'COTTAP-2,Rev 1 Theory & Input Description Manual.' · in buildings where compartments are...

COTTAP-2, REV. 1

THEORY AND INPUT DESCRIPTION MANUAL

Prepared by:

H. A. Chaiko

aIld

H. J. murphy

NOVEMBER 5, 1990

9203230299 920313PDR ADOCK 05000387P PDR

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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 Specihl Purpose Models 24

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

I2.2 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

APPENDIX A THERMODYNAMIC AND TRANSPORT PROPERTIES OFAIR AND WATER

122

126

1

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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 1

and Unit 2 secondary containments consists of approximately 120

compartments and 800 slabs. Tn addition to the large size of the problem,

the temperature behavior is to be simulated over a long period of time,

typically one hundred days. It is therefore necessary to develop a code

that can not only handle a large volume of data, but can also perform the

required calculations with a reasonable amount of computer time.

Xn addition to large scale problems COTTAP is capable of modeling room

heatup due to breaks in hot piping and cooldown due to condensation and

rainout. Zt also contains a natural circulation model to simulate

inter-compartment flow.

The purpose of this calculation is to demonstrate the validity of thiscomputer 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 the

mass-tracking parameter MASSTR (see problem description'data cards in

section 3.2) .

2.1.1.1 Balance Equations without Mass Transfer between Com artments

If MASSTR=O, the compartment mass balance equations are neglected and the

total mass in each compartment is held constant throughout the

calculation. This option can be used if there is no air flow between

compartments or if air flow is due to ventilation flow only (i.e., there

are no leakage or circulation flow paths) . In COTTAP, ventilation flow

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rates are held constant at their initial values'hus, if the net flow out

of each compartment is zero initially, then there is no need for a

compartment mass balance because the mass of air in each compartment

remains constant.

In this mode of calculation, the moisture content of the air (as specified

by the value of compartment relative humidity on the room data cards, see

section 3.32 ) is only used to calculate the film heat transfer

coefficients for thick slabsr the effect of moisture content on the heat

capacity and density of air is neglected. The compartment energy balance

used in COTTAP for the case of MASSTR=O is

PC VdTQ.+0 +0+Qa va —r light Qpanel Qmotor cooler Qwall Qmisc pipingdt

N+ P W . (T . +a) C (T .)

j=l vj vj o pa vj

where T compartment (room) temperature ( F),0rt time (hr),

p ~ density of air within compartment (ibm/ft ),3a

C ~ constant-volume specific heat of air (Btu/ibm F),0va

V ~ compartment volume (ft ),3

Q1 h compartment 1 ighting heat 1cad (Btu/hr)lightQ ~ compartment electrical panel heat load (Btu/hr),panel

= compartment motor heat load (Btu/hr),otor

(2-1)

OI'l

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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 compartmentair (Btu/hr),

MscNv

miscellaneous compartment heat loads (Btu/hr),

number of ventilation flow paths connected to thecompartment,

WVjTVj

C (T .)pa vj

ventilation flow rate for path j (ibm/hr),

air temperature for ventilation path j ( F),0

specific heat of air evaluated at T . (Btu/ibm F),0Vj

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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temperature. Coolant temperature is input for each cooler and remains

constant throughout the transient. See section 2.1.3.5 for a detailed

description of this calculation.

The initial compartment piping heat loads and overall heat transfer

coefficients are calculated by COTTAP based on piping and compartment

input data. Overall heat transfer coefficients for hot piping are held

constant throughout the transient and heat loads are calculated based on

temperature differences between pipes and surrounding air. No credit is

taken for compartment heat rejection to a pipe when compartment

tempe'rature exceeds pipe temperature. When this situation occurs, the

piping heat load is set to zero and remains there unless compartment

temperature decreases below pipe temperature. Xf this should occur a

positive piping heat, load would be computed in the usual manner. Piping

heat loads as well as room cooler loads may be tripped on, off, or

exponentially decayed. See Section 2.1.3.6 for a detailed description of

the piping heat load calculation.

The rate of heat transfer from walls to compartment air is calculated from

Nh.A.(T . - T ),w

wall . 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 'I

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and

A. = surface area of wall (ft ),2j

T f. = wall surface temperature ( F) .0

surfj

Use of MASSTR=O is only valid for the case where compartment temperatures

undergo small or moderate variations. For these situations, maintaining

constant mass inventory in each compartment is a fairly good approximation

since density changes are small. If large temperature changes occur,

compartment mass inventories will undergo significant fluctuations inorder to maintain constant pressure. In this situation a model which

accounts for mass exchange between compartments is required. Use of

MASSTR=O, where applicable, is highly desirable especially for problems

with many compartments and slabs because large savings in computation time

can be realized. The more general case of MASSTR=1 is described below.

2.1.1.2 Balance E ations with Mass Transfer Between Com artments

When the mass-tracking option of COTTAP is selected (MASSTR=1), special

purpose models are available for describing air and water-vapor leakage

between compartments, circulation flows between compartments, and the

effect of pipe breaks upon compartment temperature and relative humidity.

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Temperature changes within compartments generally occur at essentially

constant pressure because leakage paths such as doorways and ventilation

ducts allow mass transfer from one compartment to another. The leakage

path model in COTTAP allows sufficient mass transfer between two

compartments so that pressure equalization is maintained during a

transient. The leakage path model is discussed in section 2.1.3.2.

The circulation path model allows for mixing between two adjacent

compartments which are connected by flow paths at different elevations.

The driving force for. the circulation flow is the difference in airdensity between the two compartments. Further discussion of this model is

given in section 2.1.3.8.

The pipe break model in COTTAP accounts for leakage from a steam pipe or a

pipe containing saturated liquid water. The total mass flow out of the

break must be specified as input. Xn the case of a pipe containing

liquid, the amount of liquid that flashes to steam is calculated by the

code. As a conservative approximation, any liquid that does not flash to

steam is cooled to compartment temperature and the heat given off by the

liquid is deposited directly into the air/water-vapor mixture. COTTAP

allows for condensation of steam on compartment walls and for vapor

rainout. Details of this model are given in sections 2.1.3.1, 2.1.3.3,

and 2.1.3.4.

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The air and vapor mass balance equations that are solved by COTTAP for the

case of MASSTR=1 are

NVQP =E W Y

dt 3=1

Nl+ E W . Y

3 3

N+ E [W .. Y .. -W . Y . ],

j=l cj,in cj,in cj,out cj,out (2-3)

NVdP = E W . (1Y .)

dt 1vj vj

N+ E W . (1 Y .)lj lj

N+ E [W .. (1-Y .. ) -W . (1-Y . )J

3=1 cj,in cj,in cj,out cj,out

+W -W -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 . i total inlet mass flow through circulationcj,in

Wcg,out

path j (ibm/hr),

m total outlet mass flow through circulation

path j (ibm/hr),

Y . ~ air mass fraction for ventilation path j,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,

W steam flow rate from pipe break (ibm/hr),bs

W ~ water vapor condensation rate (ibm/hr),cond

W ~ water vapor rainout rate (ibm/hr).ro

The compartment energy balance for MASSTR~l is

V[(T +a )p dC (T ) + p C (T ) + p dh (T )r o atda r a pa r v~ 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- V h (T )dp + (T +a ) (R dp + R dp )Vv r~ r o v~d a —adt

+Q . +Q +O +Q + Qlight panel motor cooler piping+0 +0. +Q +W hQwall Qmisc break bs v,break- W h (T ) - W h (T )ro f r cond f r

N+ g W .[Y .(T .+a )C (T .) + (1-Y .)h (T .)]

j=l vj vj rj o pa vj Vj V Vj

N

+QW1[Y1(T1+a)C(T1)+(1Y1)h(T1)]j=l lj lj 1 j o pa 1 j lj v ljN

+g W.. [Y.. (T..+a)C (T..)j=l cj,in cj,in cj,in o pa cj,in

+ (1-Y .. )h (T . )]cj,in v cj,inN

W . [Y . (T+a)C (T)cj,out cj,out r o pa rj=l+(1-Y . )h (T )]«cg «out v 7 (2-5)

where hvhv,break

PrP

P

saturated water vapor enthalpy (Btu/ibm),

enthalpy of steam exiting break (Btu/ibm)

= h (P ) if pipe contains liquid,v r= h (P ) if pipe contains steam,V P

compartment pressure (psia),

pressure of fluid within pipe (psia),

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R = ideal gas constant for steam (0.1104 Btu/ibm R)0

v

R ~ ideal gas constant for air (0.0690 Btu/ibm R),0a

Qb k heat transferred to air and water vapor frombreakliquid exiting break as it cools to compartment

temperature (Btu/hr),

W = steam flow rate exiting pipe break (ibm/hr),bs

h = saturation enthalpy of liquid water (Btu/ibm).f

All other variables in (2-5) are as previously defined. The basic

assumption used in deriving (2-5) is that the air and water vapor behave

as ideal gases. This is a reasonable assumption as long as compartment

pressures are close to atmospheric pressure which should nearly always be

the case.

2.1. 2 Slab Heat Trans fer E ations

The slab model in COTTAP describes the transient behavior of relatively

thick slabs which have a significant thermal capacitance. For each thick I

slab, the one-dimensional unsteady heat conduction equation is solved toI

I

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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 sax2 2

s s (2-6)

subject to the following boundary and initial conditions:

8T3X

XaaO

t)T3X X~L

= — h [T (t) - T (oit)] I—1 r1 sk

- h [T (Lit) - T (t)] I—2 sk 12

(2-7)

(2-8)

where

T (xo) ax+ b,s (2-9)

T (xit) = slab temperature ( F)i0s

t ~ time (hr),

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x m spatial coordinate (ft),thermal diffusivity of slab = k/(p C ) (ft /hr),2

s psthermal conductivity (Btu/hr ft F),

P s

Cps

h

slab density (ibm/ft ),3

specific heat of slab material (Btu/ibm F),

film coefficient for heat transfer between thy slaband the room on side 1 of the slab (Btu/hr ft F),

h film coefficient for heat transfer between thy slaband the room on side 2 of the slab (Btu/hr ft F),

T (t) Temperature of room on side 1 of slab ( F),

andT 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 (oat) T (t) J «1 s 'l (2-10)

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ql (t) ~q tt)

Room on side 1 of slabat temperature T.l(t)rl

SlabTemp f

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)], (2-11)

where A is the surface area of one side of the slab.

A slab can also be in contact with outside ground. Calculation of the

heat loss from a slab to outside ground would involve modeling of

multi-dimensional unsteady conduction which would greatly complicate the

analysis. As a simplifying approximation, heat transfer from below grade

slabs to the outside ground is neglected by setting the film coefficient

equal to zero at the outer surface of every slab in contact with the

outside ground. This is a conservative approximation in the sense that

the heat loss from the building will be underpredicted giving rise to

slightly higher than actual room temperatures. The governing equations

for a below grade slab with side 2 in contact with ground are (2-6)

through (2-9) but with h set equal to zero. Zf side 1 of the slab is in2

contact with ground then h 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 constantr

throughout the entire calculation. Natural-convection film coefficients

are, however, temperature dependent, and values representative of the

average conditions during the transient should be used.

Suggested values of natural convection film coefficients for interior

walls and forced convection coefficients for walls in contact with outside

air are given in ref. 11, p. 23.3r note that the radiative heat transfer

component is already included in these coefficients.

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Correlations are also available in COTTAP for calculation of natural

convection film coefficients. Coefficients for vertical slabs are

calculated from (ref. 8 p.442)

h = kclC

0.825 + 0.387 Ra

[1+(0.492/Pr)9/16)8/27(2-12)

where h = natural convection film coefficient for verticalclslab (Btu/hr ft F),2 0

k = thermal conductivity of air (Btu/hr ft F), raJ

C = characteristic length of slab (slab height in ft).

The Rayleigh and Prantl numbers are given by

Ra g8(3600) (T f-T )CL/(jjn)2 3

(2-13)

Pr aa IjC /k,P

(2-14)

where g ~ acceleration due to gravity (32.2 ft/sec ),2

o -18 ~ coefficient of thermal exp'ansion for air ( R ),v = kinematic viscosity of air (ft /hr),2

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u ~ thermal diffusivity of air (ft /hr),2

p viscosity of air (ibm/hr-ft) .

Air properties are evaluated at the thermal boundary layer temperature

which is taken as the average of the slab surface temperature and the bulk

air temperature of the compartment. The moisture content of the air 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 Ra '/5c2

L

(2-15)

and for the case of upward heat flow the correlations are (ref. 8, p.445)

h ~ 0 54 k Ra1/4

c3L

(Ra<10 )7 (2-16)

h ~015k Ra1/3

c3L

(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 the

radiation coefficient:

h ~ (c +1) (4+a+b-c) e oTa<n 3

s w,av av2

(2-18)

where a

Tav

Stetan-Boltzman constant (0.1712x10 Btu/hr ft R ),([(T +a ) +(T +a ) J/23 ( R)

4 4 1/4 o

compartment air temperature ( F),0

T = slab surface temperature ( F),0surf

es

e w,av

~ slab emissivity

~ water vapor emissivity evaluated at Tav

a = 459.67 F.0

Only the water vapor contribution to the air emissivity is included inecgxation (2-18) because gases such as N and 0 are transparent to therma2 2

ppht. Form 2454 t 10/83)Cat. rr973401

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radiation (ref. 11, p.3.11), and the effect due to CO is negligible2

because of its small concentration (0.03tit by volume, ref. 12, p.F-206) .

The emissivity of water vapor is a function of the partial pressure 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 approximation

to the emissivity charts of Hottel and Egbert (ref. 22), are used tocompute the water vapor emissivity. These euqations are given by

e (T,P,P,P L ) = A (1-exp(-A X ) ]1/2

w ''' m o 1 (2-19)

X(TgP gP gP L ) P L] 300%a'' m w m L T 3

P + [5(300/T) + 0.5] 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 for0 1 I

purposes of this work, they are represented by the following polynomial

expressions:

Ppkl Form 2454 n0/83)Cat. t9r3co>

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and

A (T) ~ 0.6918 — 2.898x10 T — 1.133x10 T0 (2-21)

A (T) = 1.0914 + 1.432xl0 T + 3.964x10 T (2-22)

where 273K < T < 600K. Tabular values of A and A over the widero 1

temperature range 300K < T < 1500K are available (ref. 21). Zn equation

(2-18), c has the value 0.45, and a and C are defined by

n ging (TgP gP gP L )]a w ''' mBln(P L )

w m

(2-23)

and

b = Bin[a (T,P ,P ,P L )]w ''' m3ln (T)

(2-24)

Values of a and b are obtained through differentiation of the Cess-Lian

equations. The average mean beam length L for a compartment ism

calculated from

L = 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.

PPAL Form 2l54 na/83)Ca~. sermon

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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 0)/dx 0,2 2

s (2-26)

dT (x,0)dx

-h [T (0) - T (0,0) ],kl rl s (2-27)

and

dT (x,o)dx

—2 s r2-h [T (L,O) — T (0) ] .

x=L(2-28)

The solution is

where

T (xO) =ax+b,s (2-29)

h2 [T 2(0) - T 1( )]k+hL+kh/h

(2-30)

b~T (0) +kh [T (0) - T (0)].r1 2 r2 rlh [k+hL+kh/h]

(2-31)

Equation (2-29) is an implicit relation for the temperature profilebecause of the temperature dependence of the film coefficients. An

iterative solution of eq. (2-29) is carried out in COTTAP.

PP8 L Form 2454 {1N83)Gal. N97340i

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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) . If the pipe

contains water, the following energy balance is solved simultaneously

with the continuity equation to determine the flowrate of steam exiting

the break:

W h (P ) =W h (P ) + [W -W ]h (P ),bt f p bs v r bt bs f r (2-32)

where Wb ~ total mass flow existing the break (ibm/sec.),

W = steam flow exiting break (ibm/sec.),bs

h = enthalpy of saturated liquid (Btu/ibm),fh ~ enthalpy of saturated vapor (Btu/ibm),vP ~ fluid pressure within pipe (psia) g

P

P ~ compartment pressure (psia) .r

As a conservative approximation, the liquid exiting the break is cooled to

room temperature and the sensible heat given off is deposited in the

ppAL Form 2lsl (ro/83)Cat, rr913401

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compartment air space. This heat source is represented by the term,

Q, in eq. (2-5) and is calculated frombreak'

(~ ~ ) (h (P ) h (T )] ~ (2-33)

where T is the compartment temperature.r

The total mass flow out the break and the pipe fluid pressure are

specified as input to the code.

I

In the case where the pipe contains high-pressure steam, all of the mass0

and energy exiting the break is deposited directly into the air space of

the compartment. This is a reasonable approximation for steam line

pressures of interest in boiling water reactors.

2.1.3.2 Com artment Leaka e Model

Inter-compartment leakage paths such as doorways and ventilation ducts can

be modeled using the leakage path model in COTTAP. Leakage paths are

specified on leakage path data cards (Section 3.14) by inputting the

leakage path ID number, flow area, pressure loss coefficient, TD numbers

of rooms connected by the leakage path, and the allowed directions for

pphL Form 2454 n0/83)Cot. rr973l01 SE -B- N A-0 4 6 Rev.0 >

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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 proportional

control model:

W = C (A /A ) DP1 pl 1 max (2-34)

where W = leakage flow rate (ibm/hr),

cplA

1

proportionality constant (ibm-in /hr-lb ),2

leakage path flow area (ft ),2

A = max flow area for all leakage paths (ft ),2

hP = pressure differential between compartments (psia) .

The constant C1

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 to

compartment heat up.

ppbL Form 2a5w (IO/83)Cat. e97%0>

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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. In this case the leakage rate is computed

by balancing the intercompartment pressure differential with an

irreversible pressure loss:

1 1 I 1 I (3600) = hP i

2g Pl 1 144)2

(2-35)

where Kl = loss coefficient for leakage path (based on Al),2

A = leakage area (ft ),1

W = leakage flow rate (ibm/hr),1

p = density within compartment which is the source of the leakage1

flow (ibm/ft ),3

hp = pressure difference between compartments associated with

leakage path (psia) .

