 1 ~ ~ ~ 4 4 4 1 4 4 ~ ~
PROBLEM DESCRIPTION DATA ( CARO 3 OF 3 )
NSH TFC0 'I . 0-5
41 1 ~ 14 ~ ~ ~ 444 ~ ~ 1 ~ ~ ~ 14 ~ ~ 4 ~ ~ ~ ~ ~ ~ ~ ~ ~ 444 ~ 4 1 ~ 4144444 ~ 44 ~ 4444 ~ ~ ~ ~ ~ 44 ~ 4 ~ ~ 4 ~ ~ 444PROBLEM TIME ANO TRIP TOLERANCE DATA
T TEND TRPTOL TRPEND0.0 40.0 0.005 40.0
~ 4 ~ 4 ~ 44414444 ~ 44444 ~ ~ ~ ~ ~ ~ 44 ~ ~ ~ ~ 4 ~ 4 ~ ~ I4 ~ 4I~ ~ I~ 4 ~ ~ 4 ~ 41 ~ ~ ~ ~
TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANC( OMIT THIS CARO IF NFLOW = 0 )
4 ~ 4 ~ 41414 ~ 4 ~ ~ 44441
DELFLO
~ ~ 4 ~ 1 ~ ~ ~ 4 4 1 4 ~ 4 ~ ~ 4 4 ~ ~ 4 ~ ~ ~ ~ 4 ~ 1 4 ~ 4 4 4 ~ ~ 4 4 4 4 1 4 4 ~ 4 4 4 4 4 4 4 1 4 ~ ~ 4 4 ~ ~ ~ ~ ~ 4 ~ ~ ~ ~ 4 1 4 4 1
EDIT CONTROL DATA CARDS
IDEC TLAST TPRNT1 60. 2.0
~ 4 ~ ~ 44444414 ~ 44 ~ ~ 44 ~ ~ ~ ~ ~ ~ ~ 4 ~ 4 ~ ~ ~ 41 ~ 44414 ~ 414 ~ 4444444144 ~ ~ ~ 4 ~ 41 ~ 44 ~ 4 ~ 11 ~
EO I T DIMENSION CARO
NRED2
441444414NS1ED NS2ED
0 1
~ 1 ~ ~ ~ ~ 4 4 ~ ~ 4 1 ~ ~ ~ 4 4 ~ ~ 1 ~ 4 ~ 4 ~ 1 1 4 1 1 4 4 4 ~ 4 4 4 4 4 ~ 4 ~ ~ ~ ~ ~ 4 4 4 4 ~ ~ ~ ~ ~ ~ 4 4 ~ ~ 4 4
ROOM EDIT DATA CARO( 5)
~ 4 4-1
4444444 ~ 4 4 4 ~ 4 ~ 4 4 4 4 4 4 ~ ~ 4 ~ 4 ~ ~ 4 4 ~ 4 ~ ~ 4 ~ ~ 1 ~ 1 ~ 4 1 ~ 4 1 ~ ~ ~ 4 4 4 4 ~ ~ 4 ~ 4 ~ 4 4 ~ 1 4 ~ 4 1 4 ~ 4
EDIT CARO(S) FOR THICK SLABS
~ 444444444 ~ 1 4 4 4 4 ~ ~ ~ 1 4 4 4 ~ ~ ~ ~ 4 4 4 ~ ~ 1 ~ ~ ~ ~ 4 4 4 4 1 4 4 1 4 4 4 4 4 4 ~ 4 ~ ~ ~ ~ 4 ~ ~ 1 ~ 1 ~ ~ ~ ~ 4 4 \ 4 1
EDIT CARDS FOR THIN SLABS
~ ~ 1 ~ ~ ~ ~ 1 ~ 4 4 1 4 4 4 ~ 4 4 4 4 4 4 ~ ~ ~ ~ ~ 4 4 4 4 1 4 ~ 4 4 4 4 4 4 4 4 ~ 4 4 4 4 ~
REFERENCE PRESSURE FOR AIR FLOW(OMIT THIS CARD IF NFLOW=O)
4 ~ 4414 ~ 414 ~ 41 ~ ~ 44 ~ 4 ~ 4444
TREF PREF
f 4414 ~ 4441 4 4 4 4 4 ~ ~ 4 4 4 ~ ~ ~ 1 ~ ~ ~ 4 4 4 ~ ~ 1 ~ 4 1 4 4 4 4 ~ 1 4 ~ 1 ~ 4 4 1 4 4 ~ 4 4 1 ~ ~ 4 4 1 1 ~ ~ ~ 4 1 1 4 4 4 4 1
ROOM DATA CARDS(DO NOT INCLUDE TIME-DEPENDENT ROOMS)
~ I DROOM10
~ ~ 1114 ~ 444
VOL PRES TR RELHUM RM HT000. 14.7 100.0 0.5 10.04 1 ~ 4 4 ~ 1 ~ ~ 4 4 ~ ~ ~ ~ ~ ~ ~ ~ 1 ~ ~ 4 4 4 ~ 4 1 4 4 4 1 ~ 1 4 ~ 4 4
AIR FLOW DATA CARDS( OMIT THIS CARO IF NFLOW = 0 )
4 ~ 4411 ~ ~ ~ 444 ~ ~ 1 ~ 41 ~ 14144
1nri nw IFROM ITO VFLOW
1 ~ ~ ~ 0 0 0 ~ 1 0 ~ ~ ~ 0 ~ ~ ~ 0 ~ 1 ~ 1 ~ ~ ~ ~ 0 ~ 0 ~ 1 0 ~ 1 ~ 1 ~ ~ ~ 1 1 1 1 1 ~ 1 1 ~ 1 1 1 1 ~ ~ 1 ~ ~ ~ 1 1 1 ~ 0 ~ 1 0 ~ ~ ~ ~ ~
LEAKAGE PATH DATA( OMIT THIS CARO IF NLEAK = 0 )
IOLEAK ARLEAK AKLEAK LRMI LRM2 LDIRN
~ ~ ~ 0 ~ ~ ~ ~ ~ ~ 0 1 0 1 0 ~ ~ 0 0 0 ~ 0 ~ ~ 0 ~ ~ 1 ~ ~ 0 0 0 0 ~ 0 0 0 0 0 0 ~ 0 0 0 ~ 0 ~ 0 0 1 1 1 0 0 1 ~ 0 1 1 0 ~ 1 1 0 0 ~ ~ ~ ~ 0
AIR FLOW TRIP DATA
IDFTRP KFTYPI KFTYP2 FTSET IDFP
1 ~ ~ ~ ~ 00000 ~ ~ 00 ~ 0 ~ 0 ~ ~ ~ ~ 0 ~ ~ ~ ~ ~ ~ ~ 0 ~ ~ ~ ~ ~ 0 ~ 0 ~ 00 ~ 0 ~ 0 ~ 0 ~ ~ ~ ~ 1 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
HEAT LOAD DATA CARDS
IDHEAT NUMR ITYP QDOT TC WCOOLI I 2 'I 000. -1. 0.2 I 3 'I 000. —I . 0.3 I 3 3000. -1. 0.4 I 8 2000. —I . 0.
- ~ ~ 1 ~ ~ 000 ~ 0 ~ I ~ ~ Ol ~ ~ 0 ~ 0 ~ 0 ~ 0 ~ ~ ~ ~ ~ 00 ~ 0000 ~ 00 ~ 0 ~ 00 ~ eeel ~ ~ 00 ~ ~ ~ ~ 10000 ~ ~ ~ ~ ~ 000 ~ 0 ~
PIPING DATA CARDS
IDPIPE IPREF POD PID AIODN PLEN PEM AINK PTEMP IPHASE
1 ~ 1 0 0 0 ~ ~ ~ ~ 0 1 ~ 1 0 ~ ~ ~ ~ ~ ~ 0 0 1 1 ~ 0 ~ ~ ~ ~ ~ ~ ~ 0 0 0 0 0 ~ ~ 0 0 0 0 0 1 0 ~ ~ ~ 0 1 ~ 1 1 ~ 1 ~ 0 ~ 0 ~ ~ ~ ~ 1 0 ~ ~ 1
HEAT LOAD TRIP CARDS
I DTR IPI2345
s \ 00000000
IHREF ITMD TSET TCON'I 2 1.0 0. 0 TRIP ONI I 5.0 0. 0 TRIP OFF2 I 10.0 0. 0 TRIP OFF3 2 15.0 0. 0 TRIP ON4 I 20.0 5. 0 EXPON DECAY
~ ~ ~ ~ ~ ~ 011 ~ 0 ~ 0 ~ ~ ~ 0 ~ ~ ~ 010 ~ ~ ~ ~ 10 ~ ~ 110 ~ ~ ~ ~ 0 ~ ~ ~ 0 ~ ~ 00000000 ~ ~ 0 ~ 1 ~ ~ ~ ~
STEAM LINE BREAK DATA CARDS
~ IOBRK IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMPI1000000000
II OSLB I
oeooooo ~ 00
IDSLB I
t ~ ~ ~ ~ ~ 0000
o
~ I OSLB I
1 ~ ~ 1 ~ 100 ~ 0
ITYPE NGRIO IHFLAG CHARLIRM2IRMI~ 1 ~ ~ 0 ~ ~ 0 ~ 1 ~ 0 ~ 010 ~ ~ ~ ~ 00 ~ ~ ~ ~ 0 ~ 0 ~ ~ 11 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0000 ~ 0 ~ ~ 0 ~ ~ ~ ~ 0 ~ 00 ~
THICK SLAB DATA CARD (CARD 2 OF 3)
ROS CPS EMI SALS AREASI AKS
00001 ~ ~ ~ 000 ~ 1 ~ 0010 ~~ ~ ~ ~ ~ ~ ~ ~ ~ 0 ~ 0 ~ 00000 ~ ~ 0 ~ 00 ~ 1 ~ 1 ~ 0
K SLAB DATA CARD (CARO 3 OF 30000 ~ ~ ~ ~ 0 ~ ~
THI C
HTCI(2) HTC2(2)HTCI ( I) HTC2( I)0 ~ 0 ~ ~ ~ ~ ~ 0 ~ ~ 1 1 1 ~ 0 0 0 0 1 ~ 1 1 1 ~ 1 0 0 ~ ~ 0 0 1 0 ~ 0 ~ 0 0 0 0 0 0 ~ 1 ~ 0 ~ ~ 1 0 ~ ~ ~ 1 0 1 ~ 0 0 0 ~
THIN SLAB DATA CARO (CARO I OF 2)
~ ~ ~ ~ ~ ~ ~ 0 ~ ~ 0 ~ ~ 0 ~ ~ 0 ~ 00 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ 000 ~ ~ ~ 00 ~ 00 ~ ~ 1 ~ ~ ~ 111 ~ 1 ~ ~ 0 ~ 0 ~ ~ ~ 1
THICK SLAB DATA CARD (CARO I OF 3)
IDSL82I
~ 11111111 ~
JRM I JRM2 JTYPE AREAS2I -I I 500.
