'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

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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

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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

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5 . REFERENCES

APPENDZX A THERMODYNAMZC AND TRANSPORT PROPERTZES OFAZR AND WATER

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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.

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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.

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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

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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),

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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

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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

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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.

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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.

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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,

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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

«

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- 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

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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 , ~

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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)

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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)

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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

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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.

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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

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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

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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) .

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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

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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

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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

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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>

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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

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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

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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

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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

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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

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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

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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)

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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

~ )

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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

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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

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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

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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

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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

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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

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-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

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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

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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

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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

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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>

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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

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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

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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

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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 ]

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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

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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

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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

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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~

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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>

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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

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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>

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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

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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).


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

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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

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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

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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

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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


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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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= 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):

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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

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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

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Approved by


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

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Approved by



W2-I ZBRM = ID number of room in which pipe break occurs.

W3-R BFLPR = Fluid pressure within pipe (psia).

W4-I ZBFLG Fluid State flag.= 1 ~> fluid in pipe is steam

= 2 => fluid in pipe is licpxid water

W5-R BDOT = Total mass flow exiting the break (1bm/hr) .

W6-R TRZPON Time at which break occurs (hr).

W7-R TRZPOF = Time at which break flow is turned off (hr).

W8-R RAMP ~ Time period (hr) over which the break develops. The

total mass exiting the break increases linearly from a

value of zero at tMRZPON to a value of BDOT at

t-ZRIPON+RAMP.

3.21 Thick Slab Data (card 1 of 3)

Omit this card(s) if NSLB1 0.

PPAt. Fotm 2454 (tDt83)Cat. tt97340 I

SE -8- N A -0 4 6 Rev.0 >t

Dept.

Date 19

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Approved by


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


I


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


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

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PROJECT Sht. No. ~ oi


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


= 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



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


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

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= 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

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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


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

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Date 19

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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

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Approved by



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 ~


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 ~


~ 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


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



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 ~


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


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 ~ ~


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


~ ~ 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


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 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


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


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


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


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


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


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


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


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


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



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


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


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 ~


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 ~


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


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


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


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 ~


~ 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


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


~ 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


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 ~


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 ~


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

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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

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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

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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) .

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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.

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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 )

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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)

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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

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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.

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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)

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ER No.

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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

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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.

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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)

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Table A.3 Thermal Conductivity of Air

Thermal Conductivity of Air(Btu/hr ft F)

Temperature( F)

0.0140

0.0184

32

212

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Table A.4 Thermal Conductivity of Water Vapor*

Thermal Conductivity of Water Vapor(Btu/hr ft F)

Temperature( F)

0.010

0.0136

32

212

*Values from Appendix 12 of ref. 15 and p. 296 of ref. 14.

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