A maximum leakage flow rate for each path is calculated from

N =pmin (V,V) C1 t lIlax 1' p2'2-36)

ppAL Form 2454 n0/83)car. rr973lo1

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where V and V are the volumes (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 (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.

PPdL Form 2454 (f0/83)Gal. a973401

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In order to avoid numerical instabilities caused by rapid fluctuation

between natural convection and condensation heat transfer modes, the

condensation coefficient is linearly increased to its full value over a 2

minute period. Similarly, the condensation coefficient. is decreased over

a' minute period if condensation is switched off. Modulating the

transitions between the two heat transfer modes allows use of much larger

time steps than would otherwise be possible. The condensation heat

transfer coefficient is calculated from the experimentally determined

Uchida correlation which includes the diffusional resistance effect of

non-condensible gases on the steam condensation rate (ref. 16 p. 65, ref.

20) .

Values of the Uchida heat transfer coefficient, as a function of the

compartment air/steam mass ratio, are given in Table 2.3. COTTAP uses

linear interpolation to obtain the condensation coefficient at the desired

conditions.

PPlLL Form 2L54 (10/83)CS1, 11973401 SE -B- N A-0 4 6 Rev:0 1

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Table 2.3 Uchida Heat Tranfer Coefficient*

Mass Ratio(Air/Steam)

Heat Transfer Coefficient(Btu/hr«ft - F)

(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 2454 (1883)Cat. N91~(

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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. In

addition, radiation heat transfer between the vapor and walls also occurs

during condensation. Under conditions where condensation occurs, the rate

of heat transfer to a wall is calculated from

a =-h A (T — T )u w r surf (2-38)

where

q .= rate of heat transfer to the wall (Btu/hr),

h = Uchida heat transfer coefficient (Btu/hr-ft - F),2 0

A = wall surface area (ft ),2w

T compartment air temperature ( F),0r

T = wall surface .temperature ( F).0surf

pp&L Form 24&i n0/83)Cat, %73401

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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 ,cr'Btu/hr-ft —F),2 0

h = natural convection coefficient (Btu/hr-ft - F),2 0c

h = thermal radiation coefficient (Btu/hr-ft - F).2 0r

Ecyxation (2-39) accounts for the fact that during condensation a

significant fraction of the total heat transfer rate to the slab surface

is in the form of sensible heat. In computing the sensible heat fraction,

it is assumed that the condensate temperature is approximately ecgxal to

the slab surface temperature, i.e., the major resistance to condensation

heat transfer is associated with the diffusion layer rather than the

condensate film.

pphL Form 2454 na/83)Car. eonei

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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%. It is activated

when the relative humidity reaches 99%. The rain out of vapor is

calculated from

and

W = (200.0 RH — 198.0) max(W ., C ) (RH > 0.99),ro vap,in'l (2-40)

W = 0.0ro (RH < 0.99), (2-41)

where

W = rate of vapor rainout (ibm/hr),roC = user specified constant (see section 3.2),r'1

W . = net vapor mass flow into the compartment (ibm/hr),vap,in

RH = relative humidity.

PP8 1. Form 245'10I83)C4t rr973401

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2.1.3.5 Room Cooler Model

The room cooler load is assumed to be proportional to the difference

between compartment ambient temperature and the average coolant

temperature. Zt is calculated as follows:

=C(T -T),Qcool c,avg r (2-42)

where Q = cooler load (Btu/hr),coolo

C = Q ... / (T ... - T ... ),Btu/hr F,cool initial c,avg initial r initial0

T = average coolant temperature ( F),c,avg= (T . +T )/2c,in c,out

and

oT = compartment temperature ( F).r

The inlet cooling water temperature, T . , is supplied as input, and thec,in'utlet

cooling water temperature, T , is calculated from the coolingcgout

water energy balance,

where

Q =C(T — T) =W C (T - T )gcool c,avg r cool pw c,in . c,out (2-43)

W = cooling water flow rate (ibm/hr),cool

PPd t. Form 2454 (10/83)Cat. 4973401

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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 in Model

In COTTAP, the entire piping heat load is deposited directly into the

surrounding air. This is a conservative modeling approach because in

reality a substantial amount of the heat given off by the piping is

transferred directly to the walls of the compartment by radiative means.

If film coefficients accounting for radiative heat transfer between

compartment air and walls are used in compartments containing large piping

heat loads some of this conservatism may be removed.

The piping heat load term in Equations (2-1) and (2-5) is calculated from

Q, . r= U'OLD (T - T ),piping f r (2-45)

PPE L Form 2454 (10/83)car. rr973l01

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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),0f

T = Compartment temperature ( F).0r

COTTAP calculates U based on initial conditions and holds the value

constant throughout the transient. Calculation of U for insulated and

uninsulated pipes is considered separately. In both cases, however, the

thermal resistance of the fluid and the metal is neglected. For insulated

pipes, the overall heat transfer coefficient is calculated from

D. ln (Di/D ) + 1

2k. H +Hi c r

(2-46)

where D. = Insulation outside diameter (ft),iD = Pipe outside diameter (ft),

P0k. ~ Insulation thermal conductivity (Btu/hr ft F),i

2 0H = Convective heat transfer coefficient (Btu/hr ft F),c

H ~ Radiation heat transfer coefficient (Btu/hr ft F).2 0r

PP8 L Form 2454 (lor83)Cat. rr973a01

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For uninsulated pipes,

U = H + Hc r (2-47)

The convective heat transfer coefficient, H , is calculated from thec

following correlation for a horizontal cylinder (ref. 8, p. 447):

c air 0 0.60 + 0.387 Ra9/16 8/27

[1+(0.559/Pr) )

(2-48)

where k . = thermal conductivity of air (Btu/hr-ft- F),oair

D = pipe outside diameter for uninsulated pipes (ft),0

= Insulation outside diameter for insulated pipes (ft),Ra = Rayleigh number,

and

Pr = Prandtl number.

In (2-48), the air thermal conductivity, Rayleigh member, and Prandtl

number are all evaluated at the film temperature which is the average of

the surface temperature and the bulk air temperature (ref. 8, p. 441) .

H is calculated from (ref. 10, pp. 77-78)Z

H CG(T - T )/(T -T )4 4

r r surf r s(2-49)

where E pipe surface emissivity,

ppa,L Form 2454 nOI92)ca1. «912401

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and

-8 2o40 = Stephan Boltzman constant (0.1712x10 Btu/hr-ft — R ),

0T = compartment ambient temperature ( R),r

T = pipe surface temperature ( R) for uninsulated pipes0surf

0m insulation surface temperature ( R) for insulated pipes.

The Rayleigh number is given by:

R = (3600) g (T -T )D2 3

a surf r oVG

(2-50)

where g = 32.2 ft/sec 2

g m volumetric thermal expansion coefficient (1/ R),2kinematic viscosity (ft /hr),

a

Tsurf

thermal diffusivity (ft /hr),24

0pipe surface temperature ( F) for uninsulated pipe,0insulation surface temperature ( F) for insulated pipe,

0T = compartment ambient temperature ( F),r

D m pipe outside diameter (ft) for uninsulated pipe,0

= insulation outside diameter (ft) for insulated pipe.

The Prandtl number is calculated from

Pr = C 4/k,P

(2-51)

pal Form 2454 n0/83>Car. s973401

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where C = specific heat (Btu/ibm F),0pll = viscosity (ibm/ft hr),

k = thermal conductivity (Btu/hr ft F) .0

2.1.3.7 Com onent Cool-Down Model

In COTTAP, the cooling down process of a component such as a pipe 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 ) = 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.

pp8.L Form, 245'ols3)Car. II9r24O1 Sf -B- Z A =0 4 6 Rev.O 1

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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 )1 = -UA[T(t)-T (t )l.UA dt

(2-54)

Rewriting (2-45) in terms of the heat loss from the component, Q, gives

~d= -Q(t),

dt(2-55)

where Y is the thermal time constant of the component and is given by

Y = pC V/UA.P

The solution to (2-46) is

Q(t) = Q(t ) exp[-(t»t )/Y].0 o

(2-56)

(2-57)

The approximation given by (2-48) is used in COTTAP when a heat load is

tripped off with an exponential decay at time, t0

The time constant, Y, for a component can be specified on the heat load

trip cards (see section 3.19), or in the case of hot piping, the time

constant may be calculated by the code. For pipes filled with liquid, th i

ppaL Form 2454 n0/831Cat. rr970l01

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volume average density and the mass average specific heat of the liquid

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

TroM

m

total internal energy of the fluid (Btu),

the initial fluid temperature ( F),0the initial room temperature ( F),

mass of metal (ibm),

M m mass of fluid (ibm),f

C = specific heat of the metal (Btu/ibm F).0PIll

2.1.3.8 Natural Circulation Model

The natural circulation model in COTTAP can be used to described mixing of

air between two compartments which are connected by flow paths at

different elevations. The rate of air circulation between compartments is

calculated by balancing the pressure differential, due to the difference

in air density between compartments, against local pressure losses within

the circulation path;

ppct. Form 2459 notmtGal, 9973401

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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 circulationa1 a2

path (P2

P 1), ibm/ft3

E ,E elevations of lower and upper flow paths respectively (ft),1'

K ,K = pressure-loss coefficients for lower and upper flow paths1'

respectively,

A ,A ~ flow areas of lower and upper flow paths respectively1'

(ft ),and

g = acceleration due to gravity (32.2 ft/sec ).2

A leakage path (see Section 2.1.3.2) is included in the circulation path

model in order to maintain the same pressure in both compartments. Thus,

the flow rate calculated from eq. (2-59) is adjusted to account for this

leakage.

PPaf. Form 2«5« <for83fCaf. «9ncaf

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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.

In this model, transient environmental conditions are supplied as input

data. The data is supplied in tabular form by entering up to 500 data

points for each time-dependent room, with each data point consisting of a

value of time, room temperature, relative humidity, and pressure.

A method is also available in COTTAP to describe periodic (sinusoidal)

temperature variations within a room. In using this option, the amplitude

and frequency of the temperature oscillation and the initial room

temperature are supplied in place of a data table.

2.1.3.10 Thin Slab Model

It is not necessary to use the detailed slab model discussed in section

2.1.2 to describe heat flow through thin slabs with little thermal

capacitance. Slabs of this type have nearly linear temperature profiles,

and thus, the heat flow through the slab can be calculated by using an

overall heat transfer coefficient. The rate of heat transfer through a

thin slab is obtained from

PAL Form 295'IO/83>Cat, 997340 l

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CALCULATIONSHEET

= UAtT (t) — T (t) i I (2-60)

where q = rate of heat transfer from the room on side 1 of the slab to12

the room on side 2 (Btu/hr),

U ~ overall heat transfer coefficient for the thin slab

(Btu/hr ft F),20

A = heat transfer area of one side of the thin slab (ft ).2

Overall heat transfer coefficient data is input to COTTAP for each of the

thin slabs and the values are held constant throughout the calculation.

For thin slabs that model floors or ceilings, two values of U must be

supplied; one for upward heat flow and the other for downward heat flow.

For thin slabs that are vertical walls only one value of U can be IIsupplied. Up to 1200 thin slabs can be modeled with COTTAP.

2.2 Numerical Solution Methods

The governing equations to be solved consist of 3N + Nt ordinarysr tdrdifferential equations and N partial differential equations, where N is

s sr

the number of standard rooms, N d is the number of time-dependent rooms,tdr

ppdl Form 2c5c n0r83>Cat, rr973401

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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 airtemperature, air mass, and vapor mass. In addition, the one-dimensional

heat conduction equation is solved for each of the thick slabs. Ordinary

differential equations are also generated for the time-dependent rooms;

these equations are used only for time step control and will be discussed

later in this section.

The initial value ordinary differential equation solver, LSODES (Livermore

Solver for Ordinary Differential Equations with General Sparse Jacobian

Matrices), developed by A.C. Hindmarsh and A.H. Sherman is used within

COTTAP to solve the differential equations which describe the problem.

LSODES is a variable-time-step solver with automatic error control. This

solver is contained within'he DSS/2 software package which was purchased

from Lehigh University (ref. 2).

Before LSODES can be applied to the solution of the governing equations in

COTTAP, the N partial differential equations describing heat flow throughs

thick slabs must be replaced with a set of ordinary differentialequations. This is accomplished through application of the Numerical

Method of Lines (NMOL) (ref. 3) . In the NMOL, a finite differenceI

approximation is applied only to the spatial derivative in equation (2-6),

PP3l Form 2«5«(lOI83)C«t, «973«01 SE -B- N A -0 4 6 Rex'.0 ]

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thus approximating the partial differential equation with N coupled

ordinary differential equations of the form

dT . = T ., i=1,2«...)N,~i SXX3.(2-61)

where N is the number of equally spaced grid points within the slab, TSi

is the temperature at grid point i, and T . is the finite-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 subroutinesxxiDSS044 which was written by W.E. Schiesser. This subroutine is also

contained within the DSS/2 software package. For the interior grid points

a fourth-order central difference formula is used to compute TSXX1

T . ~ 1 f- T . +16T . -30T . +16T . — T . ]SXXi —2 Si-2

126si-1 Si si+1 si+2

+O(~ )« (2-62)

where i m 3,4,...,N-2, and b is the spacing between grid points. A

six-point slopping difference formula is used to approximate T . at iSXX3.

equal to 2 and N-lr

!IIli

ppdt. Form 245a n0/83|Gal. a97340)

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T = 1 [10 T — 15 T - 4 T + 14 T — 6 T + T ]sxx2 —2 sl s2 s3 s4 s5 s6

+ 0(~ )a (2-63)

and

T 1 [10 T — 15 T — 4 T + 14 T - 6 T + T ]sxxN-1 —2125 sN sN-1 sN-2 sN-3 sN-4 sN-5

+ o(h ). (2-64)

The finite difference approximations at the end points are formulated in

terms of the spatial derivative of the slab temperature at the boundaries

rather than the temperature, in order to incorporate the convective

boundary conditions (2-7) and (2-8) . The formulas are '

= 1 [-415 T + 96 T — 36 T + 32 Tsxxl —2 ~ —s1126 6s2 s3 — s4

3

4-35

- 508T ] +O(b ),2

(2-65)

and

T ~ 1 [-415 T + 96 T — 36 T + 32 TsxxN —2 —sN126 6sN-1 sN-2 — sN-3

3

4-3T 4+508 T]+O(h),2

(2-66)

where T and T are given bysx1 sxN

T -h [T (t) — T (t) ]k

(2-67)

PP&1. Form 24&i u0,'831Car. e 973401

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and

T = -h [T (t) — T (t)) ~

k(2-68)

The total number of ordinary differential equationsg N r to be solved isI qlnow given by

NN =3N +N + N

seq sr tdr .~

gj'=l

(2-69)

where N . is the number of grid points for slab j. Note that at least sixgj

grid points must be specified for each slab.

Zt was previously mentioned that equations are generated for each

time-dependent room and are used for purposes of influencing the automatic

time step control of LSODES. The equation generated for each time

dependent room is

dT = g(t),dt

(2-70)

where T is the time-dependent room temperature and g(t) is the 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 temperatureIr

PP2 L Form 2454 (10/83>Cat. 4973401

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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

1yn = Z yn 3j=1

"2S. F

0 3 73(2-71)

where h is the step size, and the constants a.,'nd 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 ~

0(2-73)

PPbL Form 24ba n0'M)CaL a97bao>

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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

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 9 is non-zero.0

I

Since 8 go, the finite-difference equations comprise an implicit algebraic0I

system for the solution y . In LSODES, the difference equations are

n'olved

by either functional iteration or by a variation of Newton's

method. If the functional iteration procedure is chosen, an explicit

method is used to estimate a value of y ; the predicted value is then

n'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. MF=10 corresponds to Adam'

method with functional iteration, and MF=20 corresponds'to Gear's methodil

with functional iteration.

Unfortunately, the functional iteration scheme generally requires small

time steps in order to converge. The method can, however, be useful for

rapid transients of short duration'.

The time step limitations associated with the functional iteration

procedure can be overcome, at least to some degree, by using Newton's

pp2,L Form 2454 n0r83)Car. s92340l

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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

~[s+1] ~ [s] h g~ t ~ [s]

WB

k— Ea. 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-h8 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-h8 BF/By] is carried out only when convergence of the finite difference0

equations becomes slow. This technique is called chord iteration (ref. 5)I

ppd r. Form 2454 r10/83)Car. rr97340r

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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 2454 n0/83)Cat, «en<0>

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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.

PPCL Form 2«54 nor82)Cat. «913«01

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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).

ppbL Farm 2s5c nar83>Car. %73401

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WS-I NPZPE = Number of hot pipes (maximum value is 750).

W9-I NBRK = Number of pipe breaks (maximum is 20).

W10-Z NLEAK = Number of leakage paths (maximum is 500) .

Wll-I NCZRC = Number of circulation paths (maximum value is 500).

W12-I NEC = Number of edit control cards. (At least one card must be

supplied, and a maximum of 10 cards may be supplied) .

3.2 Problem Descri tion Data (Card 2 of 3)

Wl-I NFTRZP = Number of flow trips (maximum value is 300). Flow 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 solved; the total mass in each

compartment is held constant. In cases where thisoption can be used, it results in large savings in

p p6 4 Form 2454 (10r83)Gal. 0973401

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computer time. Zn order to use this option, the

following input variables must be specified as:

NBRK=NLEAK=NCZRC=NFTRZP=O

~1~> Mass tracking is on; mass balances are solved for

each compartment.

W3-Z MF ~ Numerical solution flag. MF=222 should only be used ifMASSTR 0. Zf MASSTR 1, the recommended methods are MF=13

and MF=23. MF=10 and MF=20 use functional iteration

methods to solve the finite difference equations and

generally require smaller time steps arid larger

computation times than MF~13 and MF=23.

=10~> Zmplicit Adam's method. Difference equations

solved by functional iteration (predictor-corrector

scheme) .