~ oo ~ ~ ~ ~ ~ 1 ~ 1 ~ ~ 1 ~ ~ ~ ~ ~ 1 ~ 11 ~ 01 ~ ~ ~ ~ ~ ~ ~ ~ 0 ~ 0 ~ ~ ~ 1
THIN SLAB DATA CARD (CARO 2 OF.~ ~ 1 ~ 1 ~ 111 ~ 111 ~ ~ 1111 ~
2)
IOSI
t11111 ~ ~
I DTDR-I01111111
IRMFLG NPTS TORTO AMPLTD FREDI 3 0.0 0.0 0.00
ooooo~o ~ ~ ~ oooo ~ ~ 1 ~ ~ ~ ~ 1111 ~ ooooeo ~ ooooooe ~ ooeoeooooeoo ~ ~ ~ 1 ~ 1
~IMF <ERSIIS TEMPFRATURE DATA
nnF (
LB2 UHI( I ) UHT(2)0.33
~ 111 ~ 1 ~ ~ ~ ~ ~ ~ ~ 1 ~ ~ ~ 1 ~ 1 ~ 11 ~ ~ ~ 1 ~ 1 ~ ~ ~ 111 ~ ~ ~ ~ ~ 1 ~ 111 ~ ~ 1 ~ 11 ~ ~ ~ 111111 ~ 111TIME-DEPENDENT ROOM DATA
-1 0.00 100.0 0.50 14.7050.00 100.0 0.50 14. 70
100.00 100.0 0.50 14. 70~ ~ ~ ~ ~ ~ ~ ~ ~ I j 4 4 ~ I1 ~ 0 ~ ~ ~ 0 4 4 0 I ~ ~ 0 ~ ~ 0 ~ 0 ~ ~ 1 4 I 0 ~ 0 ~ ~ ~ ~ ~ 1 0 ~ 0 0 ~ I~ 0 ~ I 4 4 4 4 4 0 ~ 0 0 i 4 4 ~ i 0 0~ 4 1 J 4 4 ~ 4 0 ~ ~ ~ 0 ~ 0 4 0 4 4 ~ 0 ~ 0 t 4 ~ 1 0 0 ~ ~ ~ 4 l ~ ~ i 1 ~ 0 ~ ~ ~ 0 ~ 0 ~ ~ ~ ~ 0 0 ~ ~ l ~ 4 0 4 4 ~ 4 4 4 ~ ~ 0 ~ ~ ~ 0 ~
FIGURE 4.6 COMPARISON OF COTTAP CALCULATEO COMPARTMENTTEMPERATURE WITH ANALYTICALSOLUTION
FOR SAMPLE PROBLEM 2135
130
OO
OLLI
LJJ,0
125
120
115
110
105
LegendANALYTICAL
~ COTTAP
1000 10 20
TIME (hr)30 40
PP8,L Form 24'10/N)Ca). t973401
SE -9-. N A =04 6 Rev.0g
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER 8c LIGHT COMPANY ER No.
CALCULATIONSHEET
The walls of the compartment consist of 3 slabs: a vertical wall
(slab l), a ceiling (slab 2), and a floor (slab 3) which is in contact
with the outside ground. The temperature, relative humidity, and pressure
within the time-dependent compartment are held constant throughout the
transient. The COTTAP input data file for this problem is shown in
Table 4.4. The COTTAP results for this problem are given in Figure 4.7.
4.4 COTTAP Results for Com artment Heat-U Resultin from a Hi h Ener
Pi e Break (Sam le Problem 4)
A high energy pipe break is modeled using a standard COTTAP compartment
that is connected via a leakage path to a time dependent volume. The pipe
break is initiated in the standard compartment at time 0.5 hr and is
terminated at time 2.5 hr. The time dependent volume is maintained at0
95 F and 14.7 psia. The leakage path maintains constant pressure in the
standard compartment by allowing flow between it and the time dependent
compartment.
The COTTAP input file is shown in Table 4.5 and results of the COTTAP run
are given in Figure 4.8 ~
TSO FOREGROUND HARDCOPY ~ ~ 10 PRINTED 89304.0951OSNAME=EAMAC.COTTAP.SAMPL3.DATAVOL=OSK533
COTTAP SAMPLE01101000000000~ PROBLEM OESC0
NROOM,NSLABII 3
~ ~ ~ ~ 1 ~ 0 ~ ~ ~ ~ ~ ~ ~
PROBLEM OESC
PROBLEM 3~ 0 0 0 0 0 0 0 ~ 0 ~ 1 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0 1 0 0 0 0 1 0 0 ~ 0 0 0 0 0 0 0 0 0 0 ~ 0 ~ 0 1 0 1 ~ 0 ~ 0 0 0RIPTION DATA ( CARD I OF 3 )
NSLA82 NFLOW NHEAT NTDR NTRIP NPIPE NBRK NLEAK NCIRC NEC0 2 'I I 'I 0 0 I I 8
~ 0 0 0 0 ~ 1 ~ 0 0 0 1 1 1 0 1 0 0 0 ~ 0 ~ ~ 0 ~ ~ ~ 0 0 0 0 ~ ~ 0 1 0 ~ ~ 0 ~ ~ 0 ~ ~ 0 1 1 ~ 1 1 ~ 0 ~ 1 1 0 1 1RIPTION DATA ( CARD 2 OF 3 )
MASSTR MF „ CPI CP2 CR'I INPUTF IFPRT RTOLI 10 2.04 150. 5. I I I . D-5
0 1 0 ~ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ~ ~ 0 ~ ~ 0 0 0 ~ ~ ~ ~ 0 0 0 ~ 0 0 1 0 0 ~ 1 0 ~ ~ 0 0 0 ~ ~ ~ 0 1 0 0 ~ 0 1ESCRIPTION DATA ( CARO 3 OF 3 )
NFTRIP5
~ 001 ~ 00OBLEM 0
~ ~ 0 0
PR10 NSH
1001100 ~ 0 ~10
TFC1. 0-5
0 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 1 ~ 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ~ ~ 1 ~ 1 ~ ~ ~ ~ 1 1PROBLEM TIME AND TRIP TOLERANCE DATA
TEND TRPTOL TRPENO3.0 0.005 3.0
~ ~ I~ 1 1 0 1 0 0 ~ ~ ~ ~ ~ 1 1 ~ ~ 0 ~ 0 ~ ~ 1 0 ~ ~ 1 ~ ~ I~ ~ 1 ~ 0 0 1 ~ ~ ~ ~ ~ ~ ~ ~ I~ ~ ~ 1 1 1 1 1 1 1 1 ~ 1 ~ ~ lI 1 ~ ~TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE
( OMIT THIS CARD IF NFLOW = 0 )
0
0.0111111011111 DELFLO
I.D-51111010 1 ~ 1 ~ ~ ~ 1 1 1 ~ ~ 0 ~ 1 ~ 1 1 1 1 ~ 1 1 1 1 1 1 1 ~ ~ 1 ~ ~ 0 1 0 1 ~ 1 1 ~ 1 0 1 1 ~ ~ 1 1 ~ 1 1 ~ 1 1 ~ ~ 0 ~ ~ 1 1
EDIT CONTROL DATA CARDS~ 111
11 [ OEC
I23
5678100010 ~
TLAST0.11.01.12.2.2
10.024.0
500.00 ~ 000101
TPRNT0.010. 100.010. 100.010. 100.205.00
1 1 0 1 1 ~ 0 1 1 0 1 0 1 ~ 1 1 1 1 1 1 ~ ~ 0 0 ~ ~ 1 ~ 0 ~ 1 1 ~ 0 1 0 0 0 1 1 ~ 1 1 ~ ~ ~ 1 ~ ~ 1 1 1 1EO I T 0 IMENS I ON CARO
0111011 NRED NSIEO NS2ED
2 2 01 1 0 ~ 0 0 ~ ~ 0 0 0 ~ ~ 0 0 ~ ~ 1 1 ~ ~ 1 0 ~ 0 0 0 1 0 0 0 1 1 1 1 ~ 1 1 1 ~ ~ ~ 1 ~ 1 ~ 1 ~ ~ 1 ~ 0 0 ~ 0 0 1 1 0 1 1 1 ~ 0 ~ ~ 0 1 1
ROOM EDIT DATA CARO(S)1 1 ~00
I1 1 ~0
I1111
11~ 1 1
11