~13~> Implicit Adam's method. Difference equations

solved by Newton's method with chord iteration. An

PPdr. Form 245a (10/83)Car. «9nrror

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internally generated diagonal approximation to the

Jacobian matrix is used.

=20=> Implicit method based on backward differentiation

formulas (Gear's method) . Difference equations are

solved by functional iteration; Jacobian matrix is

not used.

=23=> Implicit method based on backward differentiation

formulas. Difference equations are solved by

Newton's method with chord iteration. An

internally-generated diagonal approximation to the

Jacobian matrix is used.

=222~> Implicit method based on backward differentiation

formulas. Difference equations are solved by

Newton's method with chord iteration. An

internally-generated sparse Jacobian matrix is

used. The sparsity-structure of the Jacobian is

determined. by the code.

PP3,L Form 2454 (10/83)Cat, rt97340t

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W4-R CP1 = Parameter used in calculation of leakage flows.

Zncreasing CP1 increases the leakage flow rate for a

given pressure difference. The recommended value of CP1

4is lx10 . Larger values of CP1 can be used ifcompartment 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.

Zncreasing CP2 increases the maximum leakage flow rates.

W6-R CR1 = Parameter used in rain out calculation. Zncreasing this

parameter increases the rain-out rate when rain out isinitiated. The recommended value of CR1 is 10.

LW7-Z ZNPUTF = Flag controlling the printing of input data.

=0=> Summary of input data will not be printed.

1 > Summary of input data will be printed.

ppaL Form 2454 nOI83)Cat. «973l01

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WS-I IFPRT = Ventilation-flow edit flag.

=0=> Ventilation-flow edits will not be printed.

=1=> Ventilation-flow edits will be printed.

W9-R RTOL = Error control parameter. RTOL is the maximum relativeerror in the solution. The recommended value of RTOL's

lxl0

3.3. Problem Descri tion Data (Card 3 of 3)

Wl-I NSH = Number of time steps between re-evaluation of slab heat

transfer coefficients. If a pipe break is being

modelled, this parameter must be set to zero. If there

are no pipe breaks included in the model, NSH may have a

value as large as 10 without introducing significanterrors into the solution. For problems involving a large

number of slabs (but no pipe breaks), a value of 10 isrecommended.

ppa L Form 2454 (10/83)Gal. «973401 8< -B- N A -0 4 6 Rev.'0

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. PROJECT Sht. No. 40 of

PENNSYLVANIAPOWER & LIGHT COMPANY ER No.CALCULATIONSHEETS

W2-R TFC ~ mass fraction threshold value. If the mass fraction of

air or water vapor drops below the value specified for

TFC, that component is essentially neglected during the-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 24& (ror83)Cal. rr92340i

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3.5 Error Tolerance for Com artment Ventilation-Flow Mass Balance

Omit this card if NFLOW=O.

Wl-R DELFLO The maximum allowable compartment ventilation flow

imbalance (cfm), i.e., the following condition must be

satisfied for each compartment:

Net Ventilation Flow (cfm)

into Compartment < DELFLO.

-5The recommended value of DELFLO is lx10 . It isparticularly important to ensure that there are no

ventilation flow imbalances when the mass-tracking option

is not used (MASSTR~O) because in this case the code

assumes that the mass inventory in each compartment

remains constant throughout the transient.

3e6 Edit Control Data

NEC edit control data cards must be suppliedt on each card the followingthree items must be specified.

PP8 1 Form 2i54 (10r83)C4I. 4973401 SE -B- N A-046 Rev.01

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Wl-I IDEC = ID number of the edit control parameter set. The ID

numbers must start with 1 and they must be sequential,

i.e., IDEC=1,2,3,...,NEC.

W2-R TLAST = Time (hr) up to which the edit parameters apply. When

time exceeds TLAST, the next set of edit control

parameters will control printout of the calculation

results.

W3-R TPRNT ~ Print interval for calculation results (hr), i.e.,results will be printed every TPRNT hours.

3.7 Edit Dimension Data

Wl-I NRED Total number of rooms for which the calculation results

W2-I NS1ED

will be printed. This includes both, standard rooms and

time-dependent rooms.

~ Number of thick slabs which will be edited. Associated

heat transfer coefficients are edited along with the slab

temperature profiles.

PPdL Form 2454 n0183)Cat. 197340l

~E -8- N A -0 4 6 Rev.Q gI

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PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.CALCULATIONSHEET

W3-I NS2ED = Numbers of thin slabs which will be edited.

3.8 Selection of Room Edits

On this card(s) enter the ID numbers of the rooms to be edited. Include

both, standard rooms and time-dependent rooms (note that time-dependent

rooms have negative ID numbers) . Enter the ID numbers across the line

with at least one space between each item. The data can be entered on as

many lines as necessary. Room edits will be printed in the order that

they are specified here. For each room specified, calculation results

such as temperature, pressure, relative humidity, and mass and energy

inventories will be printed along with the various heat loads contained

within the room. Omit this card if NRED~O.

3.9 Selection of Thick Slab Edits

Enter the ID numbers of the thick slabs to be edited. Each ID number

should be separated by at least one space. If the ID numbers cannot 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

pp&L Form 245a (10/83)car. a973401

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the locations do not correspond to grid points. Omit this card ifNS1ED=O.

3.10 Selection of Thin Slab Edits

Specify the ID numbers of the thin slabs to be edited. Enter the items

across each line and use as many lines as necessary. Thin slab edits 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 NFLOW=O.

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 PREF ~ Pressure (psia) used to calculate the reference density

PPd r. Form 2td4 (r0/83)car. rr973401

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3.12 Standard Room Data

Wl-I IDROOM = Room ID number. The ID numbers must start with 1 and

must be sequential.

3W2-R VOL = Room volume (ft ) . In order to maintain constant

properties in a compartment throughout the calculation,15enter a large value for VOL (e.g. 1x10 ).

W3-R PRES = Initial room pressure (psia) .

W4-R TR = Initial room temperature ( F).0

W5-R RHUM = Initial relative humidity (decimal fraction). For the

case of MASSTR=O, this parameter is only used in

calculating heat transfer coefficients for thick slabs.

W6-R RMHT = Room height (ft). This parameter is used in the

calculation of condensation coefficients for thick slabs.

PPdL Form 2154 (10/83)Col, rr97340l SE -B- N A -0 4 6 Rev.'0 >

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3.13 Ventilation Flow Data

Omit this card(s) if NFLOW~O.

Wl-I IDFLOW = ZD number of the ventilation flow path. Values must

start with 1 and be secgxential.

W2«Z ZFROM = ID number of room that supplies ventilation flow. This

can be a standard room or a time-dependent room.

W3-I ITO = ID number of room that receives flow. This can be a

standard room or a time-dependent room.

W4-R VFLOW = Ventilation flow rate (ft /min). This volumetric flow 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.

PPSt. Form 2454 (1883)Cat rr9134rt1

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3.14 Leaka e Flow Data

Omit this card(s) if NLEAK=O.

Wl- I IDLEAK = ID number of the leakage path. Values must start with 1

and must be sequential.

W2-R ARLEAK = Area of leakage path (ft ).2

W3-R AKLEAK = pressure loss coefficient for leakage path based on flow

area ARLEAK. Specify a -1 for AKLEAK if the simple,

proportional control model is desired, seer

Section 2. 1.3.2.

W4- I LRMI = ID number of room to which leakage path is connected.

This can be a standard room or a time-dependent room.h

W5- I LRH2 = ID number of the other room to which the leakage path is

connected. This can be a standard room or a time-

dependent room.

W6-I LDIRN = Allowed direction for leakage flow.

PPIL L Form 2454 110/83)C«1. «9%401

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'PROJECT Sht. No. ~@of


1 => leakage from compartment LRM1 to compartment LRM2

only.

2 => leakage can be in both directions: from LRM1 to

LRM2 and from LRM2 to LRM1

3.15 Circulation Flow Data

Omit this. card(s) if NCIRC=O.

Wl-I IDCIRC = ID number of circulation flow path. Values must start

with 1 and must be sequential.

W2-I KRM1 = ID number of room to which circulation path is connected.

This can be a standard room or a time-dependent room.

W3-I KRM2 ID number of other room to which the circulation path is

connected. This can be a standard room or a

time-dependent room.

W4-R ELVL m Elevation of the lower flow path (ft) .

W5-R ELVU ~ Elevation of the upper flow path (ft).

pprL( Form 2454 (10/83)Car. rr9ruoi SE -B- N A -0 4 6 R« o

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W6-R ARL = Flow area of the lower flow path (ft ) .2

W7-R ARU = Flow area of the upper flow path (ft ) .2

WB-R AKL = Loss coefficient for lower flow path referenced to ARL.

W9-R AKU = Loss coefficient for the upper flow path referenced to

3.16 Air-Flow Tri Data

Omit this card(s) if NFTRIP=O.

Wl-I IDFTRP Trip ID number. The ID numbers must start with 1 and

must be sequential.

W2-I KFTYP1 = Type of flow path.

= 1 => Ventilation

= 2 ~> Leakage

= 3 ~> Circulation

PP8 L Form 2454 (1 0/83)Car, r97040r

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PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.CALCULATIONSHEET

W3-I KFTYP2 = Type of trip.= 1 => trip off= 2 => trip on

Note that all air flows are initially on unless tripped

off.

W4-R FTSET = Time of trip actuation (hr).

W5-I IDFP = ID number of flow path upon which the trip is acting.

3.17 Heat Load Data

4

Omit this card(s) if NHEATmO.

Wl-I IDHEAT = Heat load ID number. ID numbers must start with 1 and

must be sequential.

W2-I NUMR = ID number of room containing heat load.

W3-I ITYP = Type of heat load.

m 1 ~> Lighting

m 2 > Electrical panel

pp6L Form 245< ttar83)Cat. l973401

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PROJECT Sht. No. 2l of


= 3 => Hotor

= 4 => Room Cooler

= 5 => Hot piping

8 => Hiscellaneous

W4-R (DOT = Hagnitude of heat load (Btu/hr).

heat load ( ITYP=5) enter 0.0 for

value of (DOT will be calculated

(DOT should be negative.

If this is a pipingr

this parameter; the!

by the code. If ITYP=4,

W5-R TC = Temperature ( F) of cooling water entering cooler ifITYP=4. If ITYP is not equal to 4 enter a value of -I.

W6-R WC Cooling water flow rate (ibm/hr) if ITYP=4. If ITYP is

not equal to 4 enter a value of 0.

3.18 Hot Pi in Data

" Omit this card(s) if NPIPE=O.

Wl- I IDPIPE - ID number of pipe. The ID numbers must start with I and

must be sequential.

PPEL Form 2954 tt0/831Cat. tt07340 1

SE -8- N A -0 4 6 Rev.o >:r

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W2-Z ZPREF 1D number of associated heat load.

W3-R POD ~ Outside diameter of pipe (in) .

W4-R PZD Inside diameter of pipe (in).

W5-R AZNQD Outside diameter of pipe insulation (in). Zf the pipe isnot insulated set AZNOD equal to POD.

W6-R PLEN Length of pipe (ft).

W7-R PEM ~ Emissivity of pipe surface.

WB-R AZNK ~ Thermal conductivity of pipe insulation (Btu/hr ft F).

If the pipe is not insulated set AZNK 0.0.

W9-R PTEMP ~ Temperature ( F) of fluid contained in pipe.0

W10-I IPHASE ~ 1 if pipe is filled with steam. II~ 2 if pipe is filled with licgxid.

ppdt. Form 2a54 (lor83)Cat. «9nao>

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CALCULATIONSHEET

3.19 Heat Load Tri Data

Omit this card(s) if NTRIP=O.

W1-I ZDTRIP = Trip ID number. IDTRIP must start with 1 and all values

must be sequential.

W2-I IHREF = ID number of heat load that is to be tripped.

~ W3-I ITMD = Type of trip.=1=> Heat load is initially on and will be tripped off.=2=> Heat load is 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:

~ If TCON=O.O, the entire heat load is tripped off at

PPAt. Form 2454 ($ 183)Cat. 9973401

SE -B- N A -0 4 6 Rev.Q 1

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CALCULATIONSHEET

~ If the heat load is a piping heat load (ITYPm5), TCON

can be set to -1 and a time constant will be

calculated by the code. This time constant will then

be used to exponentially decay the heat load when itis tripped off.

~ A time constant can be supplied by setting TCON equal

to the desired time constant (hr) . When the heat load

is tripped off, it will exponentially decay with the

user-supplied time constant. This option can be used

with any heat load; it is'ot restricted to just

piping heat loads.

= 0.0 if ITMD=2.

3.20 Pi e Break Data

Omit this card(s) if NBRK 0.

Wl-I IDBK ~ ID number of break. IDBK must start with 1 and allvalues must be sequential.

PPLL Form 2454 (10/83)Car. 0973401

SE -B- N A -0 4 6 Rev.o

1'ept.

Date 19

Designed by

Approved by



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

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

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

= 2 => fluid in pipe is liquid water

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

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

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

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

total mass exiting the break increases linearly from a

value of zero at t=TRZPON to a value of BDOT at

t-ZRIPON+RAMP .

3.21 Thick Slab Data (card 1 of 3)

Omit this card(s) if NSLB1=0.

PPtt t. Form 2454 (10/83)Cat( rr973401

SE -B- N A -0 4 6 Rev.'0 >~

Dept.

Date 19

Designed by

Approved by



Wl-I IDSLB1 = Slab XD number. IDSLB1 must start with 1 and all values

must be sequential.

W2-I IRMl = ZD number of room on side 1 of slab. A standard room or

a time-dependent room can be specified. Zf side 1 of the

slab is in contact with ground enter a value of zero.

W3-I IRM2 = ID number of room on side 2 of slab. A standard room or

a time-dependent room can be specified. Xf side 2 of th

slab is in contact with ground enter a value of zero.

W4-I ITYPE = Type of slab.

= 1 if slab is a vertical wall

= 2 if slab is a floor with respect to room ZRM1.

= 3 if slab is a ceiling with respect to room ZRM1.

W5-I NGRIDF = Number of grid points per foot used in the

finite-difference solution of the unsteady heat

conduction equation. A minimum of 6 grid points per slab

is used by the code, and the maximum number of grid

points used per slab is 100. Zf the specified value of

NGRIDF causes the total number of grid points for the

pp6L Form 2454 (10r83)C41. 4973401

Dept.

Date 19

Designed by

Approved by

PROJECT Sht. No. I 7 of


slab to be outside of these limits, the appropriate limitwill 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.


for side 2 of the slab. The code will calculate

natural-convection and radiation heat transfer

coefficients for side 1.


for both, side 1 and side 2 of the slab.

ppaL Form 2454 (10/831Cat. /1073401 SE -B- N A -0 4 6 Rev.0

1'ept.

Date 19

Designed by

Approved by


CALCULATIONSHEET

Allow the code to calculate film coefficients for slab surfaces in contact

with ground.

W7-R CHARL characteristic length of the slab (ft).= height of the slab if ITYPE=1.

= the heat transfer area divided by the perimeter ifITYPE=2 or 3.

If the value of CHARL is set to 0.0, the code willcalculate a value for the characteristic length. In this

case, the code assumes that the slab is in the shape of a

square.

3.22 Thick Slab Data (Card 2 of 3)


Wl-I IDSLB1 = Slab ID number.

W2-R ALS Thickness of slab (ft).

},

ppa,L Form 2454 n0/83)car. «97uot

SE -B- N A -0 4 6 Rev;0 y

Dept.

Date 19

Designed by

Approved by


CALCULATIONSHEET

W3-R AREAS1 = Slab heat transfer area (ft ) . This is the surface area2

of one side of the slab.

W4-R AKS = Thermal conductivity of slab (Btu/hr ft F).

W5-R ROS = Density of slab (ibm/ft ) .3

W6-R CPS = Slab specific heat (Btu/ibm- F).

W7-R EMZSS = Slab emissivity

3.23 Thick Slab Data (Card 3 of 3)

If ZHFLAG=O for a slab, then do not supply a card in this section for that

particular slab. Zf IHFLAGml or 2, only supply the required data; leave

the other entries blank. Zf ZHFLAG=12, supply all the heat transfer'I

coefficient data for that slab. Omit this card(s) if NSLB1=0.

Wl-I IDSLB1 ~ Slab ID number.

W2-R HTC1(1) ~ Heat transfer coefficient for side 1 of slab if ITYPE=1

(Btu/hr-ft - F).2 0

PP41. Form 2454 (10/83)Ca1. SerSC01

SE -B- N A -0 4 6 Ftev.'0

1'ept.

Date 19

Designed by

Approved by



= Heat transfer coefficient for upward flow of heat between

slab and room IRMl if ZTYPE 2 or 3 (Btu/hr-ft - F).2 0

W3-R HTC2(1) Heat transfer coefficient for side 2 of slab if ZTYPE=1

(Btu/hr-ft - F).2 0

= Heat transfer coefficient for upward flow of heat between

slab and room IRM2 if ZTYPEm2 or 3 (Btu/hr-ft - F).2 0

W4-R HTC1(2) = Heat transfer coefficient for downward flow of heat

between slab and room ZRM1 if ZTYPEm2 or 3

(Btu/hr-ft - F) . Do not supply a value if ITYPE=1.2 0

W5-R HTC2(2) ~ Heat transfer coefficient for downward'low of heat

between slab and room ZRM2 if ITYPEm2 or 3

(Btu/hr-ft - F) . Do not supply a value if ITYPE=1.2 0

3.24 Thin Slab Data (Card 1 of 2)


pprt L Form 2454 n0r83)Cat. rr9nao>

SE -B- N A-0 4 6 Rev.0 gt

Dept.

Date 19

Designed by

Approved by



Wl-I ZDSLB2 = Slab ID number. IDSLB2 must start with 1 and all values

must be secpxential.

W2-I JRM1 = ZD number of room on side 1 of slab. A standard room or

a time-dependent room can be specified. A thin slab

cannot be in contact with ground, i.e., do not specify

JRM1 or JRM2 equal to zero.

W3-Z JRM2 = ZD number of room on side 2 of slab. A standard room or

a time-dependent room can be specified.