-I~ 1 1 ~ ~ 1 1 0 1 1 1 ~ 1 ~ 0 ~ ~ 1 ~ 1 ~ 1 ~ ~ 1 0 1 ~ ~ 1 ~ ~ 1 ~ 1 ~ 1 ~ 1 ~ 0 1 1 1 1 ~ ~ 1 1 1 ~ 1 ~ ~ ~ 1 1 ~ 1 ~ 1 ~ ~ 1 1 ~ 1 1 1
EDIT CARD(S) FOR THICK SLABS
21 1 1 1 ~ 0 ~ ~ ~ 1 ~ ~ ~ ~ 0 1 1 ~ 1 1 1 1 0 0 ~ 0 0 1 ~ ~ 1 1 ~ ~ ~ ~ ~ 1 1 1 1 1 ~ 0 ~ 1 1 1 ~ 1 1 1 1 1 1 1 1 1 1 ~ 1 1 ~ 1 ~ 1 ~ 1 1
EDI T CARDS FOR THIN SLABS
1 ~ 1 1 1 1 1 ~ 1 ~ ~ ~ ~ 1 1 1 1 1 ~ 1 ~ 1 1 ~ 1 1 ~ 1 1 1 1 ~ 1 ~ ~ 1 ~ 1 ~ 1 1 1 ~ ~ 1 1 ~ ~ ~ ~ ~ 1 1 1 1 1 1 1 1 1 1 1 1 1 ~ ~ 1 1 1REFERENCE PRESSURE FOR AIR FLOWS
(OMIT THIS CARO IF NFLOW=O)
ROOM DATA CARDSNOT INCLUDE TIME-DEPENDENl'OOMS)
1
i issci)IIM vwc S iw l(t I HIIM IIM HT
TREF PREF100. 14. 7
0 ~ 0 0 ~ 1 ~ 0 1 ~ 1 ~ 1 1 1 ~ ~ ~ 1 ~ 1 1 1 1 ~ 1 0 1 1 1 1 0 0 1 ~ ~ 1 ~ ~ ~ 1 1 ~ 1 1 1 1 0 ~ ~ ~ 1 ~ 1 1 ~ 1 1 1 1 1 1 1 1 1 ~ 1 ~ 0 ~ ~ 0
111111
30000. 14.7 80.0 0.5 27.51 1 1 0 1 1 0 0 1 0 ~ ~ ~ 0 1 ~ ~ 1 1 1 0 1 ~ 1 1 1 0 1 1 1 0 ~ 1 ~ 1 1 0 0 0 0 ~ ~ 1 1 ~ 0 ~ ~ 0 0 0 ~ ~ 0 ~ 0 1 0 0 1 1 ~ 1 1 1 0 1 1 0
AIR FLOW DATA CARDS( OMIT THIS CARO IF NFLOW = 0 )
IDFLOW IFROM ITO VFLOWI -I I 'I.D4 FAN2 I -I I . D4 0 FAN
11011 111 ~ 11 ~ 1 ~ 000 ~ 1 100100000000000001 ~ 00000LEAKAGE PATH DATA
( OMIT THIS CARD IF NLEAK = 0 )
11100
0
0 ~ ~ ~ ~ 000 ~ 00 ~ 0 ~ 0 ~ ~ 1 ~ 0001001
111001 IDCIRC KRMI KRM2 ELEVI ELEV2 ARIN AROUT AKIN AKOUT
I I -I 3. 12. 50. 50. 5. 5.~ 0000000101010 ~ 10001'00 ~ 0 ~ ~ ~ 0 ~ 0 ~ 0000 ~ 011 ~ 0 ~ ~ 0 ~ 000 ~ 001 ~ 000011111100
AIR FLOW TRIP DATA0010
0 IDFTRP KFTYPI KFTYP2 FTSET IDFPI 3 I 0. 0 I 0 TRIP CIRC FLOW OFF .AT2 I I 1.0 I 0 TRIP FAN OFF3 I I 1.0 2 0 TRIP FAN OFF4 2 I 2.0 I 0 TRIP LEAKAGE PATH OFF5 3 2 2.0 I 0 START NATURAL CIRC
~ 1 1 1 ~ 1 1 0 1 ~ 1 1 0 ~ 1 0 0 1 0 1 1 1 ~ 1 ~ 1 1 0 ~ 0 ~ 0 ~ ~ 0 0 ~ 0 0 ~ 0 0 1 0 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 1 1 1 11 HEAT LOAD DATA CARDS1
IDHEAT NUMR I TYP OOOT TC WCOOLI I 3 100000. -1. 0.
~ 1 1 1 1 1 1 ~ ~ 1 1 0 ~ 0 1 ~ 0 1 1 ~ 0 1 ~ 0 ~ 1 1 0 ~ ~ ~ 1 ~ 1 ~ 0 ~ 0 0 0 0 0 ~ ~ ~ 0 ~ 0 1 0 ~ 0 1 1 1 1 1 0 ~ 1 1 ~ ~ 1 ~ 1 ~
1 PIPING DATA CARDS1
IDPIPE IPREF POD PID AIODN PLEN PEM AINK PTEMP IPHA
1 1 0 0 0 0 1 0 0 0 ~ 1 0 0 1 0 ~ 0 0 0 ~ 1 0 0 0 ~ 0 1 1 ~ 0 0 ~ 0 0 1 0 0 0 ~ ~ ~ 1 ~ 0 0 0 0 ~ 0 0 0 0 0 1 0 1 0 0 ~ ~ 0 0 0 ~ 0 0HEAT LOAD TRIP CARDS
START
01100
01111
SE
IDLEAK ARLEAK AKLEAK LRMI LRM2 LDIRNI 1.0 -1.0 I - 'I 2
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 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 ~ 0 0 ~ 0 0 0 1 1 1 0 0 0 0 0 0 0
CIRCULATION PATH DATA
IHREF I TMD TSET TCONI I 10. 0 0.
1 1 0 1 0 0 0 0 0 0 1 ~ 0 ~ ~ 0 1 ~ ~ ~ ~ 1 0 0 0 0 1 1 0 1 ~ 1 ~ 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 0
STEAM LINE BREAK DATA CARDS
IRM I I RM2 I TYPE NGR ID IHFLAG CHARLI -I I 10 2 30.I -I 3 10 2 30.I 0 2 'I 0 0 30.
~ 1 ~ ~ 1 1 1 0 ~ 1 1 ~ 1 ~ ~ ~ ~ ~ ~ ~ 1 1 ~ ~ ~ ~ 1 ~ ~ ~ 1 1 ~ ~ ~ ~ 0 ~ ~ ~ ~ 1 1 1 ~ ~ ~ ~ 1 1 1 0 ~ 1 0 1
THICK SLAB DATA CARD (CARO 2 OF 3)11111
EMI S0.800.800.80
1111111111110
HTCI ( I ) HTC2(1) HTCI(2)3.73.7 3.7
1 1 1 1 1 ~ 1 1 II 1 1 1 ~ 1 ~ ~ ~ 0 1 ~ ~ ~ 1 1 ~ 1 ~ 1 0 ~ ~ ~ ~ I~ 0 ~ 1 0 0 0 ~ 0 0 1 1 ~
THIN SLAB DATA CARD (CARO I OF 2)
HTC2(2)
~ 1 ~ 1111 ~ 110 ~ ~ 00
IDTRIPI
00111100000 0001100
IDBRK IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP0~ 1 0 0 0 0 0 1 1 0 1 ~ ~ 0 0 0 1 1 ~ 1 1 1 ~ ~ 1 ~ ~ 1 0 1 0 0 0 0 1 1 0 0 0 0 0 ~ ~ 0 ~ ~ 1 0 ~ 0 ~ ~ ~ ~ ~ ~ ~ 0 0 1 ~ 0 0 1 ~ 0 0 0 1 1 0 1
THICK SLAB DATA CARD (CARD I OF 3)
IDSLBII23
1001010111101
IDSLB I ALS AREASI AKS ROS CPSI 3.0 3800. 'I . 0 140. 0.222 2.0 960. 1.0 140. 0.223 4.0 960. 1.0 140. 0.22
1 ~ ~ ~ ~ ~ ~ ~ ~ 1 ~ 1 1 1 ~ 1 ~ 1 1 1 1 1 0 1 ~ 1 1 ~ 1 1 ~ ~ 1 1 1 ~ 1 ~ 1 1 ~ 1 0 0 0 1 1 ~ 1 1 1 1 ~ ~ 0 0 ~
1 THICK SLAB DATA CARO (CARD 3 OF 3)
IDSLBII2
1 ~ 1 ~ 1 ~ 11111
lRM l IRM'7 ITVPF ARFaS'P
1~ 1111
00
010000
IOT-1
~ ~ 0 0 ~
~ I OT-I
00 ~ 01010 ~ ~
~ 1 0 ~ 1 1 0 1 ~ ~ 0 0 0 1 ~ 1 0 0 1 ~ ~ ~ ~ 0 1 ~ 1 0 ~ 1 1 ~ 0 0 ~ 0 0 0 ~ 1
THIN SLAB DATA CARD (CARD0 0 ~ 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0
2 OF 2)
IDSLB2 UHT(1) UHT(2)
OR
11010111IRMFLG NPTS TDRTO AMPLTO FREQ
'I 4 80. 0 0.0 0.00 0 OUTSIDE AIR~ ~ ~ ~ ~ ~ I I~ ~ 0 I~ I~ ~ I~ 1 I~ 0 1 ~ ~ ~ 0 I~ ~ ~ 0 I~ ~ 1 0 ~ 0 ~ ~ 0 0 ~ ~ ~ 1 0 0 0 0 0 1 0 1 ~ 0 0 ~ 0 ~ 0 ~ ~ 1 ~ 1
TIME VERSUS TEMPERATURE DATA
DR TT01
25
0010111 ~000 ~ 0010
I ME.00.00.00.000 ~ 0 ~ 0 ~ ~ 0 ~
~ 0 ~ 110 ~ 0 ~
TTEMP80.080.080.080.0
0000 ~ 000~ ~ ~ ~ ~ 000
RHUM0.500.500.500.50
~ ~ 00000 ~ 0 ~ 0 ~ 000~ ~ ~ 00 ~ ~ 00 ~ ~ ~ 000
PR14.14.14.14.
0 ~ 00~ 0 ~ 0
ES7070707000 ~ 100001 ~ 1 ~ ~ 01011 ~ 11 ~ ~~ 0 ~ 00 ~ ~ ~ 00 ~ ~ ~ 00 ~ ~ ~ 11 ~ ~ ~
0 ~ 0 ~ 0 1 1 0 0 1 0 ~ 0 ~ 0 0 ~ 0 ~ 1 ~ ~ ~ ~ 0 0 0 ~ 0 0 0 1 ~ 0 0 0 0 0 ~ 0 0 ~ 0 ~ 0 0 0 0 1 0 0 0 1 1 0 ~ 0 1 1 1 1 ~ 0 0 ~ ~ 0
TIME-DEPENDENT ROOM DATA
figure 4.7 COTTAP TEMPERATURE PROFlLE FOR SAMPLE PROBLEM 3
100
CD
I—
I—CL
OO
O
Ck'—
CLLIJCL
I—
95
90
85
800 0.5 1.5
TIME (hr)2.5
TSO FOREGROUND HAROCOPY 1 ~ ~ 0 PRINTED 89285. 1301OSNAME=FAMAC.CQTTAP.SAMPL4.DATAVOL=DSK540
COTTAP SAMPLE PROBLEM 4~ ~ ~ ~ 1 ~ ~ ~ I ~ ~ 00 ~ ~ ~ 0000 ~ 00 ~ ~ ~ ~ ~ 0 ~ 001 ~ 1 ~ 0 ~ ~ ~ 000I~ 00110I ~ 10 ~ 1101 ~ 11010 ~ 0 ~ 1 ~ ~ ~ 000
PROBLEM DESCRIPTION DATA ( CARO 1 QF 3 )
NROOM NSLAB'I NSLA82 NFLOW NHEAT NTOR NTRIP NPIPE NBRK NLEAK NCIRC NEC1 3 0 0 0 1 0 0 'I I 0 6
~ 1 ~ 1 ~ ~ ~ ~ ~ ~ 0 0 ~ 1 ~ ~ 1 0 ~ ~ ~ ~ 0 ~ ~ ' ~ 0 ~ ~ ~ ~ ~ ~ ~ 0 ~ ~ ~ 1 ~ ~ 0 1 0 0 0 0 ~ ~ 1 ~ ~ ~ 0 1 1 1 1 1 0 ~ 0 0 0 1 1 ~ 1 0 0 ~
PROBLEM DESCRIPTION DATA ( CARD 2 OF 3 )0~ NFTRIP MASSTR MF 'PI CP2 CRI INPUTF IFPRT
0 1 13 S.D4 150. 50. I 'I
~ 1 ~ ~ 0 ~ 000000 ~ 00 ~ ~ 00 ~ 0 ~ 00 ~ 0 ~ 00 ~ 0 ~ 0 ~ 000 ~ 00 ~ 0 ~ 00000000000 ~ ~ 0 F 00PROBLEM DESCRIPTION DATA ( CARO 3 OF 3 )
NSH TFC0 I . 0-5
0010I ~ 000 ~ 0 ~ ~ 0000000001000000 ~ ~ 0 ~ ~ 00 ~ ~ 0 ~ 00 ~ ~ 00 ~ 000000 ~ 01010000 PROBLEM TIME ANO TRIP TOLERANCE DATA
RTOLI.D-5
~ ~ 1000 ~ 10100
~ 011 ~ 00000 ~ 0
TRPTOL TRPEND0.005 6.0
0 ~ 000000010 ~ 001001 ~ 00001000 ~ ~ 00000 ~ 00 ~
COMPARTMENT-AIR-FLOW MASS BALANCECARD IF NFLOW = 0 )
T TEND0.0 6.0
~ 1 ~ ~ 000 ~ 1 ~ 10 ~ 0 ~ ~ 00 ~ ~ ~ 1
0 TOLERANCE FOR( OMI T THIS
1 OELFLO1.0-5
~ ~ 10 ~ 0 ~ ~ 0011 ~ 110 ~ ~ 0 F 010 EDI00
111000000000
0 ~ 0 0 1 0 0 ~ ~ ~ 1 0 0 1 0 1 ~ ~ ~ ~ 0 0 0 0 0 1 1 0 0 ~ ~ ~ ~ ~ 0 ~ 0 1 ~ ~ 1 ~ 0 ~ 0 1 0 1 1 1
T CONTROL DATA CARDS
TLAST TPRNT0.5 0. 100.6 0.0052.5 0. 102.6 0.0056.0 0.20
25.0 0.500001 ~ 00 ~ 00 ~ 001000 ~ ~ 0001 ~ ~ 00100000000000 ~ 1000 ~ 000 ~ I~ ~ 1 F 1 '00000
EDIT DIMENSION CARO
OECI23456000000000 ~ 0
0
0 NREO NS1ED NS2ED2 3 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 0 0 0
ROOM EDIT DATA CARD(S)0 ~ ~ ~ 0 0 0 1 1 ~ 0 ~ 0 0 0 ~ 1 0 ~ 0 0 0 0 1 00000
0
I010 ~10
I~ 01 ~
00011 ~
10
~ 11111
0
ID
-I0 0 0 ~ 0 ~ 0 0 0 0 1 0 0 0 1 ~ 0 1 1 1 1 0 ~ 0 ~ 0 ~ 0 0 0 ~ 0 0 0 0 0 ~ 0 0 1 0 0 1
EDIT CARD(S) FOR THICK SLABS~ 00 ~ 00011000 ~ 0 ~ ~ 0 ~ ~ 0000 ~ ~
~ ~ ~ I~ ~ 1 1 1 1 1 1 ~ ~ 1 1 1 1 ~ I ~ 0 1 1 1 ~ 1 0 0 I~ ~ ~ 1 ~ ~ ~ 1 ~ 0 1 ~ 0 1 1 1 ~ ~ ~ 0 I~ 1 I~ ~ ~ ~ 1 1 ~ 1 ~ 0 0 0 0 0 0 0 0 I~ 0
REFERENCE PRESSURE FOR AIR FLOWS(OMIT THIS CARD IF NFLOW=O)
TREF PREF100. 14. 7
~ ~ ~ 0 1 Ol ~ ~ ~ ~ 1 ~ 0 1 I~ I~ ~ 0 0 I~ 0 ~ ~ 1 1 0 ~ I~ ~ ~ 1 0 1 ~ ~ 0 0 I~ ~ 1 ~ I~ 1
ROOM DATA CARDS(00 NOT INCLUDE TIME-DEPENDENT ROOMS
ROOM ~ PRES TR RELHUMI 105~ 14.7 95.0 1.0
11 ~ 11 '1 ~ 0 a ~ ~ 1 111
~ ~ ~ 1 ~ 10 ~ ~ 111 ~ ~ ~ ~ ~ 11 ~ ~ 1 ~ 1 ~
~ ~ 11, ~ 11
2 30 1 0 ~ ~ ~ 0 ~ 1 0 1 0 0 0 1 0 ~ 0 1 1 ~ 0 ~ ~ 1 1 0 0 0 0 0 0 0 0 ~ ~ ~ 0 0 ~ 0 0 0 1 ~ ~ 0 1 1 0 1 0 0 0 ~ 0 1 ~ 1 1 1 0 0 ~ 0 1 0 0
EO I T CARDS FOR THIN SLABS
AIR FLOW DATA CARDS( OMIT THIS CARO IF NFLOW = 0 )
tttttttttttt
IDFLOW IFROM ITO'FLOWttttttttttttttttttttttttttttttttttttttttttt
NLEAK = 0 )
t t t t t ~ ~ t t t t t t t t t t t t t t t t t t tLEAKAGE PATH DATA
( OMIT THIS CARD IF
TC WCOOL
I TMD TCON
ROS140.140.140.
CPS EMI S0.22 0.800.22 0.800.22 0.80
AKS'1.001. 001 . 00
AREAS11000.800.800.