W4-I JTYPE = 1 if slab is a vertical wall.

= 2 if slab is a floor with respect to room JRM1.

= 3 if slab is a ceiling with respect to 'room JRM1.

W5-R AREAS2 = Slab heat transfer area (ft ) . This is the surface area2

of one side of the slab.

3.25 Thin Slab Data (Card 2 of 2)

Omit this card(s) if NSLB2 0.

pP&L Form 2454 (10/83)car. «9ruoi

SE -8- N A -0 4 6 Rev.'Q

Dept.

Date 19

Designed by

Approved by


CALCULATIONSHEET

Wl-I IDSLB2 = Slab ZD number.

W2-R UHT(1) = Overall heat transfer coefficient for slab is JTYPE=l

(Btu/hr-ft — F) .2 0

Overall heat transfer coefficient for upward flow of heat

through slab if JTYPE~2 or 3 (Btu/hr-ft - F).2 0

W3-R UHT(2) = Overall heat transfer coefficient for downward flow of

heat through slab if JTYPE~2 or 3 (Btu/hr-ft - F). Do2 0

not supply a value of JTYPE~1.

3.26 Time-De endent Room Data (Card 1 of 2)

I

Omit this card(s) if NTDR~O.

Wl-I ZDTDR = ZD number of time-dependent room. ZDTDR must start with

-1 and proceed secgxentially (i.e.,ZDTDR 1 r 2 t 3 r ~ ~ r NTDR) ~

W2-I IRMFLG ~ 1 if temperature, pressure, and relative humidity data

will be supplied.

ppa r. Form 2«54 (10/83)Car. «973401

SE -B- N A -0 4 6 Rev. 0

g'ept.

Date 19

Designed by

Approved by



= 2 if a sinusoidal temperature variation will be used for

this room. If this option is chosen there cannot be any

flow to or from this room.

W3-I NPTS = Number of data points that will be supplied if IRMFLG=1.

Each data point consists of a value of time, temperature,

pressure, and relative humidity. NPTS must be less than

or equal to 500. Since output is determined by

interpolation, time-dependent-room data must be supplied

at least one time step beyond the problem end time.

= 0 if IRMFLG=2.

W4-R TDRTO = Initial room temperature ( F) if IRMFLG=2.0

= 0.0 if IRMFLG~1.

W5-R AMPLTD = Amplitude ( F) of temperature oscillation if IRMFLG=2.0

~ 0.0 if IRMFLG=1.

W6-R FREQ = Frequency (rad/hr) of temperature oscillation ifIRMFLG~2 .

0.0 if IRMFLG~1.

PPIL Form 2454 n0r83>Car. rr913401

SE -B- N A -0 4 6 Rev.'0

y'ept.

Date 19

Designed by

Approved by


CALCULATIONSHEET

3.27 Time-De endent Room Data (Card 2 of 2)

Supply the following data for each time-dependent room that has a value of

ZRMFLGml. Omit this card(s) if NTDR=O.

Wl-I ZDTDR ~ ZD number of time-dependent room

W2-R TTIME = Time (hr) .

W3-R TTEMP Temperature ( F).o

W4-R TRHUM = Relative humidity (decimal fraction).

W5-R TPRES = Pressure (psia).

Repeat words 2 through 5 until NPTS data points are supplied. Then

start a new card for the next time-dependent room.

pp3L Form 2454 n$ 831Cat. N973401 B- N.A=04 6 ReV-G.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 ison side 1 of the slab and a time-dependent room is in contact with side 2.

The temperature in the time-dependent room oscillates with amplitude A0

and frequency'. There are no heat loads or coolers within the standard

room; heat is only transferred to or from the room by conduction through

the slab.

The equations describing this problem are

aT /at = aa T /ax ,2 2

s s

BT = — hl [T 1(t) — T (0 t) ],Bx x=0 k

BT 1 = -h [T (L,t) — T (0) - A sin(et)],gs l =L k2 s '2 0

(4-1)

(4-2)

(4-3)

and

T (x 0) = ax+b,s (4-4)

I3 C V dT Ah [T (Ort) T (t) ]dt

(4-5)

PP6L Forrtt 245« (10/83>

Cat. «973401SE -B- N A -0 4 6 Rem„Q y

Dept.

Oath t«

Designed by

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Sht. No. Q6 of IPROJECT


Room 1Standard Room

Room 2Time-Dependent- Room

Room temp, T (t)rlVolume, V

Air density, p

Specific heat, CvlInitial pressure, P

Film coefficient, hl

SlabTemp«

T (x,t)s

Room temp,

2()- 2(o)+Oi ( )r2 r2Film coefficient, h

Side 1 of slab Side 2 of slab

X=O X=L

Figure 4.1 Description of Sample Problem 1

PAL Form 2454 ttN83)Cat. N7340t

SE -B N A -04 6 Rev.00

Dept.

Date 19

DesIgned by

Approved by


CALCULATIONSHEET

where a and b are given by equations (2-30) and (2-31). Zt is assumed

that both rooms have been at their initial temperatures long enough forthe 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 4.4g again, the results show good agreement.

PPttt. Form 2454 (t ttt83)Cat. 4973401

SE -B- N A-04 6 Rev.og

Dept.

Date 19

Designed by

Approved by


CALCULATIONSHEET

Table 4.1 Values of Parameters used in Sample Problem 1

Parameters Value

T 0)r1T (0)

A0

h

h

Vl

80 F

200 F

100 F

0.5 rad/hr

1.46 Btu/hr ft F2 0

6.00 Btu/hr ft F2 0

0.0325 ft /hr2

1.0 Btu/hr ft F

800 ft300 ft2 ft

1014e7 psia

~ 111 TSO FOREGROUND HARDCOPY 1 1 1 1 PRINTED 89284. 1100JSNAME=EAMAC.COTTAP.SAMPLI.DATAJOL=OSK533

COTTAP SAMPLE PROBLEM 1 -- RUN 1a ~ 1 ~ Off ~ Offff111 ~ ~ ~ 11 ~ 1 ~ ~ 1 ~ 11 ~ 1 ~ 1 ~ ~ 11 ~ ~ ~ ~ 11111111111 ~ Offfffffff~ 11 ~ 1111 ~

PROBLEM DESCRIPTION DATA ( CARD 1 OF 3 )

NROOM NSLAB1 NSLAB2 NFLOW NHEAT NTDR NTRIP NPIPE NBRK NLEAK NCIRC NEC1 1 0 0 0 I 0 0 0 0 0 1f1111111111111111111 '1111111111111111111111111111111111t111111111111111


~ 1 1

p1

NFTRIP MASSTR MF CP'I CP2 CR1 INPUTF0 0 222 2.04 2.0 10. 1

1 ~ 1 ~ 1 ~ 1 1 1 ~ ~ 1 1 ~ 1 1 1 ~ ~ 1 1 ~ ~ 1 ~ 1 ~ ~ 1 1 ~ ~ 1 1 1 1 ~ 1 1 O 1 ~ ~ ~ ~ 1 1 1 1ROBLEM DESCRIPTION DATA ( CARD 3 OF

IFPRT RTOL1 1. 0-5

111 ~ ~ 1 ~ ~ ~ ~ 1 ~ ~ ~ ~ 1 1 ~ ~ 1

NSH0

~ 1111111

TFC1.0-5

~ 11 ~ ~ 1111111 ~ 1 ~ 1 ~ ~ ~ ~ 11 ~ ~ OOOOOOO ~ Offtfff~ ~ ~ Offffffftt~ 11111 ~ 111111PROBLEM TIME AND TRIP TOLERANCE DATA

T0.0

f 111111TEND TRPTOL TRPENO

2000.0 10.00 O.DO1 ~ ~ tftf ~ 1 ~ ~ 1 ~ ~ Offf ~ 1 ~ Offffff~ ~ Off ~ 111111 ~ 1 ~ ~ ~

TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALA( OMIT THIS CARD IF NFLOW = 0 )

1 1 1 1 t 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

NCE

DEL1.D

f 111 111

t I DEC TLAST TPRNT1 2000. 100.

~ 111111111111 ~ 11 ~ ~ Offff~ 1 ~ ~ ~ 11111111ftf1111 ~ 11111EDIT DIMENSION CARD

1 1 1 ~ 1 1 ~ f f 1 1 1 f 1 f f 1 1

FLO-51 1 1 1 1 1 1 ~ 1 1 1 ~ ~ ~ 1 ~ ~ 1 ~ 1 1 1 1 1 1 1 1 t 1 1 1 1 1 1 1 1 1 1 ~ 1 ~ 1 1 1 1 1 1 1 1 1 1 1 1 1 f 1 1 1 1 1 1 1 1 1 1

EDIT CONTROL DATA CARDS

NRED NS LEO NS2ED2 1 0

1 11 ~ Of 1111 111 ~ ~ ~ ~ ~ 1 ~ ~ ~ 1 ~ 1 ~ Offfff111 ~ ~ 1111 ~ ~ 111 ~ 1 1 ~ tf 1 1 1 1 1 11'11 1 tf 1 11 f 1

ROOM EDIT DATA CARO(S)

-1O 1 1 1 1 1 1 1 ~ 1 1 1 1 ~ ~ ~ ~ ~ ~ ~ 1 ~ 1 ~ ~ 1 1 1 ~ 1 1 ~ ~ 1 1 1 1 1 1 1 1 1 ~ 1 1 1 1 1 ~ 1 ~ tf ~ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

EDIT CARO(S) FOR THICK SLABS

1 11111111 ~ 1 ~ 11 ~ 1 ~ 11 11 ~ 11 f 111111 ~ 11 ~ 11111 1111111 ~ 111 ~ Of 111111tf tftfOtf 111DI T CARDS FOR THIN SLABS

f 11111111 1 11 ~ 111 ~ ~ 1 Otf 1111 ~ Of ff1 ~ ~ 11tf 1 1 1 ~ Of 1 1 ~ 1111 Of 11 Of 11111111REFERENCE PRESSURE FOR AIR FLOWS

(OMIT THIS CARD IF NFLOW=O)

TREF100.

PREF14. 7

~ ~ 1 1 ~ 1 1 1 1 1 1 1 1 1 ~ 1 ~ 1 1 1 1 ~ 1 1 1 1 1 1 1 1 1 ~ 1 1 1 1 1 ~ 1 ~ 1 1 1 ~ ~ ~ ~ 1 ~ 1 1 1 ~ ~ 1 ~ ~ 1 1 1 ~ 1 1 1 1 1 1 1 t 1 ~ 1

ROOM DATA CARDS(00 NOT INCLUDE TIME-DEPENDENT ROOMS)

~ I DROOM1

1 1111 ~ tf 1

VOL PRES TR RELHUM RM HT800. 14.7 80.0 0.5 10.0

1 11 1 1 11111 1111111 11111111 Of 111111 1 ~ 1 1t 1 1 1AIR FLOW DATA CARDS

( OMIT THIS CARD IF NFLOW = 0 )

~ 1 ~ 1 1 ~ 1 1111 tf ~ 11 1111

IDFLOW IFROM ITO VFLOW

~ ~ t ~ t ~ t t t ~ t ~ ~ t ~ t t t t t ~ ~ ~ ~ t ~ t ~ ~ ~ ~ t t t t t t t t t t t t t ~ ~ ~ t t ~ t ~ ~ ~ t t t t t t ~ t t t ~ ~ ~ t ~ t ttLEAKAGE PATH DATA

( OMIT THIS CARD IF NLEAK = 0 )

IDLEAK ARLEAK AKLEAK LRMI LRM2 LOIRN

~ t ~ t t t ~ t ~ ~ ~ t t ~ ~ t ~ t t ~ ~ ~ t ~ ~ t t ~ t t ~ t ~ ~ t t t t ~ t t t t t t t t t t t 1 t t t ~ t t ~ t t t t t t t tAIR FLOW TRIP DATA

IDFTRP KFTYP1 KFTYP2 FTSET IDFP

sttttttt ~ ~ ttHEA

~ IDHEAT NUMR

~ 0000 ~ ttttttQOOTITYP TC WCOOL

t ~ t t t ~ t t ~ t t t ~ t t t t ~ t t t t t t t ~ t t t t t t t t t ~ t t t t t ~ t t t t t t t t ~ ~ t ~ t t t t t tPIPING DATA CARDS

~ t ~ ~ ~ ~ ~ ~ t ~ t ~ t ~ t t ~ ~ ~ ~ ~ t t t t t ~ ~ t t t ~ t t ~ ~ t ~ t ~ ~ ~ ~ t ~ t ~ t t t t t ~ t t t t t t ~

T I.OAD DATA CARDS C ~ I

~ IDPIPEttttttttt

IPREF POO PIO AIODN PLEN PEM A1NK 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 ~ ~ tHEAT LOAD TRIP CARDS

I OTRI P IHREF ITMD TSET TCON

~ tttttttt~ IOBRK

~ ttttttt ~

IOSL81I

~ tttttttt

t ~ ~ t ~ ~ t ~ ~ ~ t ~ ~ ~ t ~ ~ t t t t t t ~ t t t ~ t t t t t t t t t t t t t t t t t t ~ t t ~ t t ~ t t t t ~ ~ t t t ~

STEAM LINE BREAK DATA CARDS

IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP

t t t t t t t t t t t t t t t ~ ~ t t t t t t t t t t t t t t t t t t t t t t t ~ t t t t t t t t t t t t t t t t t t t t t tTHICK SLAB DATA CARD (CARO 1 OF 3)

IRM I I Rhl2 I TYPE NGRIO IHFLAG CHARL1 -1 I IS 12 10.

~ ~ t ~ t t t t ~ ~ ~ t t ~ t t t t t t ~ t t t t t t t t ~ t t t ~ t t t t t ~ t t ~ t t t t t ~ t t ~ t t t ~ t ~ t t t t tTHICK SLAB DATA CARD (CARD 2 OF 3)

IOSL811ttttttttttt~

ALS AREAS1 AKS ROS CPS EMI S2.0 300. 1.00 140. 0.22 0.8

~ ~ ~ ttttttttt~ tt ~ ttttttttttttt~ ttttttttt~ ~ ~ tt ~ ~ ~ 0004 ~ ttttttTHICK SLAB DATA CARO (CARD 3 OF 3)

IDSL811

~ t ~ tttttttttt

IDSL82~ ttttttt ~ ttt

JRM1 JRM2 JTYPE AREAS2

~ ~ t t t t t t ~ ~ ~ t ~ ~ t ~ t t t t t t t t t t t t t t t t ~ t t t t t tTHIN SLAB DATA CARD (CARO 2 OF

HTC1(1) HTC2(1) HTC1(2) - HTC2'1.46 6.00ttttttttttttttttttttttttttttttttttttt~ t

THIN SLAB DATA CARD (CARD 1 OF 2)

(2)tt ~ ttttt ~ ttttt ~ t ~ t ~ t ~

t ~ ~ t t t t ~ ~ t t t t ~ t t t t t t t2)

IDSL82 UHT(1) UHT(2)

o ~ ~ ttttttttt~ t t ~ t t ~ t ~ t t ~ ~ t t t t t t ~ ~ t t t t t t t t ~ t ~ t ~ t t t ~ ~ t ~ t t t ~ t t t t t t t t t t t ~ t t tTIME-DEPENDENT ROOM DATA

4

I OTDR-I~ tt ~ ttttt ~ t ~

IRMFLG NPTS TDRTO AMPLTD2 0 200.0 100.0t ~ ~ t ~ ttt ~ ~ ~ ~ ttttt ~ ttttttt ~ ttt ~ ~ t ~ t ~ t ~ ~ ~

TIME VERSUS TEMPERATURE DATA

FRED0.50tt ~ tt ~ ~ ~ ~ tt ~ ~ ttttttt

~ I OTOR TTIME TTEMP TT IME TTEMP TTIME TTEMP

oo ~ ~ ~ t ~ et ~ ~

~ ttttt ~ t ~ tttt tt t tttttttt ~

t t t ~ ~ t t ~ t t ~ t ~ ~ t t ~ t t t t t t t t t t t t t t t ~ t t t ~ t t ~ t t ~

~ ~ ti~ ~ ~ t ~ ~ ttttttt ~ ttttttttttttt~ ttt ~ t ~ ttt ~ tt

TSO FOREGROUND HARDCOPY ~ ~ 11 PRINTED 89284.1045>SNAME=EAMAC.COTTAP.SAMPLI.DATAOL=OSK533

COTTAP SAMPLE PROBLEM I -- RUN 2ft ~ 11111 ~ 111111111 ~ 1111 ~ 1 ~ ~ 111 ~ 1111111111111tfffffffffPROBLEM DESCRIPTION DATA ( CARD I OF 3 )

tf 1 1 1 1 ~ 1 ~ Of ~ 111

NROOM NSLAB I NSLA82 NFLOW NHEAT NTDR NTRIP NPIPE NBRK NLEAK NCIRC NECI I 0 0 0 I 0 0 0 0 0 2

~ 1 1 1 1 1 1 ~ 1 ~ ~ 1 1 ~ ~ 1 1 1 1 1 1 1 1 1 ~ 1 1 ~ ~ ~ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 t 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 fPROBLEM DESCRIPTION DATA ( CARD 2 OF 3 )

NFTRIP MASSTR MF CPI CP2 CRI INPUTF IFPRT RTOL0 0 222 2.04 2.0 10. I I 1.0-5

1 11 11111 ~ ~ t 11111111 ~ ~ t 1 ~ 1 ~ ~ ~ 1 ~ 11111 1111111111 ~ tf1111 ~ 11 1 1 1 1 t 1 1 1 1 1 1 1 ~ 111PROBLEM DESCRIPTION DATA ( CARD 3 OF 3 )

NSH0

~ 111 11111

TFCI . D-51111 ~ ~ 11 ~ 11 1 ~ ~ ~ ~ ~ ~ ~ ~ 11 ffttf1 1 1 1 ff11111111 ~ 11 111 ~ 1 111 1 Of 11111t

PROBLEM TIME AND TRIP TOLERANCE DATA

T TEND TRPTOL TRPEND0.0 1520.0 IO.DO O.DO' 1 1 1 1 ~ 1 1 1 ~ 1 ~ 1 1 ~ 1 1 1 1 ~ 1 1 1 1 1 ~ ~ ~ 1 1 ~ 1 ~ 1 ~ 1 1 1 1 1 1 1 ~ 1 1 1 1 1 1 1 1 1 1 1

TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE( OMIT THIS CARO IF NFLOW = 0 )

1 1 1 1 111111111111 1

OELFLO1.0-5

~ 1 ~ 1 1 11 ~ 111 11 1 ~ 1 11 ~ ~ ~ ~ ~ ~ ~ 1 ~ ' ~ 1 ~ 11111111111 ~ 1111111111 11111 1111 ~ 1 ~ ~ ~ ~ ~ ~ 1


IOECI2

~ f ~ 1111111

TLAST TPRNT1500. 1500.1520. I.

1 1 1 111111111 t ~ ~ 1 ~ ~ 1 ~ 1 ~ 11 ~ 11111111111111111 11 111EDIT DIMENSION CARD

11 f 111 11 ~ 11 ~ ~ 1 ~

NRED2

~ f ~ 1 1 ~ 1 ~ ~ ~ 11111NS I ED NS2EO

I 011111 1 1 1 1 1 1 11 ~ 1 1 ~ 1111111111111111 11111 1111 1111 ~ f ~ 111111 11

ROOM EDIT DATA CARD(S)

~ 1 1-I

~ 1 1 1 1 ~ tf 1 1 11111 ~ t111 Of ~ 1 ~ ~ 111 ~ ~ 1111 ~ Of 11 1 f ~ 11111 1 tf 1 1 1 111 11 f 1 1 ~ 1 f 11 ~ 1

EDIT CARD(S) FOR THICK SLABS

~ ~ 11 ~ 1 ~ 11111111 111111 1 1111 ~ 1 ~ ~ 11111 111111111f Otf 1 11 1 1 1 1 tf f Off 1 11 1 ~ ~ 1111 1

EDIT CARDS FOR THIN SLABS

f 1 1 1 1111 ~ f 1111 1 11111 111 ~ ~ 1 1 111 ~ 11 ~ 111 ~ 1111 f 1 111 1 tf 1 111 111 1 tf 1 1 1 1 ~ 1 ~ 111 1 1REFERENCE PRESSURE FOR AIR FLOWS


TREF100.

~ ~ 111 ~ 11 ~ ft ~ 1 ~ ~

(00

PREF14. 7~ 1 1 1 1 tf 1 ~ 1 1 ~ 1 1 t 1 1 1 1 ~ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 t 1 1 1 1 1 1

ROOM DATA CARDSNOT INCLUDE TIME-DEPENDENT ROOMS)

1 1111 ~ 111 Of 1

~ I IiROOMI

~ ~ 1 11 f f f f ~

VOL800.11111

PRES TR RELHUM RM HT14.7 80.0 0.5 10.0

~ ~ ~ 1 ~ 11 ~ 11 ~ 1 1 ~ 1 ~ 1 ~ 1 11 11 ~ 11 111111111111 ~ 1I1A I R FLOW DATA CARDS

OMIT THIS CARD IF NFLOW = 0 )

1111 tf ~ ~ 11 1 1 11 ~

IUFLOW IFROM ITO VFLOW

TSET TCON

BOOT TR IPON TRIPOF RAMP

JRM2

IDSL82 UHT(1)

~ eeet ~ ~ 1 ~ ~ 1 ~ ~ 11 ~ ~ ~ 0 ~ ~ 01 000000 ~ 0 ~ 1100 ~ ~ 01 ~ 1 ~ 0 ~ 011 ~ 01000111111f f000000101 ~

LEAKAGE PATH DATA( OMIT THIS CARD IF NLEAK = 0 )

IOLEAK ARLEAK AKLEAK LRMI LRM2 LDIRN

i ee 1 1 00 0 1 ~ 1 111 101 ~ 0 ~ ~ f 00000 ~ ~ ~ 0 ~ ~ 0001000000000000 ~ ~ ~ 00 ~ ~ ~ ~ 0 ~ 1 0 ~ ~ 1 ~ 11 ~ 01 1

AIR FLOW TRIP DATAe

IDFTRP KFTYPI KFTYP2 FTSET IOFP

e 1 1 1 0 0 0 0 0 1 0 0 0 0 ~ 0 ~ 0 0 ~ 0 0 0 ~ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ~ ~ 0 1 ~ 1 0 0 0 0 1 1 0 1 0 0 0 0 0 ~ ~ ~ 0 ~ ~ 0

e HEAT LOAD DATA CARDS

IDHEAT NUMR ITYP QDOT TC WCOOL

~ e 1 1 1 1 1 1 1 1 1 1 1 1 ~ 0 ~ 1 ~ 1 ~ ~ 0 1 ~ ~ ~ ~ 1 ~ ~ ~ ~ ~ 0 0 0 0 0 0 0 0 ~ 0 ~ ~ ~ 1 1 0 ~ 1 1 1 1 ~ 0 ~ 0 1 ~ ~ 0 0 ~ ~ ~ 1 ~ 1 0 0

PIPING DATA CARDS

IDPIPE IPREF POD PID AIOON PLEN PEM AINK PTEMP IPHASE

~ 11 1 00110101f 00 0 tf0 ~ 000 ~ 0000000000f Off fOf ~ 00000000 ~ 000101000011ff 00 011 ~ 0

1 HEAT LOAD TRIP CARDSe

I OTR IP IHREF I TMO

~ 1 1 1 0 0 1 1 0 t 1 0 ~ ~ 1 0 ~ ~ t 1 1 ~ 0 ~ 0 1 0 t 0 0 0 0 0 0 0 1 1 ~ 1 0 1 0 1 1 0 1 0 1 ~ ~ 0 0 0 1 0 1 0 0 1 0 0 0 0 ~ 0 1 0 1 1 1 1 1

e STEAM LINE BREAK DATA CARDS

~ IDBRK IBRM BFLPR IBFLGe

~ 1111110 ~ 1 f 11000 ~ 000 ~ 11 ~ f 0000 1 1100000 000 000000001 0 ~ 0100 0101 1 tf 1 1 1 1 1 110114 THICK SLAB DATA CARO (CARO I OF 3)

IDSI 81 IRMI IRM2 I TYPE NGRIO IHFLAG CHARL1 I -I 1

'I 5 12 10.~ e 1 1 1 ~ 1 ~ 1 1 ~ 1 ~ 1 1 1 0 0 0 ~ 1 ~ 0 0 0 1 ~ 0 0 ~ 1 1 ~ 0 0 ~ 0 0 0 0 0 0 0 0 f 0 0 ~ ~ ~ 0 1 0 0 0 0 0 0 1 ~ 0 0 0 1 0 ~ 0 1 0 1 0 0

e . THICK SLAB DATA CARO (CARD 2 OF 3)

IDSL81 ALS AREAS1 AKS ROS CPS EMI S

I 2.0 300. 1.00 140. 0.22 0.8~ 1 1 1 1 1 1 ~ 1 0 1 0 1 ~ 1 0 ~ ~ 0 1 ~ 0 1 0 1 1 ~ ~ 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 ~ 1 ~ 1 ~ ~ 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 ~ ~ 1 0

THICK SLAB DATA CARD (CARD 3 OF 3)e

ID&LBI HTCI (I) HTC2(1) HTCI (2) HTC2(2)I 1.46 6.00

~ ~ e ~ e 1 1 ~ 1 e 1 1 t 1 1 ~ ~ ~ 1 1 ~ 1 1 0 ~ ~ 0 0 0 t 1 1 0 1 1 ~ ~ ~ 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 ~ ~ 1 1 1 1 1 1 1 0 0 1 '1 1 1 ~ 1 0

THIN SLAB DATA CARO (CARD I OF 2)e

e I OSL82 JRMI JTYPE AREAS2e

1 1 1 1 0 1 1 1 1 1 f 1 0 1 ~ 0 ~ 1 1 t ~ ~ ~ 1 0 0 0 0 0 0 f 0 0 0 0 0 ~ 0 0 1 0 1 0 0 0 0 1 1 1 ~ 0 1 ~ ~ 0 1 0 ~ 1 0 1 0 1 1 1 0 0 1 0 '1 1 1

e THIN SLAB DATA CARO (CARO 2 OF 2)

e UHT(2)

i ~ i e 1 1 1 1 ~ 1 1 ~ 1 ~ ~ 1 1 ~ ~ ~ 1 1 1 1 1 1 1 1 ~ 1 ~ 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 ~ 1 1 1 ~ ~ \ 1 1 ~ ~ 1 1 1 ~ 1 ~ 0 1 1 1 1 1

TIME-DEPENDENT ROOM DATA

~ I UIOR- I

IRMFLG NPTS TDRTO AMPLTO FREQ2 0 200.0 100.0 0.50

~ ~ 1 ~ ~ 1 ~ ~ 11 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ ee ~ ee ~ eee ~ eee ~ 11 ~ 1 ~ 1 ~ ~ effete ~ ee ~ eeeeeeef teeTIME VERSUS TEMPERATURE DATA

~ I DTDR

see ~ eeetoeeeeeee

T E TTEMP

tee~ 1 1

TTIME TTEMP TTIME TTEMP

~ ~ 1 1 1 1 1 1 t ~ 1 ~ 1 1 1 1 1 ~ 1 1 1 1 1 ~ 1 1 0 ~ 0 1 ~ ~ 1 1 1 ~ 1 1 1 ~ 1 1 1 1 1 1 1 1 1 1

1 1eeetef 01 ~ 11111 ~ 1 111111111 ~ 1 ~ 01 111101 ~ 1111111111 ~

FIGURE 4.2 COMPARISON OF COTTAP CALCULATED TEMPERATUREPROFILE WITH ANALYTICALSOLUTION (t=900 hr)

FOR SAMPLE PROBLEM I220

210

QlQ)

200

I~

190I—

180

LegendANALYTICAL

~ COTTAP

1700.5

x (tt)1.5

FIGURE 4.3 COMPARISON OF COTTAP CALCULATEDTEMPERATUREPROFILE WITH ANALYTICALSOLUTION (t—2000 hr)

FOR SAMPLE PROBLEM t

250

240

U)230

LIJ

220l~

210

200

LegendANALYTICAL

0 COTTAP

190

1800.5

x (tt)1.5

RGURE 4.4 COMPARISON OF COTTAP CALCULATED TEMPERATUREOSCILLATION WITH ANALYTICALSOLUTION

FOR SAMPLE PROBLEM 1

IIll

O

LJJCiMKO

OOCL

OW

4JI—

200.6

200A

200.2

200

199.8

199.6

199.4

150 1505 1510

TIME (hr)

LegendANALYTICAL

~ COTTAP

1515 1520

cC)

PAL Form 2l5l 00t83)Ca<. N973401

$F -8- N A -04 6 «V 0m

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); the temperature in the other compartment is calculated by

the code. The compartment for which the temperature is calculated

contains 4 heat loads and 5 associated heat load trips. The timing of

these trips matches the plot in figure 4.5.

The analytical solution for the room temperature is

T (t) =T (0)e 8 +T (1-e )Z Z con

.t-tB/aJ

y8/a0 a

(4-6)

where the constants a and 8 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.

PPd 1. FO m 2t54 <10 831

Cdt, 091%01 ~

SE -g N A.-04 6 ReV.PX

Dept.

Date 19

Designed by

Approved by



n

C 00 D o

gQ

aA

I- IIt

0 o

6 4'1

4

ZI

0

00

4)

QQ 0

Q Q0 0

C$

(+H/ ~d Q) $ 'nd wZ.

pal Form 2454 nOI83)Col. l913401

SF g tu p .-04 6 Rev:ox

Dept.

Date 19

Designed by

Approved by


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); at t = 2 hr, two vents at different elevations are opened allowing

natural circulation flow through the compartment. In order to simulate

this, a natural circulation flow path is tripped on at t = 2 hr, and at

the same time, the leakage flow is tripped off because the circulation

flow model already allows for air leakage.

TSO FOREGROUND HARDCOPY '1000 PRINTED 89284. 1412SNAME=EAMAC:COTTAP.SAMPL2.DATA ~

OL=DSK534

COTTAP SAMPLE PROBLEM 2iiiti~ 1 ~ f ~ 000 ~ 0 ~ ~ ~ 0 0 ~ ~ ~ ~ ~ ~ 00 ~ 0 1t0 it 0 tfiiiiitiiiiiii0 0 tfit 0 ~ ~ 0000 ~ 0 1 111 tPROBLEM DESCRIPTION DATA ( CARD 1 OF 3 )

NROOM NSLAB1 NSLAB2 NFLOW NHEAT NTDR NTRIP NPIPE NBR1 0 1 0 4 1 5 0 0if000001 000011 ~ ~ ~ ~ ~ ~ 00 ~ ~ ~ 00 ~ 0 ~ 0 ~ 00 ~ ~ 0 ~ ~ ~ 000 ~ 00 ~ 00000 ~

PROBLEM DESCRIPTION DATA ( CARO 2 OF 3 )

K NLEA0

00 ~ 000

K NCI RC NEC0 1000000110000

NFTRIP MASSTR MF CP1 CP2 CR1 INPUTF IFPRT RTOL0 0 222 2.04 2.0 10. 1 1 I . 0-5

1 ~ 1 1 0 0 0 0 0 ~ 0 0 0 ~ ~ 0 ~ ~ ~ ~ ~ 0 1 0 0 0 ~ ~ ~ 0 0 0 0 0 0 1 0 \ 1 0 0 0 0 0 0 0 0 0 ~ 0 0 ~ 0 ~ 0 ~ 0 ~ ~ ~ 0 ~ ~ ~ 0 0 0 1 0 t 1PROBLEM DESCRIPTION DATA ( CARD 3 OF 3 )

NSH TFC0 I . 0-5

~ 11 ~ 00 ~ 0 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ 0 ~ ~ 1 ~ ~ ~ ~ 0 ~ 00 ~ 0 t ~ 0 ~ ~ 0 ~ ~ ~ 0 10 t ~ ~ ~ ~ 0 ~ ~ ~ 0 ~ 1 1 0 1 ~ ~ ~ ~ ~ f J 0 0 1 00PROBLEM TIME ANO TRIP TOLERANCE DATA

T TEND TRPTOL TRPEND0.0 40.0 0.005 40.0000001 11 ~ 0 0 ~ ~ ~ 01 ~ 1 ~ ~ ~ ~ 0 ~ ~ ~ 0 ff1 ~ f 0101 1 Jf 0001 0 0 f 00010

TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANC( OMIT THIS CARO IF NFLOW = 0 )

111 ~ 01110000 ~ 11 ~ ~ 1

OELFLO

~ 1 101 ~ ~ 111 1 1 1 ~ ~ ~ ~ ~ ~ 1 ~ ~ ~ ~ f ~ 11 00 ~ 01 t titfif001000101 0011011 01 1 ~ 11 ~ 1 1 01 100 f 0


I DEC TLAST TPRNT1 60. 2.0<1001000000000 ~ 0000 ~ ~ ~ 11100 ~ 00000 ~ fffffiiiiiittttttt00000000010000001011

EDIT DIMENSION CARO

~ i itNRED NSIED NS2ED

2 0 1~ 111 1110 1 1 0 ~ 0 ~ ~ ~ ~ ~ ~ 0 ~ ~ 1 ~ 000 ~ 00010 ~ 00111010001 ~ 01100 ~ ~ 11 ~ ~ ~ ~ 0110 10011


1 -1~ 11001000 0 0 0 0 0 0 0 1 ~ 0 0 0 ~ ~ 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 '1 0 0 0 0 0 0 0 t 0 0 0 t 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0


1

~ 111 1 0000 00J ~ 100 ~ 00000001 ~ 01 ~ ~ 00 ~ 1 10000101010000000000100111100010tiiiifEDIT CARDS FOR THIN SLABS

~ 111 0 0000 0 ~ ~ ~ 1 ~ 011001 10 ~ ~ ~ ~ 0 f 0 1 0 0 10 10 iff t010100 JfREFERENCE PRESSURE FOR AIR FLOWS


01101 1 111111 1 ~ 11f 000011

TREF PREF

y J 0 0 J 0 00 0 ~ 11111 ~ 111 ~ ~ 11111 ~ iii~ 110111 ~ ~ 1110110110 ~ 00 ~ ~ 1111111111111011 ~ 0


IDROOM1 1

~ 1 tifVOL PRES TR RELHUM RM HT

0000. 14.7 100.0 0.5 10.0~ 1 ~ ~ 1 ~ 1 10 ~ ~ 01 ~ 11 ~ 11110 ~ JiiffJifiiiiiiiii

A IR FLOW DATA CARDS( OMIT THIS CARD IF NFLOW = 0 )

~ 11111 1 Jit ~ 011 0 11 0 01011

IDFLOWf

IFROM ITO VFLOW

LRMIARLEAK

IOFTRP KFTYPI

0 0 1 ~ 1 1 0 ~ t 0 1 0 0 0 0 0 0 0 1

s 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 ~ t 0 0 0 t 1 1 0 1 1 t 1 ~ 1 1 1 1 ~ ~ 1 ~ ~ 0 1 1 0 0 0 0 0 0 0 ~ 0 1 1 0 ~ ~ ~ 1 1 0 1 1 ~ 1 1 1 0 0 1 1 ~ 0

LEAKAGE PATH DATA( OMIT THIS CARD IF NLEAK = 0 )

0

IOLEAK AKLEAK LRM2 LD I RN0

~ t 0 1 0 0 1 1 0 0 0 0 1 t 1 0 1 0 0 0 0 0 ~ 0 0 0 0 1 1 0 0 0 0 0 0 t 0 0 ~ 0 0 0 0 0 0 0 0 0 t 0 0 1 1 1 0 0 1 0 1 ~ 1 0 0 0 ~ 1 0 0 ~ 1 0 ~

AIR FLOW TRIP DATA

KFTYP2 FTSET IDFP

s 1 1 1 1 1 0 ~ ~ 0 0 t 0 t ~ 0 1 ~ ~ 0 0 ~ 0 0 0 ~ 0 ~ ~ ~ ~ ~ 0 0 0 0 ~ 0 0 0 0 0 ~ ~ 0 1 ~ 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 ~ ~ 0 0 1 1 0 ~ 0

HEAT LOAD DATA CARDS

IDHEAT NUMR ITYP QDOT TC WCOOLI I 2 1000. -1. 0.2 I 3 1000. —1. 0.3 I 3 3000. -1. 0.4 I 8 2000. - I . 0.