ALS2.754.002.75
IDLEAK ARLEAK AKLEAK LRM1 LRM2 LDIRN1.0 -1.0 I -1 2
~ t t t ~ t t t ~ ~ t t t ~ t t t t t t t t t t t ~ t t t t t t t ~ t ~ ~ ~ t t ~ t t t t t t t ~ t t t t t t t t t t ~ t 't ~ ~ t ~ t ~ t t t ~t CIRCULATION PATH DATAt
IDCIRC KRM1 KRM2 * ELEV1 ELEV2 ARIN AROUT AKIN AKOUTttttttttttttttttttttttttttttt~ t ~ ~ ttt ~ ttt ~ tttt ~ t ~ t ~ ttttttt~ ~ ttttt ~ ~ t ~ tttttt AIR FLOW TRIP DATA
IOFTRP KFTYP1 KFTYP2 FTSET IDFP
t t t t t ~ t ~ t t t ~ t t t t t t t t t t ~ t t t t t ~ t t ~ t 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 HEAT LOAD DATA CARDS
IOHEAT NUMR ITYP QDOT
t t 't t ~ t t t t t t ~ t ~ t t t ~ t t t t ~ t t t t t ~ t t t t ~ t t t ~ t t ~ t t t 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 PIPING DATA CARDSt
IOPIPE IPREF POD PID AIOON 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 t t t ~ t t ~ tt HEAT LOAD TRIP CARDSt
IDTRIP IHREF TSETtt t t t ~ ~ t t ~ t t t ~ ~ ~ t t t t t t t t t t t t t t t t ~ ~ t t ~ ~ t t t ~ t 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 CARDSt
IDBRK IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP1 1 1000. 2 1800. 0.5 2.5 0.5tttt ~ tt ~ ttt ~ ttttttttttttt ~ ttttttt ~ t ~ ~ tt ~ t ~ t ~ ~ t ~ ttttttttttttt ~ ttt ~ ~ ttt ~ t ~
THICK SLAB DATA CARD (CARO 1 OF 3)
I DSLB I I RM1 IRM2 ITYPE NGRID IHFLAG CHARL1 1 -1 1 15 2 0.2 1 0 2 'I 5 0 0.3 1 -1 3 15 2 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 t t t t t t ~ t ~ t t t t t t t t
THICK SLAB DATA CARD (CARD 2 OF 3)tIDSL81
1
23
~)0
0100000 0 tt ~ 1000 1000 ~ 01 ~ 10 ~ 00 0 ~ 010 ~ 10000 ~ 0 0 t10101000 tf0 ~ 101 ~ 00 0
THICK SLAB DATA CARD (CARD 3 OF 3)
HTCI(i) HTC2(i) HTCI(2) HTC2(2)0.60.9 0
~ 00 ~ 00 0010 1 ~ 1 f 10 0100 ~ 0 00 0 110000 0 ~ 11 0 ~ ~
THIN SLAB DATA CARD (CARD I OF 2)
00 00000 0
IDSLB II3
11110 010
0
IDSLB2 JRMI1000000000
IOSL820101000000
IDTDR-I00101000100 IDTDR-I
.40 0 ~ 1101 ~ 1 0 0 t0001000111 0
JRM2 JTYPE AREAS2
UHT(1) UHT(2)1 tttftf 0 0 0000 ~ 001010 1000 0 ~ 000 0 ~ 01000 ~ 010 1 ~ ~ 0110 11110000110011100
TIME-DEPENDENT ROOM DATA
IRMFLG NPTS TORTO AMPLTD FREQI 3 0.0 0.0 0.00 0 OUTSIDE AIR
0 0 0 0 0 0 0 0 ~ tf0 0 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 0 ~ 0 0 0 f 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 1 0 0 0 0
TIME VERSUS TEMPERATURE DATA
TTIME0.00
10.0050.00
1010 0 11 0 00000100 0 0 0 0 0 0 0000
TTEMP RHUM PRES95.0 0.60 '14. 795.0 0.60 14.795.0 0.60 14. 7
0 0 0 0 t 0 ~ 0 t t 0 0 0 0 0 0 t tf0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0000 00 0 000 00 0 ~ 0 00 0 0 0 0 tf0 0 f0 00 00 0 00 000 0
110101010 1000000
00001 ~ 0 0000 ~ 1000010001f 0 000 0
0 1 ~ 00 00 000000000 0 00 00 ~ 0 000 0 0 0 0 00 ~ 0 ~ 0 ~ 0 0 0 10 000 ~ 100010 t00000011010THIN SLAB DATA CARD (CARD 2 OF 2)
FIGURE 4.8 COTTAP TEMPERATURE PROFILE FOR SAMPLE PROBLEM 4
180
CA
I—Z:IJJ
OOZ'-
I—
LxJCL
I—
160
140
120
100
803
TIME (hrs)
o 7c
QClCD
n
O
ppdL Form 2«5«nar83)c«r. «073«0r
SE -B- N A-0 4 6 Rev. 01
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ 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 of0
550 F. It is a 20 inch diameter insulated pipe having a wall thickness of
one half inch and an insulation thickness 'of 2 inches. The piping heat
load is tripped off at 1 hour. At this time the heat load exponentially
decays. The thermal time constant associated with the decay is calculated
by the code.
The unit cooler is rated at 20,000 Btu/hr with a cooling water inlettemperature 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 0000 PRINTED 89285. 1403OSNAME=EAMAC.COTTAP.SAMPLS.DATAVOL=DSK536
COTTAP SAMPLE PROBLEM 514 ~ ~ 0 ~ 4000000 ~ 000000 ~ 011 ~ 00 ~ 11 ~ ~ 0 ~ 004000000100000 ~ 0104 ~ 400014
PROBLEM DESCRIPTION DATA ( CARO I OF 3 )0=
NROOM NSLABI NSLAB2 NFLOW NHEAT NTDR NTRIP NPIPE NBRK NLEAK2 0 0 0 2 0 I . 1 0 I
0 0 1 0 0 0 0 0 0 0 ~ 0 0 ~ 0 ~ 0 0 ~ ~ 0 0 ~ 0 0 t 0 0 ~ 0 0 ~ 0 0 ~ 0 1 0 ~ 0 0 ~ 0 ~ 0 ~ 1 ~ ~ ~ 0 ~ 0 ~ ~ 0 0 0 0 00 0
PROBLEM DESCRIPTION DATA ( CARO 2 OF 3 )
440100000
NC IRC NEC0 I
0000000000
NFTRIP MASSTR MF 'P I CP2 CRI INPUTF IFPRT0 1 23 5.D4 150. 10. I I I
410000100000100000400001100 ~ 00000010400 ~ ~ 00000 ~ ~ ~ ~ 004t40400 ~ ~ 1
PROBLEM DESCRIPTION DATA ( CARO 3 OF 3 )0
RTOL.0-5000044000t
NSH TFC0 1.0-5
0 1 1 4 0 4 1 1 0 0 0 4 1 1 0 ~ 0 0 0 1 0 10 PROBLEM
T TEND0.0 4.0001400t10111000000ttt
TOLERANCE FOR1 ( OMIT THIS0~ DELFLO
I.D-S~ 44 ~ 40000440 ~ 1 ~ Ot ~ 0 ~ 000 EDI
~ ~ 0 4 0 1 ~ 0 ~ 1 0 0 4 0 0 0 0 0 0 0 ~ ~ 4 ~ ~ 4 4 ~ 1 0 ~ ~ 4 ~ 4 ~ 1 1 1 4 4 1 4 4 0 1 4 0 ~ ~
TIME ANO TRIP TOLERANCE DATA
TRPTOL TRPEND0.05 4.0
~ 00 ~ 0010010 ~ ~ Ottttt ~ 0 ~ 01 ~ 0 ~ 0 ~ 0 ~ 0000000 ~ ~
COMPARTMENT-AIR-FLOW MASS BALANCECARD IF NFLOW = 0 )
0000100000
~ 1 1 1 ~ t ~ 1 1 1 1 1 ~ 0 0 4 0 t 0 ~ ~ ~ 0 ~ 4 ~ ~ 0 0 ~ 4 1 0 1 1 1 1 1 0 ~ ~ 0 1 0 1 1 0 4 0 ~
T CONTROL DATA CARDS
IDECI
~ 41114101444440
TLAST TPRNT25.0 0. 10
~ 0 4 0 '0 0 1 0 4 tt 1 '1 1 0 0 ~ 1 1 ~ 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 ~
EDIT DIMENSION CARD1 ~ 1 ~ 0 0 1 1 0 4 0 0 1 1 0 4 ~ 1 4 4 0 1
NRED2
0 1 1 4 1 1 1 0 0 4 0 0 101
I 20 1 4 0 4 0 4 4 4 0 0 1 4
0 ~ 0410 ~ ~ ~ 000 ~0
10 ~ 0410 ~ 000 ~ 0400
TREF100.
1 1 1 1 1 1 0 4 1 1 1 1 14
IDROOM VOI 100002 I .D15
4 4 1 1 4 1 4 4 4 4 0 4 4
14~ 1 nc ~ nial
0 0 0 0 0 0 ~ 0 0 0 4 0 0 ~ 0 4 0 ~ ~ ~ 0 4 4 0 t 0 4 t 0 4 0 0 0 0 0 0 4 ~ 0 0 ~ ~ 4 ~ 4 4 0 1 1 0 1 1 0 4 4 1 0 0 0EDIT CARD(S) FOR THICK SLABS
0 ~ 0 1 ~ ~ 0 0 0 0 0 0 1 0 ~ 0 0 0 0 ~ 0 0 0 ~ 1 0 0 0 0 0 ~ 0 0 ~ ~ ~ ~ ~ 0 0 1 1 1 ~ 0 ~ ~ 1 0 0 1 0 ~ ~ ~ ~ 1 0 0
EDIT CARDS FOR THIN SLABS
4 0 0 0 0 ~ ~ 0 ~ 4 0 4 ~ ~ 0 4 0 4 ~ 0 1 ~ 0 1 0 t 1 0 1 t 1 1 ~ 1 0 1 ~ 1 1 ~ 4 0 0 ~ 0 ~ 4 4 4 1 $ 1 1 1 1 1 1 1 0
REFERENCE PRESSURE FOR AIR FLOWS(OMIT THIS CARO IF NFLOW=O)
PREF14. 7
1 4 1 ~ 1 1 1 ~ ~ ~ 1 ~ 4 t ~ ~ ~ 1 1 0 1 0 4 ~ 1 ~ 1 ~ ~ 4 1 1 1 4 ~ 1 ~
ROOM DATA CARDS0 NOT INCLUDE TIME-DEPENDENT ROOMS)
4 ~ 1 1 ~ 1 1 4 1 1 1 1 1 ~ 1 ~ ~ 4004 1
L PRES TR RELHUM RM HT14.7 100.0 0.5 10.014.7 100.0 0.5 10.0
0 4 ~ 1 1 1 0 ~ 4 ~ 0 1 0 0 0 1 0 1 0 1 1 4 4 1 0 0 0 0 0 ~ 4 0 0 1 0 ~ 0
A IR FLOW DATA CARDS( OMIT THIS CARD IF NFLOW = 0 )
1 ~ 1 1 0 1 1 0 0 1 1 ~ 0 1 0 0 1 0 ~ 4 4 t
vvn$ cnnao
NS IED NS2ED0 0
1 0 1 1 1 1 0 4 0 1 1 0 4 ~ 0 ~ 4 0 1 1 0 1 ~ 1 1 0 0 ~ 0 0 0 0 ~ 4 0 0 ~ ~ 1 1 1 ~ ~ 0 ~ 0 0 0 0 0 1 0 0 0 0 0 0 0 1
ROOM EDIT DATA CARD(S)
0
40000
0~ OO0
I
044
4I
0OOO004
IDSLB2 JRMI JRM2 JTYPE AREAS2
OOOIOt4004 ~ 4000 ~ ~ OJ4410040004041 ~ OIOl ~ ~ I ~ ~ 4000 ~ ~ ~ 04 ~ 0000000 ~ 044 ~ 404 ~ 0TIME-DEPENDENT ROOM DATA
DTDR IRMFLG NPTS TDRTO AMPLTD FREQ
~ ~ ~ 0 0 4 ~ 0 4 ~ ~ 0 ~ 0 0 0 0 ~ 0 ~ 0 0 0 4 ~ ~ 0 ~ ~ 0 1 ~ 1 ~ 0 0 1 4 ~ ~ ~ 4 4 ~ 4 ~ ~ ~ ~ ~ ~ ~ 0 0 4 ~ 0 4 0 ~ 4 0 4 4 4 0 ~ 0 0TIME VERSUS TEMPERATURE DATA
DTDR TTIME TTEMP RHUM PRES
4000 ~ lO ~ 400000000000 ~ 000 ~ 0 ~ 0010000I ~ Oi0000100104000000004J ~ OOJJOOOOOJOO~ 1 ~ ~ 0 ~ ~ ~ 0 ~ 01440 ~ 0 ~ ~ 00400 ~ ~ ~ ~ 0 ~ 0 ~ 0 ~ 001004 ~ ~ ~ 00ii004 ~ 000 ~ ~ 00414 ~ ~ 0044 ~ 0
Ol ~ ~ 44 ~ ~ ~ 4044000 ~ 0 ~ ~ ~ 00 ~ 4004 ~ 00 ~ 0401 ~ 44 ~ ~ 004 ~ 400 ~ ~ ~ ~ 0 ~ OOOP 0 1 ~ J4 0 ~ I If0THIN SLAB DATA CARD (CARD 2 OF 2)
IDSLB2 UHT(1) UHT(2)
0000000000 ~
00
~ ~ ~ 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
LEAKAGE PATH DATA( OMIT THIS CARD IF NLEAK = 0 )
IOLEAKI
~ ~ ~ ~ ~ ~ 0 ~ 0 ~
0
IDCIRC
00000000000 A0
IDFTR
0000000000H
0IOHEAT
I2
0000 ~ ~ 000000
I DPI PEI
00 ~ 0 ~ ~ 000 ~
0
ARLEAK AKLEAK I.RMl LRM2 LO!RN'I . 0 -1.0 I 2 '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 ~ 0 0 0 0 0 0 0 00 ~ 0 0 0 0 0 0 ~ 0 0 ~
CIRCULATION PATH DATA
KRMI KRM2 ELEVI ELEV2 ARIN AROUT AKIN AKOUT
0000' 0 0 ~ ' 00000000000000000 ~ 00 ~ 000 ~ 0 0 0 0 t 0000 ~ 0 ~ 0 ~ ~ ~ ~ 00 ~ 0 0 0 00 0 0 0
IR FLOW TRIP DATA
P KFTYPI KFTYP2 FTSET IDFP
000000000000000000000000000000000 '00 F 000000000000t00000000tttEAT LOAD DATA CARDS
NUMR ITYP QDOT TC WCOOLI 4 -20000. 75. 2000.
5 O.DO -1. 0.00000 ~ 00 ~ ~ 00000 0 0 ~ ~ 00000000000000 ~ ~ 00000 0 0000000 0 000 0 0 0 0 ~
PIPING DATA CARDS00000
IPREF POD PID AIODN PLEN PEM A INK PTEMP IPHA2 20. I9. 24. 50. .85 .05 550. I
000 ' 000000000000000tttttt00000 F 0000000000t00000000000000HEAT LOAD TRIP CARDS
SE
00 ~ 00
IDTRIPI
~ ~ 0 ~ ~ 0 ~ 000
I OBRK I
0000 ~ ~ 0000
IOSLB I00000 '0 ' '
IDSLBI~ ~ ~ ~ 00 ~ 00 ~
00
IDSLB I0OOOO ~ ~ 00 ~ ~0
IHREF ITMD TSET TCON2 I l. -1.
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 ~
STEAM LINE BREAK DATA CARDS
BRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP
~ 0 0 0 0 0 0 0 t 0 ~ t 0 t 0 ~ 0 0 0 ~ ~ 0 0 ~ 0 0 0 0 0 0 0 ~ 0 0 ~ ~ 0 0 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 t 0 0 0 0 0 0 0 0
THICK SLAB DATA CARD (CARD I OF 3)IRM'I IRM2 ITYPE NGRID IHFLAG CHARL
0000000I ~ ~ ~ ~ ttt ~ ~ 0000 ~ ~ ~ 0000000000I ~ ~ 0 ~ ~ 00 ~ ~ 00 ~ 000 ~ 000 ~ tl~ 00 ~ 0000THICK SLAB DATA CARD (CARD 2 OF 3)
ALS AREASI AKS ROS CPS EMIS
0000 ~ 00 ~ 0 ~ t ~ 00 ~ 000000000 ~ ~ 0 ~ 0 ~ ~ ~ ~ 00 00 ~ ~ ~ 0 ~ ~ 000 0 ~ 0 ~ ~ 00 ~ 00 ~ 0 ~ ~
THICK SLAB DATA CARD (CARO 3 OF 3)
HTCI ( I) HTC2(1) HTCI (2) HTC2(2)00000 ~ 000 ~ ~ ~ 00 t ~ tt 0 0 ~ ~ ~ 0 ~ 0 0 0 t ~ 000 ~ 00 ~ ~ 00000000000000000t 0 00\00
THIN SLAB DATA CARD (CARD I OF 2)
FIGURE 4.9 COTTAP TEMPERATURE PROFILE FOR SAMPLE PROBLEM 5
120
115
U)
CL110
I—
LIDCL
I—105
1002
TIME (hr)
PPdl. Form 2cSl n0/83jCat, r973401
~E -8- N A:-0 4 6 R(,,0 )
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. JL7 of
PENNSYLVANIAPOWER & LIGHT COMPANY 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 temperature0of 150 F. The initial relative humidity is set to 0.001 so that the
compartment contains essentially pure air. This compartment (compartment
1 in the COTTAP model) is connected to a time-dependent compartment by
means of. a leakage path. The pressure in the time-dependent compartment-5is fixed at 10 psia. The leakage flow area is 0.01 ft and the2
associated form-loss coefficient has a value of 4.0. Leakage is
initiated at t=0. Table 4.7 shows the COTTAP data file for this case,
and the COTTAP output is contained in Section F.6.
Figure 4.10 shows a comparison of the COTTAP results with the
corresponding analytical solution ~
TSO FOREGROUND HARDCOPY +i+i PRINTED 89286. 1008DSNAME=EAMAC.COTTAP.SAMPL6.DATAVOL=OSK532
COTTAP SAMPLE PROBLEM 6~ ~ 4 ~ 400440 ~ ~ 0004 ~ 00004004 ~ 4 ~ 1 ~ ~ 0I4 ~ ~ ~ ~ 000 ~ ~ 0444400 ~ 00 ~ 40000 ~ 04
PROBLEM DESCRIPTION DATA ( CARD I OF 3 )
NROOM NSLABI NSLA82 NFLOW NHEAT NTDR NTRIP NPIPE NBRK NLEAKI 0 0 0 0 I 0 0 0 I
~ ~ 0 ~ ~ 0 ~ ~ ~ ~ 0 ~ ~ ~ OO ~ 0 J ~ 4400 ~ 0 ~ ~ 0 ~ 000 ~ 04 ~ ~ ~ 40004444 ~ 4 ~ ~ tO ~ 0 ~ ~ 4 ~ ~ 0 ~
PROBLEM DESCRIPTION DATA ( CARO 2 OF 3 )
~ NFTRIP MASSTR MF CPI CP2 CRI INPUTF IFPRT0 I 23 5.04 150. 10. I I I
~ 4 0 ~ 0 0 0 ~ 0 ~ ~ 0 0 1 0 ~ ~ 0 0 0 0 ~ 0 ~ ~ 4 0 ~ 0 0 0 ~ 0 1 0 ~ ~ ~ 0 4 0 ~ 0 0 0 ~ 0 0 4 0 0 4 ~ 4 0 4 4 0 4 ~ 0 0PROBLEM DESCRIPTION DATA ( CARO 3 OF 3 )
4
NSH TFC0 I . 0-5
~ ~ 0 1 4 ~ 0 ~ ~ ~ ~ 4 4 t ~ i i 0 ~ 0 0 4 ~ ~ ~ ~ ~ ~ 4 0 0 0 ~ ~ 0 0 4 t ~ ~ ~ 0 ~ ~ ~ 0 0 ~ ~ ~ 4 4 1 0 ~ ~ 0 0 ~ l ~ ~
PROBLEM TIME ANO TRIP TOLERANCE DATA0
440 ~ ~ 0 ~ 404
NCIRC NEC0 3
~ 0 ~ ~ ~ ~ ~ 4 ~ ~
RTOL.D-54400444400
44144 ~ 400 ~
T TEND TRPTOL TRPEND0.0 0.2 0.005 4.0~ ~ 04 ~ ~ 040 ~ ~ ~ ~ ~ J0 ~ ~ 4 ~ ~ ~ ~ ~ 00 ~ ~ ~ ~ i4t0 ~ ~ 0000 ~ 040 ~
TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS( OMIT THIS CARD IF NFLOW = 0 )
~ 40 ~ Oi 0 ~ 0 ~ 4440 ~ 04 i ~ 40 ~ 44BALANCE
I ~ 4
DELFLO'I . 0-5
4 I ~ 4 4 0 ~ ~ ~ ~ 0 0 4 0 4 0 4 ~ ~ 0 4 4 4 0 0 4 4 4 4 ~ ~ 0 ~ 0 ~ ~ ~ 1 ~ 0 4 ~ 4 ~ 0 0 ~ ' 0 4 ~ ~ ~ 4 0 ~ ~ ~ ~ ~ 0 ~ ~ 4 0 ~ 4 ~ ~EDIT CONTROL DATA CARDS
0 4 ~0
IDEC TLAST TPRNTI 0.5 0.012 0.6 0.013 5.0 0. 10
0 ~ ~ 4 4 ~ 4 0 ~ I 4 4 0 4 0 0 ~ ~ ~ i ~ 0 ~ ~ 4 ~ 0 ~ ~ ~ ~ 0 ~ 0 l ~ ~ 4 0 0 0 4 4 4 4EDIT DIMENSION CARD
4 ~ 4 ~ 4 4 4 0 ~ ~ ~ 4 4 4 0 I 0 4 ~ 0 4 4 0 4
0
I~ 0 ~
444044
144
0
~ 4 4
-I0 4 ~ 1 0 4 4 ~ ~ 4 ~ ~ 0 0 ~ ~ ~ ~ ~ ~ ~ 0 ~ 4 0 ~ 4 0 4 4 0 4 4 ~ ~ ~ ~ 0 ~ 4 ~ 4 0 ~ 4 ~ 0 ~ 4 I 4 4 4 4 ~ 4 4 4 ~ 4 ~ 4 4 4 ~ ~ ~ 4 ~
EDIT CARO(S) FOR THICK SLABS
~ ~ ~ 4 0 4 ~ ~ ~ ~ 4 0 ~ 0 0 0 4 ~ 0 ~ 4 4 4 0 4 1 4 0 0 0 0 0 0 ~ ~ I 4 ~ 4 ~ ~ ~ 4 0 4 ~ ~ 4 4 4 4 I 0 4 4 4 0 4 4 1 4 I 0 ~ i 0 i i yEO I T CARDS FOR THIN SLABS
l ~ ~ 04 ~ 10 ~ 4 ~ ~ 0 ~ 440 ~ 4 ~ ~ ~ 444 4 4 0 4 i 4 0 4 4 IO 4 0 ~ ~ I~ 4 ~ 0 4 0 4 ~ i 1 1 4 ~ 0 ~ 4 ~ ~ 4 0 0 ~ II 0 ~ 0 4 0 ~ 4REFERENCE PRESSURE FOR AIR FLOW
(OMIT THIS CARO IF NFLOW=O)
IReF100.