0 1 1 e ~ 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 0 ~ 0 0 0 0 ~ 0 ~ ~ 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 10 0 0 1 0 1

PIPING DATA CARDS

IDPIPE IPREF POD PID AIODN PLEN PEM AINK PTEMP IPHASE

s 1 0 0 1 0 1 0 ~ 1 ~ 0 0 1 1 1 1 0 ~ ~ 1 1 1 0 1 ~ 0 ~ ~ 1 0 ~ 0 0 1 0 0 0 1 0 0 0 0 0 00 0 1 ~ 0 0 0 0 ~ 1 1 ~ ~ 1 0 1 1 1 1 0 1 0 0 1 1 1 0

HEAT LOAD TRIP CARDS

IHREF ITMO TSET TCONI 2 1.0 0. 0 TRIP ONI I 5.0 0. 0 TRIP OFF2 I 10. 0 0. 1 TRIP OFF3 2 15. 0 0. 1 TR I P ON4 I 20.0 5. 0 EXPON DECAY

0 1 0 0 0 01 0 0 0 t 1 1 0 1 0 1 0 ~ 1 ~ 0 ~ 0 0 0 1 0 0 0 0 0 ~ ~ 0 ~ 0 0 0 0 0 0 1 ~ 1 1 0 0 t ~ 0 0 1 1 0


~ I DTR I PI2345

1111110000100

0

IDBRK IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMPt11110110

e

IDSLB I IRM20

i 1 1 1 1 1 1 ~ 0 0 ~ ~ 0 1 ~ ~ ~ 0 0 0 ~ 0 1 ~ 0 0 ~ ~ 0 0 0 ~ 0 ~ t 0 0 0 0 0 0 0 0 0 1 ~ 0 0 0 ~ 1 1 1

0 THICK SLAB DATA CARD (CARO 2 OF 3)

IDSLB1 AREAS I AKS1eeteetee0

0

IDSLB I HTC2(2)

111111111

e

IDSL82'I

10110

1 0 0 0 1 0 0 1 1 0 0 t t 0 ~ 0 0 ~ ~ ~ 1 0 ~ ~ 1 ~ ~ ~ ~ 1 ~ ~ 1 1 1 0 0 0 0 1 0 1 1 ~ 0 0 ~ 0 1 ~ 1 1 0 0 t 0 0 ~ 0

THICK SLAB DATA CARD (CARD I OF 3)

ITYPE NGRID IHFLAG CHARLIRMI~ ~ 0 ~ 1010101000

ROS CPS EMISALS

1 0 1 1 0 1 0 0 1 0 ~ 1 1 ~ 1 1 1 t ~ ~ ~ ~ 1 1 ~ t ~ 0 0 0 0 0 0 0 0 0 0 ~ 0 0 1 0 0 t t 1 0 1 t 1 1 0 1 ~ 1 ~ 0 0 0 1 0 ~

THICK SLAB DATA CARD (CARD 3 OF 3)

HTCI (I) HTC2(1) HTCI (2)

JRMI JRM2 JTYPE AREAS2I -I I 500.

~ ~ 1 0 1 1 1 ~ 1 ~ ~ 1 1 ~ ~ ~ 1 1 1 1 ~ 1 ~ 1 1 ~ ~ ~ ~ ~ ~ 1 1 1 1 1 0 0 1 ~ 1 1 ~ 1 1 1 ~ ~ ~ 0 0 0 0 0 0 0 0 0 I~ 1 1 0

THIN SLAB DATA CARO (CARO 2 OF 2)1eetttteee

1 1 0 1 1 0 0 0 0 ~ 0 0 ~ 1 ~ 1 ~ 0 1 0 1 1 ~ 1 0 t 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 ~ 0 1 0 0 ~ 0 1 0 ~ 1 1 1 0 1 ~ ~ ~ 1 0 0 ~

THIN SLAB DATA CARD (CARO I OF 2)

UHT(2)~ IOSL82 UHT( I )I 0.33

1 ~ 11111111 ~ 1 ~ 1 ~ ~ ~ ~ 1 ~ ~ ~ ~ 1 ~ 1 ~ ~ 1 ~ 1 ~ 11 ~ 11 ~ ~

TIME"DEPENDENT ROOM DATA

0 IDTDR MFLG NPTS TDRTO-I 1 3 0.0teteeeeeeee ~ 11 ~ 11 ~ ~ ~ 1 ~ 1 ~ 0111111 ~ ~ 1

AMPLTD0.0

~ ~ 1 ~ ~ ~ 11 ~ 0 ~ 110

FREQ0.0001111 ~ 1 ~ 01111

1 1 1 ~ 1 1 0 ~ 1 ~ 1 ~ ~ 1 1 1 1 1 1 1 1 1 ~ 1 1 1 1 1 1 1 1 1 1

I II I DR IT I ME

I ~ERS~ls vEMPg+URF+f A

T1EMP RHUM PRES

-1 0.00 100.0 0.50 14. 7050.00 100.0 0.50 14. 70

100. 00 100. 0 0.50 14. 70I 0 0 4 0 4 4 t 4 4 4 0 4 4 4 4 t 4 4 0 t 4 t 4 4 4 4 4 4 4 ~ 4 0 0 0 4 0 4 ~ 0 4 4 4 0 4 4 4 4 0 4 0 4 0 0 4 4 4 4 0 0 4 4 0 4 4 0 4 4 4 4 0 4l ~ 0 ~ i ~ 1 0 ~ ~ ~ 0 4 l 1 t 1 4 4 0 4 0 4 4 0 4 4 4 ~ ~ ~ ~ ~ ~ ~ 0 i ~ 0 0 4 0 4 4 4 4 4 ~ i ~ 0 0 4 1 ~ 4 t 0 ~ 1 ~ i f ~ 0 1 f 4 1 1 1 I

FIGURE 4.6 COMPARISON OF COTTAP CALCULATED COMPARTMENTTEMPERATURE WITH ANALYTICALSOLUTION

FOR SAMPLE PROBLEM 2135

130

OO

OIJJ

~l—

125

120

115

110

105

LegendANALYTICAL

~ COTTAP

10010 20

TIME (hr)30 40

pp&L Form 24&a n Dry)Cat. a973401

$F. -Q N A =04 6 Rev.0g

Dept.

Date 19

Designed by

Approved by


CALCULATIONSHEET

The walls of the compartment consist of 3 slabs: a vertical wall

(slab 1), a ceiling (slab 2), and a floor (slab 3) which is in contact

with the outside ground. The temperature, relative humidity, and pressure

within the time-dependent compartment are held constant throughout the

transient. The COTTAP input data file for this problem is shown in

Table 4.4. The COTTAP results for this problem are given in Figure 4.7.

4.4 COTTAP Results for Com artment Heat-U Resultin from a High Energy

Pi e Break (Sam le Problem 4)

A high energy pipe break is modeled using a standard COTTAP compartment

that is connected via a leakage path to a time dependent volume. The pipe

break is initiated in the standard compartment at time 0.5 hr and is

terminated at time 2.5 hr. The time dependent volume is maintained 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 1100 PRINTED 89304.0951OSNAME=EAMAC.COTTAP.SAMPL3.DATAVOL=OSK533

COTTAP SAMPLE PROBLEM 3400140 ~ 0000 ~ t000040404001100 ~ 40 ~ 0000 ~ 0000 ~

PROBLEM DESCRIPTION DATA ( CARO 1 OF 3

I NROOM NSLA81 NSLA82 NFLOW NHEAT NTDR NTR1 3 0 2 1 1 1I I I ~ ~ I 4 4 I I I I I 4 ~ I I I I ~ 4 4 ~ 4 I 4 4 I ~ I ~ I I ~ I ~ II II I 4I PROBLEM DESCRIPTION DATA ( CARD 2 OF 3I

I I I ~ I 4 4 I I I 0 0 I I I I I ~ I I I I I I I I 4 4 4 I

IP NPIPE NBRK NLEAK NCIRC NEC0 0 1 1 8I 4 I 4 II 4 I I I I ~ 4 ~ I I I 4 4 4 I 4 ~ 4 4 4 4 4 I 4

)

1 INPUTF IFPRT RTOL1 1 1.0-5

~ I I I I ~ I 4 I I ~ I I 4 I II I 4 4 I ~ I I I I ~ I I)

I NFTRIP MASSTR MF CPI CP2 CR5 1 10 2. 04 150. 5I I I I I I I I ~ I I ~ I ~ I ~ I t t I ~ 0 ~ I I ~ I I I I III 0 I I I I I 4 I 0

PROBLEM DESCRIPTION DATA ( CARD 3 OF 34 NSH

101010000044

4

TFC1.D-5I I I I I I t I ~ 4 ~ I ~ I I ~ I 4 I 4 0 0 I I 4 I I ~ t ~ I I I I I ~ I I 4 I I I I 4 ~ I 4 I ~ I 4 ~ ~ I I 4 4 I I I I I

PROBLEM TIME AND TRIP TOLERANCE DATA

1144

I4

T TEND TRPTOL TRPENO0.0 3.0 0.005 3.04 4 I I I I ~ I I I I ~ ~ I 'I I ~ I 4 I 4 I ~ 4 I I ~ I ~ I I ~ 4 ~ I ~ I I ~ 4 ~ ~ ~ I 4 ~ 4 I I ~ I 4 I ~ 4 I I 4 4 I 4 4 4 4 I 4 I I ~

TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE( OMIT THIS CARD IF NFLOW = 0 )

,DELFLO1.0-5

I I I~ I I ~ 4 4 ~ I I ~ I I ~ I I ~ ~ I I~ I I 4 I I I~ ~ I I 4 ~ ~ I ~ I~ ~ ~ I I~ I I ~ ~ ~ I I ~ ~ I I I ~ ~ ~ I I ~ I I I 4 I~ 4 4 I I I ~EDIT CONTROL DATA CARDS

414II044I4

1

1044I

1

444I4I111

1I

TLAST0.11.0I. 1

2.2.2

10. 024.0

500.000014014

TPRNT0.010. 100.010. 100.010. 100.205.00I 4 4 I 4 ~ ~ I I I I ~ I ~ ~ I I I I I 4 I I I I 4 ~ I I ~ 4 4 I ~ I I I 4 ~ I I I I I 4 I 4 I I 4 I I I 4

EDIT DIMENSION CARD

IOEC1

2345678

4110000

NRED NS IED NS2EO2 2 0

4 ~ I 4 t I 4 I 4 1 I I I I 0 ~ ~ I 4 I I t I 4 I ~ ~ I I I I I ~ ~ 4 I I I 4 ~ I ~ I I I I ~ I I ~ 4 I I 4 I ~ I I I 4 I I I I ~ I I 4 IROOM EDIT DATA CARO(S)

2I I I ~ ~ ~ ~ I ~ I ~ I t 4 t I I I I ~ I I 4 4 I 'I I I I I 4 I I 4 I I I I ~ I t I ~ I 4 I I I ~ I I ~ I t I I 4 I 4 I I ~ I I I I 4 I IEDIT CARDS FOR THIN SLABS

~ ~ I I ~ I I I I ~ I ~ I I I I I ~ 4 I ~ I I I I I I ~ I I I ~ I I I 4 I ~ I I ~ I ~ I I I ~ I ~ I I I I I I I ~ I I I I I I I I I 4 I ~REFERENCE PRESSURE FOR AIR FLOWS


-1I ~ I ~ ~ I~ I I 4 I 4 ~ ~ ~ ~ I ~ I 4 4 I ~ I 4 I I I ~ ~ ~ I~ ~ I 4 4 4 4 I 4 I I ~ I I ~ I ~ 4 4 I I I ~ I I ~ ~ I I I I I III 4 4 I 4 I I I


(g) A

A

'0p

ICOI

TREF100.

00 ~ 1000001

NOT INCLUDE TIME-DEPENDENT ROOMS)

NIOM )L ~ 'IUM HT

PREF14.7I I I 4 I I I I I I I I I ~ 4 I I I I I t I ~ I I 4 0 I ~ 4 I I 4 I I I I ~ 1 I I ~ ~ I I 4 4 I I I I

ROOM OA1'A CARDS

tttttt

ttttttt

IDFLOW "I FROM I TO VFLOW1 -1 " 1.04 FAN2 1 -1 1.04 FANttttttttttt~ tttttttttttttttttttttttttttttttttttttttttt

hatt

LEAKAGE PATH DATA( OMIT THIS CARO IF NLEAK = 0 )

tttttttttttt

IDLEAK ARLEAK AKLEAK LRM1 LRM2 LDIRN1 1.0 -1. 0 1 2ttttttttttttttttttttttttttttttttttttttttttttttttt~ ttttttttttttttttttt

CIRCULATION PATH DATA

30000. 14.7 80.0 0.5 27.5tttttttt~ ttt ~ tttt ~ ttttt ~ ttttt ~ ~ t ~ tt ~ ttttttttttttt~ tttttttttttftttttttAIR FLOW DATA CARDS

( OMIT THIS CARO IF NFLOW = 0 )

IOCIRC KRM1 KRM2 ELEV1 ELEV2 ARIN AROUT AKIN AKOUT1 1 -1 3. 12. 50. 50. 5. 5.t t t t t t t t t t t ~ t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t

AIR FLOW TRIP DATA

ET IDFP0 1 t TRIP CIRC FLOW OFF AT START0 1 t TRIP FAN OFF0 2 t TRIP FAN OFF0 1 t TRIP LEAKAGE PATH OFF0 1 t START NATURAL CIRCtttttttttttttttttt~ tttttttttttttttttt

TC WCOOL-1. 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

DS

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 tCARDS

IDFTRP KFTYP'I KFTYP2 FTS1 3 1 0.2 1 1 'I .3 1 1 1.4 2 1 2.5 3 2 2.t t t t t t t t t t t t t t t t t t t 1 t t t t t t t t t t t t t t t

t HEAT LOAD DATA CARDStIDHEAT NUMR ITYP QOOT

1 1 3 100000.tttttttttttttttttttttttttttttttttttt PIPING DATA CAR

IOPIPE IPREF POD PID AIOON PLEN PEM AINK

t t t t t t t t t t t t t t ~ t t ~ t t t t t t t t t t t t t t t t tHEAT LOAD TRIPt

t IOTR1

tIDBRK

ttttttttIDSL81

1

23tttttttt

tIOSL81

1

23tttttttt

tIDSL81

1

2t t tt t t

IP IHREF ITMD TSET TCON1 1 10. 0 0.t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t ~ t t t t t t

STEAM LINE BREAK DATA CARDSt t t t ~ t t t t t t t t t t t t t t t t t

IBRM BFLPR IBFLG BDOT TRIPON TRIPOF RAMP

t t t t t t t t t t t t t t t t t ~ t t t t t ~ t t t t t t t t t t t t t t t t t tTHICK SLAB DATA CARD (CARO 1 OF 3

t t t t t t t t t t t t t t t t t t t t t t

IRM11

1

1ttttttttALS3.02.04.0ttttttt ~

AREAS1 AKS ROS CPS EMIS3800. 1.0 140. 0.22 0.80

960. 1.0 140. 0.22 0.80960. 1.0 140. 0.22 0.80ttttttttttt~ ~ t ~ t ~ ~ ttttt ~ tttttttttttttttttt~ tttt ~ tttttt

THICK SLAB DATA CARO (CARD 3 OF 3)HTC1 (2) HTC2(2)HTC1 ( 'I ) HTC2( I )

3.73.7tt ~ ~ ttt ~ t ~ t ~ ~ tttttttttttt~ tt ~

THIN SLAB DATA CARD

3.t t t t t t t t t t t t t(CARD 1 OF 2)

t t t t t t t t t t t t t t t t t t t t t t

I RM2 ITYPE NGRID IHFLAG CHARL-1 1 10 2 30.-1 3 10 2 30.