~ 4 ~ ~ 1 ~ ~ 4 ~ 4 ~ 4
PREF14. 7~ Oi ~ ~ ~ ~ 4 ~ 0 ~ i04 ~ f4440 ~ 4 ~ ~ 4044 ~ 4l l4
ROOM DATA CARDSNOT INCLUDE TIME-DEPENDENT ROOMS)
~ ~ 0 1 4 1 4 4 4 ~ ~ 0 ~ 4 4 4 ~ 4 0 1 0 4 4 t(00
NREO NS I ED NS2ED2 0 0
~ ~ 4 4 0 0 ~ 0 0 ~ 4 4 0 ~ 4 ~ 4 ~ 1 ~ 0 ~ ~ ~ 0 0 0 ~ ~ ~ ~ ~ 4 0 4 1 0 ~ 0 ~ ~ ~ 4 4 ~ 0 ~ ~ ~ 0 0 4 ~ 0 0 0 ~ 4 ~ ~ 0 ~ 0 4 4 4 4 1 ~ROOM EDIT DATA CARD(S)
DROOM VOLI 10000.
t ~ 40 ~ 40 ~ ~ ~ ~ ~
PRES TR RELHUM RM HT14.7 150.0 0.001 10.0
~ ~ ~ 4 ~ ~ 4444I44t ~ 4000 ~ 4 ~ 0440 ~ 0 ~ ~ 444AIR FLOW DATA CARDS('H ARO NFLI 0
4 ~ 4441444 ~ ~ 444 4 4 ~44 4 4 4 0
P
IDFLOW IFROM ITO VFLOW11010100000
~ 1 1 ~ 1 0 1 0 0 ~ 0 \ 1 ~ 1 0 ~ 0 ~ 1 ~ 0 1 0 0 0 0 1 1 1 0 1 1 1 1 ~ 1 ~ 0 1 1 1 1 1 0 1 ~ 1 1 0 1 1 1 1 1 ~ 1 0 1 0 1 0 0 0
LEAKAGE PATH DATA( OMIT THIS CARO IF NLEAK = 0 )
K ARLEAK AKLEAK LRMI LRM2 LOIRN0. 01 4.0 I -I I
1 0 ~ 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 0 ~ 0 1 0 0 ~ 0 0 1 1 ~ 0 0 0 0 ~ 1 1 1 0 1 1 1 0 1 0 ~ 0 0 0 0 0 0 0 0
CIRCULATION PATH DATA
0 0 1 0 0 0 0 0 0 ~ 0 1 ~ 0 1 ~ ~ ~ 0 0 ~ ~ 0 ~ 0 0 0 0 0 ~ 0 0 0 0 0 1 ~ 1 0 0 0 0 0 ~ ~ ~ ~ ~ ~ 0 1 1 0 ~ 0 0 ~ 0 ~ 0 0 1 ~ 0
AIR FLOW TRIP DATA
I OFP
000100000100011001 ~ 0 ~ 0000 ~ 000000001011000 ~ ~ 1 ~ 1000100100 ~ 00010 ~ ~ 0
HEAT LOAD DATA CARDS
~ 1 1 1 ~ 0 0 0 1 1 ~ ~ 1 1 1 1 1 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ~ ~ 1 0 1 0 1 ~ 0 ~ 0 0 0 1 0 1 1 1 1 1 1 ~ ~ 0 1 ~ 0
PIPING DATA CARDS
1 ~ 0 ~ 1 1 0 ~ 0 1 0 0 ~ 1 ~ ~ ~ 0 1 0 0 0 ~ 0 ~ 0 ~ ~ ~ 0 ~ ~ 0 0 0 0 0 ~ ~ 1 ~ 0 ~ 0 ~ 0 0 ~ ~ 0 ~ ~ 0 ~ 0 0 0 0 0 0 1 1 1 0
HEAT LOAD TRIP CARDS
TCON
1 1 ~ ~ 1 ~ ~ ~ 0 0 ~ 0 0 1 1 ~ 0 0 ~ 1 0 ~ 0 ~ ~ 0 0 ~ ~ 0 1 0 0 1 ~ ~ ~ ~ ~ 0 0 ~ ~ ~ 0 ~ 0 0 1 ~ ~ 0 ~ 0 ~ ~ 0 1 0 0 0 0 ~ 1
STEAM LINE BREAK DATA CARDS
0 ~ 1 1 0 0 0 ~ 0 ~ 0 ~ ~ 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 ~ 0 0 0 0 0 0 0 0 ~ 0 0 0 0 ~ 0 0 0 0 0 0 1 0 0
THICK SLAB DATA CARO (CARD I OF 3)NGRID IHFLAG CHARLIRM2
~ ~ 00 ~ 1 ~ 11 ~ ~ ~ 00 ~ 0 ~ 11
CPS EMI SAREASI AKS
1 1 1 1 ~ 0 0 ~ ~ 0 ~ ~ ~ ~ 1 1 0 1 ~ ~ ~ ~ 0 ~ ~ 1 ~ 1 1 1 0 0 0 ~ 0 0 0 1 1 ~ ~ 0 ~ 0 0 ~ 1 ~ 1 ~ 1 1 1 I ~ ~ I 1 ~ 1 1 1 1 ~
THIN SLAB DATA CARD (CARD I OF 2)
IDLEAI
01000011
0
IDCIRC KRMI KRM2 ELEV1 ELEV2 ARIN AROUT AKIN AKOUT011 ~ ~ 10001
~ IDFTRP KFTYPI KFTYP2 FTSET000000000
1IDHEAT NUMR ITYP QOOT TC WCOOL
1~ 1111101
IDPIPE IPREF POD PID AIODN PLEN PEM AINK PTEMP IPHASE
10100001
~ IDTRIP IHREF I TMO TSET
01101010
IDBRK IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP
~ 10100111
IDSLB I IRMI ITYPE
~ 1 1 1 1 1 ~ 1 1 1 ~ 1 ~ 1 ~ ~ 1 0 0 ~ 0 ~ ~ 0 ~ ~ ~ ~ ~ 0 1 1 0 0 0 0 ~ ~ 0 0 ~ ~ 1 1 1 1 ~ ~ ~ ~ ~ ~ ~1 THICK SLAB DATA CARD (CARD 2 OF 3)0
IDSLB I ALS ROS
~ 1 ~ 1 0 1 0 1 1 1 1 ~ 1 0 0 ~ ~ 0 ~ 1 0 0 0 0 ~ ~ ~ 0 ~ 0 0 ~ 0 ~ ~ 0 ~ ~ 1 0 ~ 0 ~ ~ 1 0 1 0 1 ~ 1 1 ~ 0 0 ~ ~ 0 1 ~ ~ ~ 1 0 ~ 1 0 1 1 1
THICK SLAB DATA CARD (CARD 3 OF 3)1
IDSLBI HTCI ( I) HTC2( I) HTCI (2) HTC2(2)10010111
CA
ICD
"I CQOCD
(O
4
IDSL8
01014000
0
IOS00100000000
I DTDR-I0000400400
IDTDR-I
2 JRMI JRM2 JTYPE AREAS2
0 0 0 4 0 0 0 4 ~ ~ 0 0 0 0 0 4 4 1 0 4 0 ~ ~ ~ 0 0 ~ 0 0 0 0 0 ~ ~ 0 0 4 ~ ~
THIN SLA8 DATA CARD (CARO 2~ 0 ~ ~ ~ ~ 10 ~ 4440 ~ 0 ~ 004404 ~ ~ ~
OF 2)
UH1 ( I )L82 UHT(2)
0040400RMFLG NPTS TDRTO AMPLT
I 3 0.0 0.04000010040000000 ~ ~ 00 ~ ~ 04044 ~ 040 ~
TIME VERSUS TEMPERATURE DATA
0 FREQ0.0
~ 000 ~ ~ ~ 0 ~ 0440 ~ 00 ~ ~ 400 ~ 004
TTIM0.0
10.020.0
E TTEMP RHUM150. 0.01150. 0. 01150. 0.01
1 4 0 4 0 0 0 4 0 0 0 0 4 1 0 0 0 0 4 0 ~ ~ 0 0 0 0 0 4 0 1 0 00000 ~ 000000040 ~ 04000000400010040
PRESI . D-51. D-51. 0-5000404411 ~ ~ 00 ~ ~ ~ 1 ~ ~ ~ ~ 1 ~ ~ 0~ ~ 0 0 0 4 0 4 1 ~ ~ ~ 0 4 4 ~ ~ ~ 4 0 4 0 4 ~ 0
1 1 1 1 1 1 4 0 4 0 ~ 0 4 1 04 0 0 0 ~ 0 0 0 0 0 4 0 0 0 0
00 ~ 000 ~ 0 ~ 01000 ~ ~ ~ 0I~ ~ ~ 4 ~ 00 ~ 0000 ~ ~ ~ I ~ 1 ~ 4 ~ ~ 4001 ~ ~ 0 ~ 04 ~ ~ ~ ~ ~ 4114 ~ 10440TIME-DEPENDENT ROOM DATA
FIGURE 4.10 COMPARISON OF COTTAP CALCULATED COMPARTMENT AIR MASSWITH ANALYTICALSOLUTION FOR SAMPLE PROBLEM 6
700
CO
I—
I—CL
C)
zV)V)
0
650
600
550
500
450
400
LegendANALYTICAL
0 COTTAP
3500.00 0.05 0.10
TIME (HR)0.15 0.20
PPd L Form 2ddd (15831Cdl. 9973401
SE -B- N A.-O 4 6 R~v.0 ],
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER II1 LIGHT COMPANY ER No.
CALCULATIONSHEET
5 . REFERENCES
1. Gear, C.W., Numerical Initial Values Problem in Ordinar Differential
~Zations, Prentice-Hall, Englewood Cliffs, Hs, 1971, Ch. 11.
2. Pirkle, J.C. Jr., Schiesser, W.E., "DSS/2: A Transportable FORTRAN 77
Code for Systems of Ordinary and One, Two and Three-Dimensional
Partial Differential Equations," 1987 Summer Computer Simulation
Conference, Montreal, July, 1987.
3. Schiesser, W.E., "An Introduction to the Numerical Method of Lines
Integration of Partial Differential Equations," Lehigh University,
Bethlehem, PA, 1977.
4. Lambert, J.D., Com utational Methods in Ordina Differential
~E ations, 1973., Chapter B.
5. Hindmarsh, A.C., "GEAR: Ordinary Differential Equation System
Solver," Lawrence Livermore Laboratory report UCID-30001, Rev.l,
August, 1972.
PPAL Form 245l (10I83)Car, l9D40'r
SF. -B-. » a.-04 b Rev.aq
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER & LIGHTCOMPAN f 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.
ppCL Form itese n0r83)Cat, e973l01
e
SE -B- N A.=O 4 6 Rev.0 1
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,
,editor, CRC Press, Cleveland, Ohio, 1975.
13. Chemical En ineer's Handbook, 5th Edition, R. H. Perry and C. H.
Chilton, editors, McGraw-Hill, New York, 1973.
14. ASME Steam Tables, 5th Edition, The American Society of Mechanical
Engineers, United Engineering Center, New York, N.Y., 1983.
15. McCabe, W. L., Smith, J. C., Unit 0 erations of Chemical Engineering,
3rd Edition, McGraw»Hill, New York, 1976.
16. Lin, C. C., Economos, C., Lehner, J. R., Maise, L. G., and Ng, K. K.,
CONTEMPT4/MOD4 A Multicompartment Containment System Analysis
Program, NUREG/CR-3716, U.S. Nuclear Regulatory Commission,
Washington, D.C., 1984.
17. Fujii, T., and Zmura, H., "Natural convection Heat Transfer from a
Plate with Arbitrary Inclination," Znt. J. Heat Mass Transfer, 15, 755
(1972) .
PP&'L foram 2454 n$ 83)Cat. s91340t
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. /25 of
PENNSYLVANIAPOWER 5 LIGHT COMPANY 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.
ppdL Form 2I54 n0td3)Cd). t973C01 $P -g N A.-04 6 Rev 02.
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. lg6 of
PENNSYLVANIAPOWER 8 LIGHT CQINPANY 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) /Ma a ra'here
P = partial pressure of air (psia),a
p = density of air (ibm/ft ),3a
T compartment temperature ( F),0
(A-1)
and
M = molecular weight of air = 28.8 ibm/lb mole.a
The partial pressure of water vapor, P , is also calculated from thevideal gas equation of state. The total pressure with in the compartment,
P , is then obtained from
r'=P+Pr a v (A-2)
0 )
pp&L Form 2lS4 (10rN)Clt. t973401
$f -B- N A.-04 6 Rev 01
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofpENNSYLVANIAPOWER & 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 byva
and
C =C -R/M (A-3)va pa a
C = constant-pressure specific heat of air (Btu/ibm R),0pa
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 + 1.6309x10 T + 3.9826x10 Tpa r r1.6306x10 Tr
where T is compartment temperature in K.0r
(A-4)
Similarly, the specific heat of water vapor is obtained from (Table D of
ref. 7)
C = 0.4278 + 2.552x10 Tpv Z-7 2 -11 3+ 1.402x10 T - 4.77lx10 T
Z r'' (A-5)
pphL Form 245'043)Cat. 4973401
$F. -B N A.-04 6 Rev.pg
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER 8c LIGHT COMPANY ER No.
CALCULATIONSHEET
where the units of C are Btu/ibm F, and T is compartment temperature0pv r
0in K.
The mixture specific heat is taken as the molar-average value for the air
and water vapor;
(A-6)
where g and III are the mole fractions of air and water vapora v
respectively, and M and M are the molecular weights of air and watera 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.
o
pp&L Form 2454 nN83)Cat. rQU401
SE -g- g A=04 6 Rev.og
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 1II.1.2.1 of ref. 9). These routines
are simplified approximations to the functions given in the ASME 1967
steam tables.
A.S Saturation Tem erature of Water
The saturation temperature of water, as a function of saturation pressure
and saturation enthalpy, is calculated from the RETRAN-02 property
routine (Section ZZI.1.2.2 of ref. 9).
A.6 S ecific Volume of Saturated Water and Va or
The specific volume of saturated liquid and vapor is calculated from the
RETRAN-02 property routines (Section IZI.1.2.3 of ref. 9). The routines
give saturated specific volume as a function of saturation pressure and
enthalpy.
PPAL Form 245'10rLOCot. N973l01
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. LB0 of
PENNSYLVANIAPOWER 8r LIGHT COMPANY ER No.CALCULATIONSHEET
A.7 Coefficient of Thermal Ex ansion for Air/Water-Va or Mixture
The coefficient of thermal expansion, 8, for the air/water-vapor mixture
is defined as
9=1 Bvv BT Pr r
where v = specific volume of air/water-vapor mixture,
(A-7)
and
P = compartment pressure',r
T = compartment temperature ( R).0Z
Evaluation of eq. (A-7) with the assumption of ideal gas behavior for the
air/water-vapor mixture gives
9=1T
Z
(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)
u = (V iri +u P ]/[HM +9M ]1/2 1/2 (A-9)
PP&L Form 245'$ 83)Cal. t973i0r
Sf, -Q-. IS A =04 6 ReV.P g
Dept.
Date 19
Designed by
Approved by
PENNSYLVANIAPOWER 8c LIGHT COMPANYCALCULATIONSHEET
PROJECT
ER No.
Sht. No. ~3 of
where m viscosity of air and water vapor respectivelya'
( ibm/hr-ft),
and
III,ftI = 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 p are determined by fitting straight lines to the data given ina v
Tables A.l and A.2.
temperature are
The equations which give u and p as functions ofa v
p = 0.0413 + (7.958x10 )(T -32),a r (A-10)
and
p = 0.0217 + (4.479xl0 )(T -32),v r (A-11)
where p and p have units of ibm/ft hr and T is compartment temperaturea v r0in F.
PPKL Form 2454 <1182)C41. 4023401,,
ia
$E -8-. N A=04 6 Rev.PZ
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. ~ofPENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATIONSHEET
Table A.l 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.
PP&L Form 24&4 (l(VN)Ctt. t973401
B g <.-04 6 Rev.0g
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. 333 of
PENNSYLVANIAPONER & LIGHTCOMPANY ER No.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)
(A-12)
where k ,k = thermal conductivity of air and water vapora'
respectively,
and
g ,Izi = mole fraction of air and water vapor respectively,a'
M = molecular weight of air (28.8 ibm/lbmole),a
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) ga (z -13)
k = 0.010 + (2.00x10 )(T-32),-a
where k and k have units of Btu/hr ft F and T is in F.0 0
a v
(A-14)
PPE 1 Form 2454 n0/N)Cat. N973401
A
$F. -8 N A=04 6 Rev.01
Dept.
Date 19
DesIgned by
Approved by
PROJECT Sht. No. ~l~ of
PENNSYLVANIAPOWER Sc 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
pp&L Form 24s4 n0/s3)Cat. t973401
$Q -8- N A =04 6 ReV.Qg
Dept.
Date 19
Designed by
Approved by
PROJECT Sht. No. /~~of
PENNSYLVANIAPOWER 8 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.
ATTACHMENT 8
"C,i
C~
,gi
a
~ 4' a h
ae 1