0 2 10 0 30.ttttttttttttt~ tt ~ ~ ~ ~ tt ~ tt ~ ~ t ~ ttttttttt~ t ~ ttttt ~ tttttttttTHICK SLAB DATA CARO (CARD 2 OF 3)

1RM1 JRM2 JTYPE AREAS2

4444444

4

444444

IDT-1

4444444

IOT-I

4444444444

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ ~ 4 ~ 4 ~ 4 4 4 4 4 ~ 4 4 4 4 4 4 4 4

THIN SLAB DATA CARD (4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4CARO 2 OF 2)

IOSL82 UHT(1) UHT(2)

DR

44444444IRMFLG NPTS TDRTO AMPLTD FREQ

1 4 80.0 0.0 0. 00 4 OUTSIDE AIR4 ~ 4 ~ 4 4 4 4 ~ 4 4 4 ~ ~ 4 4 4 4 4 4 4 4 4 4 ~ ~ ~ 4 ~ ~ ~ 4 4 4 ~ ~ ~ 4 4 ~ ~ 4 ~ 4 4 4 4 4 4 4 4 ~ ~ ~ ~ 4 ~ 4 ~


OR TT01

25

4444444444

I ME TTEMP RHUM.00 80.0 0.50.00 80.0 0.50.00'0.0 0.50.00 80.0 0.5044444444444444444444 '444444 ' ~ 4444444444444 ~ ~ 4 ~ 4 ~

PRES14. 7014. 7014. 7014.70

~ 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ 4~ 4 ~ 4 4 4 4 44 4 ~ 4 ~ 4 4 ~ ~ 4 4 4 4 ~ 4 4 4 4 4 ~ 4 4 ~

444444444444444444 '44 ' ~ 4444444444444444444444444444444444444 '444TIME-DEPENDENT ROOM DATA

figure 4.7 COTTAP TEMPERATURE PRORLE FOR SAMPLE PROBLEM 5

100

U)

I—

I—

OO

OLLICL

I—ELLIJCL

LLII—

95

90

85

800 0.5 1.5

TIME (hr)2.5

TSO FOREGROUND HARDCOPY 0 0 0 0 PRINTED 89285. 1301DSNAME=EAMAC.COTTAP.SAMPL4.DATAYOL=DSK540

COTTAP SAMPLE PROBLEM 40000000000000 ' 0000 ' ~ 0000000 ~ tttt ~ 000000 '00000000000000000000000000000

PROBLEM DESCRIPTION DATA ( CARO 1 OF 3 )

NROOM NSLABI NSLA82 NFLOW NHEAT NTOR NTRIP NPIPE NBRK NLEAK NCIRC NECI 3 0 0 0 1 0 0 1 1 0 60 0 0 0 0 0 0 t 0 0 0 t 0 0 ~ ~ 0 0 ~ 0 0 0 0 0 ~ ~ 0 0 0 0 0 ~ ~ ~ ~ 0 ~ 0 ~ 0 0 0 ~ 0 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 ~ 0


NFTRIP MASSTR MF CP1 CP2 CR I INPUTF IFPRT RTOL0 I 13 5.D4 150. 50. I I 1.0-5tttttttttttttttttttttttttttttttttttttttt~ 0 '0000000000000000000000000000

0 PROBLEM DESCRIPTION DATA ( CARD 3 OF 3 )

0 NSH0

0 000000000

TFC1.0-5

0000000000000000000000tttttt0'0000 F 000000000000 F 0000000000000PROBLEM TIME AND TRIP TOLERANCE DATA

T0.00000000000 F 000

TOLERA( OM

0

OELFLOI.D-5

0000000000000

'END, TRPTOL TRPEND

6.0 0.005 6.00000000 ~ 0 ~ 0 ~ ~ 0000000000 'tttttttttttttttttttttttttttttttttNCE FOR COMPARTMENT-AIR-FLOW MASS BALANCEIT THIS CARO IF NFLQW = 0 )

~ 0 0 0 0 0 0 0 0 0 0 ~ ~ 0 0 ~ 0 ~ 0 0 0 0 0 ~ 0 ~ 0 0 0 0 0 0 ~ 0 0 0 0 t 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


'pt

IDECI23456

0000000000

TLAST TPRNT0.5 0. 100.6 0.0052.5 0. IO2.6 0.0056.0 0.20

25.0 0.5000 ~ 0 ~ ttt ~ 00000000 ~ 00 F 0000000000000000'0000000000000000000000000

'DITDIMENSION CARD

NRED NS I ED NS2ED2 3 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \ ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 t 0 0 00 ROOM EDIT DATA CARD(S)

I -I0 ~ 0 0 0 0 ~ ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ~ t 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 ~ ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


I 2 3000000000000000000 F 0000 '00 F 000000000000 ~ tttttttttttttttttt~ ~ 000000000000 ED I T CARDS FOR THIN SLABS

0 0 0 0 0 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 0 0 t 0 0 0 0 0 0 0 0 0 0 0 ~ 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 ~ t 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 t 00 REFERENCE PRESSURE FOR AIR FLOWS0 (OMIT THIS CARD IF NFLOW00)0

TREF PREF0 100. 14. 7

0 0 0 0 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 t ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 0

ROOM DATA CARDSNOT INCLUDE TIME-DEPENDENT ROOMS)

IDROOM PRES TR RELHUM RM HT

ICD

CD

CD

CC)

4

4 I DFLOW VFLOW

44444444444444444444444tttt ~ 444444444444444tttt ~ 444444444444444444444444 LEAKAGE PATH DATA

( OMIT THIS CARD IF NLEAK = 0 )4

I FROM I TO

ITMD TSET

AREAS I AKS1000. 1.00800. 1.00800. 1. 00

CPS EMI S0.22 0.800.22 0.800.22 0.80

4 IDLEAK ARLEAK AKLEAK LRMI LRM2 LDIRN1 1.0 -1.0 I -I 2

4 4 4 4 4 4 4 4 4 4 4 4 4 t 4 4 4 4 4 4 4 4 4 4 t tt 4 t t 4 4 ~ 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 t t 4 4 ttCIRCULATION PATH DATA

4IOCIRC KRMI KRM2 ELFV1 ELEV2 ARIN AROUT AKIN AKOUT

4 4 4 4 t 4 4 4 4 4 4 4 4 4 4 4 4 4 t t 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 t 4 4 4 t 4 4 t 4 4 4 4 t 4 4 4 4 4 4 4 4 t 4 4 4 4 t 4 4 4 4 4 4 4 ~

AIR FLOW TRIP DATA4

IDFTRP KFTYP1 KFTYP2 FTSET IOFP

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 t 4 4 t 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ t 4 4 4 4 4 t 4 ~ 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ ~ 4 4 4 4 4 ~4 HEAT LOAD DATA CARDS

IDHEAT NUMR ITYP QDOT TC WCOOL

4 4 4 4 4 4 4 4 4 4 4 4 4 t t 4 4 4 t 4 t 4 4 4 t 4 4 4 4 t4 4 4 4 4 4 4 4 4 4 t 4 4 4 4 t 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 t 4 4 4 4 4 4 4 4 44 PIPING DATA CARDS4

IOPIPE IPREF POD PID AIOON PLEN PEM AINK PTEMP IPHASE44 4 4 S 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 t 4 4 4 4 4 4 4 t 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 4 4 4 4 4 4 4 4 t 4 4 4 4 44 HEAT LOAD TRIP CARDS

I DTRIP IHREF TCON44 t 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 t 4 t 4 4 4 ~ 4 4 4 4 t 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 4 t 4 4 4 4 4 4 4 4 ~ 4 4 4 4 4 4 4 4 t t 4 4 4


IOBRK IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMPI I 1000. 2 1800. 0.5 2.5 0.544444444444444 '4444444tttttttt ~ 444444444444ttt44 ~ 444444444t4444444444t4

THICK SLAB DATA CARO (CARO 'I OF 3)IDSLBI IRMI IRM2 I TYPE NGR ID IHFLAG CHARL

I I -I I 15 2 0.2 1 0 2 15 D 0.3 I -1 3 15 2 0.

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 4 4 4 4 4 4 4 4 ~ 4 4 ~ ~ 4 4 4 4 4 4 ~ 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 4 4 4 4 \ 4 4 4 4 4 4 4 4THICK SLAB DATA CARO (CARO 2 OF 3)

IOSLBI ALS ROSI 2.75 140.2 4.00 140.3 2.75 140.

HTC2(2)

IDSL82

t t t t t t t t t t t t t t t t t t t t 't t 't t t t t t t t t t ~ t t t t t t t t t t t t 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 THICK SLAB DATA CARO (CARO 3 OF 3)

IDSL81 HTC1 ( 1) HTC2 ( 1) HTC1 (2)1 0.63 0.9 0.4t t t t t t t t t t t t t t t t t t t t t t ~ ~ t ~ ~ t t t t t t t ~ ~ t t t t t t t t t t t t t t t t t t t t t t tt t t t t ~ t t t ~ t t t

THIN SLAB DATA CARD (CARD 1 OF 2)tI DSL82 JRM1 JRM2 JTYPE AREAS2t

t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t ~ ~ t t t t t t t t t t t t t t ~ t t t ~ t t t t t t t t t t tTHIN SLAB DATA CARO (CARO 2 OF 2)

t UHT( I ) UHT(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 tt TIME-DEPENDENT ROOM DATAt

I DTDR IRMFLG NPTS TDRTO AMPLTD FREQ-I 1 3 0.0 0.0 0.00 t OUTSIDE AIRtttt ~ ttt ~ tttttttttttttttttttttt~ ttttttttt ~ ttttttttttttttttttttttttttttttt TIME VERSUS TEMPERATURE DATA

J

t I OTDR TTIME TTEMP RHUM PRES-1 0.00 95.0 0.60 14.7

10.00 95.0 0.60 14. 750.00 95.0 0.60 14.7ttt ~ tttttttttttttttt ~ tttttttttttttttttttttt ~ ttttt ~ ~ ttttttttttttttttttttt It t t t t ~ t t t t t t t ~ t t ~ t t t t ~ t t t t t t ~ t t t t t t t t t t t t t t t t t t t t t t ~ t ~ t t t t t t t t tt t t t ~ t t t t

FIGURE 4.8 COTTAP TEMPERATURE PROFILE FOR SAMPLE PROBLEM 4

180

CA

I—

I—CL

OOzLdCL

I—ELLxlCL

160

140

120

100

803

TIME (hrs)

PP4L Farm 2wR {10r83)CN. l973401

$E -8- N P-0 4 6 Rev. OJ.

Dept.

Date 19

Designed by

Approved by

PROJECT Sht. No. LLg of


4.5 COTTAP Results for Com artment 'Heat-u from a Hot Pi e Load (Sam le

Problem 5)

This test problem consists of a standard COTTAP compartment that contains

a large hot pipe and a room cooler. A COTTAP leakage path, which allows

flow between connected rooms when a pressure differential exists, links

the standard compartment to an infinitely large compartment. The large

compartment maintains steady pressure in the connected compartment.

The hot pipe being modeled contains steam at a constant temperature ofr

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 4444 PRINTED 89285.1403OSNAME=EAMAC.COTTAP.SAMPLS.DATAVOL=OSK536

COTTAP SAMPLE PROBLEM 5444444444444ftff44444444444444444444444444444444PROBLEM DESCRIPTION DATA ( CARD 1 OF 3 )

NROOM NSLABl NSLAB2 NFLOW NHEAT NTOR NTRIP NPIPE2 0 0 0 2 0 1 1

44 4 4 ~ 4 4 4 ~ 4 4 t t444 4 ~ 4 tf ~ ~ 4 4 4444444444444444 tf ~ 4 ~ 4 4 4 4PROBLEM DESCRIPTION DATA ( CARO 2 OF 3 )

4

NFTRIP MASSTR MF CP1 CP2 CR1 INPU0 I 23 5. 04 150. 10. 1

4 4 44 4 4 4 4 4 4 4 4 4444 4 4 4 4444 4 4 4 4 t4 4 t44 4 44 t4 4 4 4 444444444PROBLEM DESCRIPTION DATA ( CARO 3 OF 3 )

4 44444 4 444444444444 4 44

NBRK NLEAK NCIRC NEC0 1 0 1

4 44 4 4 44 444% ~ 44444 ~ ~ 4 4 t

TF IFPRT RTOL1 1. D-5

4444444444t44t4444444

NSH0

444 4 4 444 ~ ~

TFC1. D-5

4 444444 444 4 44 44 4 44 4 44 4 4 44 444 44 44444 44444PROBLEM TIME AND TRIP TOLERANCE DATA

4 4 44 4 4 4 4 4 ~ ~ 44 4 44 444 44 ~

T0.0

4 4 44 ~ tf 44 TO4

DELFLO1.0-5

44444444 ~ ~

4

TEND4.044444fffftft

LERANCE FOR( OMIT THIS

4 4 ~ 4444444 44EDI

TRPTOL TRPEND0.05 4.0

44444444444444444444444 'ftf444444444444COMPARTMENT-AIR-FLOW MASS BALANCECARD IF NFLOW = 0 )

4 4 4 4 4 4 4 4 4 4 ~ ~ f 4 4 4 4 t t4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 4 4 4 4 t 4 ~ t 4 4 4 4

T CONTROL DATA CARDS

TLAST TPRNT25.0 0. 10

4 4 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 4 4 4 4 4 4 4 4 tf 4 4 4 4 4 4 4 4 4 ~ 4 4 ~ 4 ~ 4 4 4 4 4 4 4 4 t 4 4 t 4 4 4 4 4 4 4 4 4

EDIT DIMENSION CARO

IDEC1

44 44 444 4 4 4

4

4 NREO NS1ED NS2ED2 0 0

4 4 4444 44 ~ 4 ~ 4 f 444 4 4444 ttftf t tf4 4 4 4 4 44 4 444ttf 4444ROOM EDIT DATA CARD(S)

4 4 t44444 ~ 4 4 44444444 ~ ~ 44 44

1

44 4

44444

44 444

44fft44

I

444 4 444 f 4444 44 4444444 444 44444444444444 444 4 4 4444 4 ~ 44t4444444444 4444444EDIT CARDS FOR THIN SLABS

4 4 4 ~ 4 44 444 44444 4 4 t4 4 4 4 44444444 444 4 4 4 4 44444444 4 444 4444 444 4 4 4 444444 4 4 4 4

REFERENCE PRESSURE FOR AIR FLOWS(OMIT THIS CARO IF NFLOW=O)

PREF14.7

4 4 4 ~ 4 4 4 4 4 4 4 4 44 4 4 4444444 4 4444 ~ 4 4 44 44 44 44 ~ 4


TREF100.

~ fffff ~ ~ 4 4 4 4 4 ~ ~ 444 4 4 444444 44

DROOM VOL PRES TR RELHUM RM HT\ 10000. 14.7 100.0 0.5 10.02 1.015 14.7 100.0 0.5 10.0

4444 4 4 4 44 4t 4 4 t444 4 t f 4 444 t4444 4 4 4444 44 44 4 4 44 444 4

AIR FLOW DATA CARDS( OMIT THIS CARO IF NFLOW = 0 )

444444444444ffffffffff414

4

4

1 OF LOW I FROM I TO VF LOW

24 4444 444 ~ 4 444444 tf444ttf 4 4 4 44 4 4 444444tf 44 44444 4 ~ 4 44444444 44 4 4 444444f 4

EDIT CARO(S) FOR THICK SLABS

AREAS2

I RMF LG TDRTO

TTEMP PRES

IDSLB2 JRMl JRM2 JTYPEtt t t t t t t t t t t t t t t t t t t t ~ t t t t t t t t ~ t t t t t t t t ~ t ~ t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t

THIN SLAB DATA CARD (CARO 2 OF 2)tIDSLB2 UHT ( 1 ) ~ UHT (2)

tttttt ~ ttttttttttttttttttttt~ ~ tttttttttttttttttttttttt~ tttttttttttttttttt TIME-DEPENDENT ROOM DATA

IDTDR NPTS AMPLTD FREQtt t ~ t t t t ~ t t t t t t ~ t t t t t t t t ~ ~ t ~ t t t t ~ ~ t ~ t t t t t 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 TIME VERSUS TEMPERATURE DATA

t I OTDR TT I ME RHUMtt t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t ~ t t t t t t t~ t t t t t t t t ~ t t t ~ t t ~ t t t t t t t ~ ~ ~ t t ~ ~ t ~ t t ~ t t t ~ t t t t t t t t t ~ t t t t t t 0 t ~ t ~ t t t ~ ~ t 1 t t t t

K ARLEAK AKLEAK LRMI LRM2 LOIRN'I . 0 -1.0- I 2 I

~ t t ~ t ~ ~ t t t t t ~ ~ t t t ~ t t t ~ ~ t t t ~ t t ~ t t ~ t ~ t ~ t ~ ~ t t t ~ t t t t t t ~ ~ .t ~ t t ~ t t ~ ~ t ~ ~CIRCULATION PATH DATA

I OLEAIttttt

t t t t t t t t t t t t t t t t t t ~ t t t t ~ t t t t t t t t t ~ t t t t t t t t t t t t t t t tt t t t t ~ ~ t t t t t t t t t t t t t t tLEAKAGE PATH DATAt ( OMIT THIS CARD IF NLEAK = 0 )

t

IDCIRC KRMI KRM2 ELEVI ELEV2 ARIN AROUT AKIN AKOUT

tttttttttt

I

IDFTRP KFTYPI KFTYP2 FTSET IDFP

tttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttHEAT LOAD DATA CARDS

DHEAT NUMR ITYP QDOT TCI 1 4 -20000. 75.2 I 5 0. DO -1.t t t t t t t t t t t t t t t t t t t t t t t t ~ t t t t t t t t t t t t t

PIPING DATA CARDS

WCOOL2000.

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 t t t t t t t t t t t t t ~ t t t t t t t t t t t t t t t t t t tAIR FLOW TRIP DATA

OPIPE IPREF POD PID AIODN PLEN PEM AINK PTEMP IPHASEI 2 20. 19. 24. 50. .85 .05 550. Ittt ~ ~ ~ ~ ~ ~ ~ ~ tttttttttttttttttt~ tttttttttttt ~ ~ t ~ t ~ ttt ~ tt ~ ttttt ~ ~ ~ ttt ~ tt

HEAT LOAD TRIP CARDS

IOTRIttttttt~

IDBRK

ttttttttt

IDSLB Ittttttttttt

I OSLB I

tttttttttt IDSLB I

tttttttt

IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP

tttttttttttttttttttttttttttttttttttttttttt~ tttttttttttttttttttttTHICK SLAB DATA CARD (CARD I OF 3)

IRMI IRM2 ITYPE NGR ID IHFLAG CHARLt t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t ~ t t ~ t t t t t t t ~ t t t t t

THICK SLAB DATA CARO (CARD 2 OF 3)ALS AREASI AKS ROS CPS EMI S

t t t t t t t t t ~ ~ t t t ~ ~ ~ t ~ ~ t t t t t t t t t t t t t t t t t t t t t t t t t t t t ~ ~ t t ~ t t t t t t t t ~THICK SLAB DATA CARD (CARD 3 OF 3)

HTCI(I) HTC2(1) HTCI(2) HTC2(2)t t t t t ~ t t t t t t t t t t ~ ~ ~ t t t t t t t t t t t t t t t t t t t ~ t t t t t t ~ t t t t t t t ~ t t t t t t t t

THIN SLAB DATA CARD (CARO I OF 2)

IP IHREF ITMD TSET TCON2 I l. -It ~ ~ t t t tt t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t ~ t ~ t t t t t t t t ~ t t t t t t t t t ~ t t


I

oaCD

C)

FIGURE 4.9 COTTAP TEMPERATURE PROFILE FOR SAMPLE PROBLEM 5

120

115

110I—CLLIJCL

EJJI—105

1002

TIME (hr)

ppdL Form 2454 n0/831C«L «913401

SE -B- N A:-0 4 6 RL".0 >

Dept.

Date 19

Designed by

Approved by

PROJECT Sht. No. JL7 of

I


4.6 Com arison of COTTAP Results with Anal tical Solution for Com artment

De ressurization due to Leaka e (Sam le Problem 6)

A compartment is initially at a pressure of 14.7 psia and a temperature

of 150 F. The initial relative humidity is set to 0.001 so that the0

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 0000 PRINTED 89286.1008DSNAME=EAMAC.COTTAP.SAMPL6.DATAVOL=DSK532

TFC1.D-5

0 0 ~ 4 1 ~ 0 4 ~ 1 1 0 t 0 ~ 0 0 ~ 4 0 0 ~ ~ ~ ~ 0 ~ 0 ~ t 0 1 ~ ~ 1 4 0 4 0 4 ~ 0 ~ t 0 ~ 1 ~ 0 4

PROBLEM TIME AND TRIP TOLERANCE DATA444 ~ ~ 101 ~ 1 ~ 01404140040

4

COTTAP SAMPLE PROBLEM 60 ~ 1 0 4 1 1 4 1 0 0 0 1 0 ~ 0 t 0 0 11 ~ 1 0 ~ 1 ~ ~ 4 ~ 0 ~ ~ 1 0 t 0 0 0 4 0 0 4 0 4 4 0 0 4 ~ 0 4 0 0 4 ~ 0 ~ 0 1 0 4 0 0 0 0 0 0 0 tt 4

PROBLEM DESCRIPTION DATA ( CARD 1 OF 3 )0

NROOM NSI.AB1 NSLAB2 NFLOW NHEAT NTDR NTR IP NP IPE NBRK NLEAK NCIRC NECI 0 0 0 0 1 0 0 0 I 0 3

0 0 ~ 0 0 0 ~ 0 0 0 \ 0 0 0 4 1 4 0 t t 0 0 t 0 0 1 0 0 0 0 t 0 0 ~ 0 0 0 0 ~ 0 0 0 0 0 4 0 1 4 ~ 0 4 t 0 0 0 0 4 4 1 ~ ~ ~ 1 ~ ~ 0 0 0 0 0 0 0

PROBLEM DESCRIPTION DATA ( CARO 2 OF 3 )0

NFTRIP MASSTR MF CPl CP2 CR1 INPUTF IFPRT RTOL0 1 23 5. D4 150. 10. 1 1 1. 0-5

0 1 1 0 0 0 4 0 0 0 0 1 0 0 0 0 ' 4 0 0 0 0 0 0 4 '0 0 0 0 0 ~ 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 4 0 4 0 4 0 1 4 0 ~ 4 0 0 0 0 4 0 0 0 4 0 0 0 4 0 0


4 NSH0

T0.0

0144101044

OELF~ 1.D-440144 ~ ~

1

TEND TRPTOL TRPEND0.2 0.005 4.0

0 0 4 4 4 4 1 4 4 1 4 4 0 4 1 1 4 4 0 0 0 1 0 4 4 0 0 0 1 0 4 0 4 0 0 4 4 0 4 1 4 4 1 0 4 0 1 0 ~ 4

TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE( OMIT THIS CARD IF NFLOW = 0 )

4 ~ ttt01440t044

LO54 0 ~ 4 4 0 4 4 4 4 0 4 0 4 1 0 ~ 1 ~ 4 4 0 0 ~ 0 ~ ~ ~ 0 10 0 0 0 0 4 4 4 4 0 ~ 0 1 ~ 4 4 0 ~ 1 0 4 1 4 ~ 0 ~ ~ ~ 1 1 t 0 4 4


TLAST0.50.65.0

4 4 4 0 4 4 4 4 4 0 1 4 0

IDEC1

23

440441440

4 NRED2

~ ~ ~ ~ 4 ~ 140040

1 -14 1 00 4 0 0 044404404014000 ~ 0 ~

11444444441

1

TREF100.

1 ~ 11 ~ 4441010

IORQOM1 1

000001014

TPRNT0.010. 010. 10

0 0 1 1 4 1 0 0 0 4 1 0 0 0 4 0 0 0 0 4 4 4 4 0 4 1 4 4 4 4 1 4 4 0 4 4 0

EDIT DIMENSION CARD4 0 0 1 0 4 4 4 4 4 4 0 0 4

NS I ED NS2ED0 0

0 4 0 t 0 0 0 0 0 t 0 4 0 ~ 0 ~ 0 1 0 0 4 4 0 0 0 0 4 0 ~ 4 0 0 ~ 0 4 4 4 4 0 4 0 0 1 0 ~ 0 0 0 4 0 4 4 4 0 0 4 0 4 4 4 4


~ 1 0 0 0 0 ~ 0 ~ 4 0 4 ~ 1 4 4 1 0 0 ~ ~ 4 ~ 1 0 0 0 0 0 4 ~ 1 0 1 4 1 0 4 4 4 1 0 4 4 0 0 ~ 0 0 0 0 0 4 1 0 ~ 0 4 0 4 0EDIT CARO(S) FOR THICK SLABS

0 4 0 4 0 4 t t t 0 t 0 1 1 0 0 0 0 ~ 1 1 0 1 0 4 0 4 4 4 0 4 4 0 0 0 4 4 1 4 4 4 4 4 4 ~ 0 0 4 4 0 4 0 0 0 0 0 0 0 1 0 0

EDIT CARDS FOR THIN SLABS

0 1 0 4 0 0 1 4 0 1 1 ~ 4 0 0 1 1 0 4 1 t 4 0 4 '4 0 1 0 4 ~ 0 1 4 t 1 0 1 4 0 0 0 4 1 ~ 1 1 1 0 4 ~ 0 1 0 1 1 0 1 1

REFERENCE PRESSURE FOR AIR FLOWS(OMIT THIS CARD IF NFLOW=O)

PREF14. 7

0 ~ 1 0 4 0 4 1 4 0 0 0 t 1 1 ~ ~ 1 0 1 1 0 0 ~ 1 1 \ 0 0 10 0 1 0 ~ 1 4 4 0 t ~ 1 1 0 0 ~ 0

ROOM DATA CARDS(DO NOT INCLUDE TIME-DEPENDENT ROOMS)

4 ~ 44414t144401

L PRES TR RELHUM RM HT14.7 150.0 0.001 10.0

~ 0 0 0 4 t 4 1 0 1 0 4 4 1 1 1 ~ t 0 1 0 4 ~ 4 0 0 4 0 0 0 1 4 4 0 4 4 4 t 4 1 4 4 1 0 1 4 0 ~ 1 0

OCD

CD

0 AIR FLOW DATA CARDS( TH~RO~FL~ 0

I OFLOW I FROM I TO

t t ttt tttt ttt

,VFLOW

tttt

tt

tItttt

tI

ttttttttt

Ittttt

t tt

tttttt

t t t t t t t t t t ~ t t t t t t t t t t t ~ ~ t t ~ ~ ~ t ~ t t t t t t t t ~ 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 NLEAK = 0 )

ARLEAK AKLEAK LRM1 LRM2 LDIRN0.01 4.0 1 -1 1t t t t t t t t t t t t ~ t t t t t t t t t t t t t t t t t t t t t t t t t t t t ~ t t ~ t t t t t t ~ t t t t t t t t t t

CIRCULATION PATH DATA

IDLEAK1ttttt

IDCIRC KRM1 KRM2 ELEV1 ELEV2 ARIN AROUT AKIN AKOUT

t ~ t t t t t t t t t t t ~ ~ t ~ t t t t t t ~ t ~ t t t t t t t t ~ ~ t t t t t t t t t t t t t t t ~ t ~ t t t t t t t t t t t t t t ~

AIR FLOW TRIP DATA

IOFTRP KFTYP1 KFTYP2 FTSET IDFP

t t t t t t t t t t t tt t t t t t t t t t t tt t t t t t t t t t t t t t t t ~ t t t t t t t t t t t t t t t t t t t t t t t t t t t tHEAT LOAD DATA CARDS

ITYP QDOT TC WCOOLDHEAT NUMR

t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t tPIPING DATA CARDS

OPIPE IPREF POD PID AIODN PLEN PEM AINK PTEMP IPHASE

t t t ~ t t t t t t t t t t t t t t t t t t t t t t t t t t ~ t t t t t t ~ t ~ t t t t t t ~ t t t tt t t t t t t t t t t t t t t tHEAT LOAD TRIP CARDS

I TMD TSET TCONI DTR IP IHREF

t t t t t t t t t t t t t t t t ~ t t t t t t ~ t t t t t t t t t t ~ ~ t t t t t t t t t t t ~ t t t t t t t t t t t t t ~ t t t ~ ~ t tSTEAM LINE BREAK DATA CARDS

DBRK IBRM BFLPR IBFLG BDOT TRIPON TRIPOF RAMP

t t t t t t t t t t t ~ t t t t t t t t t t t t t t t t t t t t t t t t t ~ t t t t t t t t t t t t t t t t t t t t t t t t t t t t t tTHICK SLAB DATA CARO (CARD 1 OF 3)

DSL81 NGR IO IHFLAG CHARLIRM2 ITYPEIRM1

t t t t t t t t ~ t t t t t t t ~ t ~ t t t t t t t t ~ t t t t t t t t t t t t t ~ t t t t ~ t t t t t t t t t t t t t t t t t t t t t tTHICK SLAB DATA CARD (CARD 2 OF 3)

AREASl AKSALS ROS CPSDSL81 EMI S

t t t t t t t ~ t t t t 1 t t t t t t t t t t t t t t t t t t t t t ~ t t t t t t t t t ~ t t t t t t t t t t t t t t ~ t ~ t ~ t ~ ~

THICK SLAB DATA CARD (CARO 3 OF 3)

HTC2(2)HTC1(1) HTC2(1) HTC1(2)DSL81

t t t t ~ t t ~ t t t t t t t t t t t t t t t t t t t t t 't 't t t t t t t t t t t t 't t t t t t t t t t t t t t t t t t t t t t t t tTHIN SLAB DATA CARD (CARD 1 OF 2)

CA

IQ3

CDOCD

4

404440

040

4~ I0044

I

j j4bib

IDSL82 JRMI JRM2 JTYPE AREAS2

0ii01ii\i40i0iiF 00 'i4ii4044404ii00 ~ ii004i0440i04THIN SLAB DATA CARD (CARO 2 OF 2

4 4 0 4 4 4 4 4 0 4 4 4 4 4 4 4 4 4 0 4

IDSLB2 UHT(1) . UHT(2)

DTDR IRMFLG NPTS TDRTO AMPLTO-I I 3 0.0 0.044404444 ~ 4440i440444444 ~ 4 ~ 4 ~ 00 ~ 40014i044440i4j404


FREQ0.0

4 4 4 4 4 4 4 4 4 4 4 4 0 4 '0 4 4

TT I ME0.0

10.020.04441i4 ~ 40 j04444 ~ 0

4 4 0 4 4 4 4 4 t ~ 0 0 0 4 4 0 4

DTDR-I TTEMP RHUM PRES150. 0.01 1. D-5150. 0. 01 I . D-5'I 50. 0.01 I . O-Si 0 ~ ~ 0 0 0 0 ~ ~ 4 i 4 ~ 0 4 4 4 ~ 0 4 4 ~ 0 4 4 0 0 ~ 4 4 0 ~ 4 0 0 4 ~ 0 4 4 ~ ~ ~ ~ 4 ~ 4 4 i ~ 4

Oi ~ 040 ~ ~ 004 ~ ~ 4444l ~ OOii440i ~ 4040004 ~ i ~ ~ f ti4 ~ 044f 1404

~ ~ ~ 4 4 4 ~ i i 0 ~ 4 4 4 0 i ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ 0 0 0 00 4 ~ 4 4 4 4 ~ 4 ~ 4 4 0 ~ ~ 4 ~ ~ ~ 4 4 i 0 I~ 1 ~ IO ~ ~ 4 4 i 0 ~ 4 i 1 0 ~

TIME-DEPENDENT ROOM DATA

FIGURE 4.IO COMPARISON OF COTTAP CALCULATED COMPARTMENT AIR MASSWITH ANALYTICALSOLUTION FOR SAMPLE PROBLEM 6

700

CQ

I—LJ

I—

OOzV)V)

Q

650

600

550

500

450

400

LegendANALYTICAL

~ 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

~Eations, Prentice-Hall, Englewood Cliffs, HJ, 1971, Ch. 11.

2. Pirkle, J.C. Jr., Schiesser, W.E., "DSS/2: A Transportable FORTRAN 77

Code for Systems of Ordinary and One, Two and Three-Dimensional

Partial Differential Equations," 1987 Summer Computer Simulation

Conference, Montreal, July, 1987.

3. Schiesser, W.E., "An Introduction to the Numerical Method of Lines

Integration of Partial Differential Equations," Lehigh University,

Bethlehem, PA, 1977.

4. Lambert, J.D., Com utational Methods in Ordinar Differential

Equations, 1973., Chapter E.

5. Hindmarsh, A.C., "GEAR: Ordinary Differential Equation System

Solver," Lawrence Livermore Laboratory report UCID-30001, Rev.l,

August, 1972.

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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.

PP3,L FOrm 2454 n0r83)Cat. 1973401 $E -B- N A =0 4 6 Rev.0 >

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CALCULATIONSHEET

12. CRC Handbook of Chemistr and Ph sics, 56th Edition, R.C. Weast,

editor, CRC Press, Cleveland, Ohio, 1975.

13. Chemical En ineer's Handbook, 5th Edition, R. H. Perry and C.-H.

Chilton, editors, McGraw-Hill, New York, 1973.

14. ASME Steam Tables, 5th Edition, The American Society of Mechanical

Engineers, United Engineering Center, New York, N.Y., 1983.

15. McCabe, W. L., Smith, J. C., Unit 0 erations of Chemical Engineering,

3rd Edition, McGraw-Hill, New York, 1976.

16. Lin, C. C., Economos, C., Lehner, J. R., Maise, L. G., and Ng, K. K.,

CONTEMPT4/MOD4 A Multicompartment Containment System Analysis

Program, NUREG/CR-3716, U.S. Nuclear Regulatory Commission,

Washington, D.C., 1984.

17. Pujii, T., and Imura, 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)/M,a a 'a'here

P = partial pressure of air (psia),

p = density of air (ibm/ft ),3a

T = compartment temperature ( F),0

and

M = molecular weight of air = 28.8 ibm/lb mole.a

The partial pressure of water vapor, P, is also calculated from thevideal gas equation of state. The total pressure with in the compartment,

P, is then obtained fromr'

P=P+Pr a v (A-2)

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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 + 1.6309xl0 T + 3.9826x10 Tpa Z Z

— 1.6306x10 Trwhere T is compartment temperature in K.0

r

(a-4)

Similarly, the specific heat of water vapor is obtained from (Table D of

ref. 7)

C = 0.4278 + 2.552x10 Tpv r+ 1.402x10 T — 4.771x10 T

Z Z(A-5)

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0where the units of C are Btu/ibm F, and T is compartment temperaturepv r0in K.

'The mixture specific heat is taken as the molar-average value for the airand water vapor;

p— aMa'pa+ v"v'pvl/™aa ™vv (A-6)

where g and gi 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.

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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 ZZZ.1.2.1 of ref. 9). These routines

are simplified approximations to the functions given in the ASME 1967

steam tables.

A.5 Saturation Tem erature of Water

The saturation temperature of water, as a function of saturation pressure

and saturation enthalpy, is calculated from the RETRAN-02 property

routine (Section ZI1.1.2.2 of ref. 9).

A.6 S ecific Volume of Saturated Water and Va or

The specific volume of saturated liquid and vapor is calculated from the

RETRAN-02 property routines (Section ZII.1.2.3 of ref. 9). The routines

give saturated specific volume as a function of saturation pressure and

enthalpy.

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A.7 Coefficient of Thermal Ex ansion for Air/Water-Va or Mixture

The coefficient of thermal expansion, 9, for the air/water-vapor mixture

is defined as

I|=1 Bvv 3T 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

8=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)

I1= [uH +I'll]/[I|IM +PM1/2 1/2 (A-9)

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where It ,I3 = viscosity of air and water vapor respectivelya'

(ibm/hr-ft),

and

9 ,III = mole fraction of air and water vapor respectively,a'

M = molecular weight of air (28.8 ibm/lb mole),a

M = molecular weight of water vapor (18 ibm/lb mole).v

and It are determined by fitting straight lines to the data given ina v

Tables A.1 and A.2.

temperature are

The equations which give It and It as functions ofa v

It = 0.0413 + (7.958x10 )(T -32),a r

and

= 0.0217 + (4.479x10 ) (T -32),v r (A-11)

where It and It have units of ibm/ft hr and T is compartment temperaturea v r0in F.

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Table A.1 Viscosity of Air

Viscosity of Air*(ibm/ft hr)

Temperature( F)

0.0413

0.0519

32

165.2

*Data from ref. 12, p. F-56

Table A.2 Viscosity of Water Vapor

Viscosity of Water Vapor*(ibm/ft hr)

Temperature( F)

0.0217

0.0290

32

195

*Data from ref. 14 p. 294.

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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)

where k ,k = thermal conductivity of air and water vapora'

respectively,

g,g = mole fraction of air and water vapor respectively,a'

M = molecular weight of air (28.8 ibm/lbmole),

and

M = molecular weight of water vapor (18 ibm/lbmole) .v

The component conductivities are determined from linear curve fits of the

data given in Tables A.3 and A.4. The curve-fit equations for the

component thermal conductivities are

and

k = 0. 0140 + (2. 444x10 ) (T-32),a (A-13)

k = 0.010 + (2.00x10 )(T-32),

where k and k have units of Btu/hr ft F and T is in F.0 0

a v

(A-14)

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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.

III

I

NRCANEND BATCH

NAN10004431 X

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