NUREG/CR-1405

BNL-NUREG-51180

AN, R-7

THE NACOM CODE FOR ANALYSIS

OF POSTULATED SODIUM SPRAY FIRES IN LMFBRs

S.S. TSAI

Manuscript Completed - September 1979

Date Published - March 1980

ENGINEERING AND ADVANCED REACTOR SAFETY DIVISION

DEPARTMENT OF NUCLEAR ENERGY

BROOKHAVEN NATIONAL LABORATORY

UPTON, NEW YORK 11973

PREPARED FOR

U.S. NUCLEAR REGULATORY COMMISSION

WASHINGTON, D.C. 20555

UNDER INTERAGENCY AGREEMENT DE-ACO2-76CHO0016

NRC FIN NO. A-3000
NOTICE

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such use, of any information, apparatus, product or process disclosed in this report, or

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The views expressed in this report are not necessarily those of the U.S. Nuclear

Regulatory Commission.

Available from

GPO Sales Program

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and

National Technical Information Service

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ABSTRACT

An analysis of potential sodium spills and fires in liquid metal fast

breeder reactors has been made to assess the maximum equipment cell loading

conditions. A computer code called NACOM (sodium combustion) has been developed at Brookhaven National Laboratory (BNL) to analyze sodium spray fires.

This report contains a detailed description of physical models used in this

code as well as programming aspects. The single droplet combustion model and

the model describing the droplets' motion are verified. Comparisons between

NACOM predictions and SPRAY-3A predictions of the Atomics International (AI)

LTV Jet Tests are made. Good agreement is found between the NACOM predictions

and the experimental data. NACOM predictions of the pressure rise are more accurate than SPRAY-3A predictions for most of the cases studied. The code has

been verified for oxygen concentrations ranging from 0 to 21%. NACOM utilizes

more realistic single droplet and spray combustion models than SPRAY-3A. Moreover, NACOM does not utilize adjustable parameters for the burning rate equations, contrary to the approach taken with SPRAY-3A. Thus, the NACOM code is a

more reliable code for use in the analysis of large-scale sodium spray fires in

LMFBR containment cells.

- iii -

TABLE OF CONTENTS

Page

ABSTRACT .............. ..................... ......

LIST OF FIGURES . ....... .....................

LIST OF TABLES ............. ........................

iii

vii

vi

NOMENCLATURE ......... ...................... ix

1. INTRODUCTION ........ ....................

2. CHARACTERISTICS OF SODIUM COMBUSTION .........

3. PREVIOUS WORK ON SODIUM COMBUSTION ............

3.1 Sodium Spray Fire Experiments . . . .... ...

3.2 Single Sodium Drop Tests ..... ...........

4. MODELING OF*SODIUM SPRAY FIRES ..............

4.1 Combustion Model for a Spherical, Stationary

4.2 Combustion Model for a Free-Falling Droplet

4.3 Droplets' Motion ..... ......... .......

4.4 Drop Size Distribution .................

4.5 Spray Combustion . . . . . . . . . . . . . .

4.6 Heat Transfer .......... ................

4.6.1. Heat Transfer to the Gas ...........

4.6.2 Heat Transfer to the Walls .........

4.6.3 Heat Balance on the Gas ............

4.6.4 Heat Balance on the Walls .........

5. THE NACOM COMPUTER PROGRAM .................

5.1 Code Structure ...... .................

5.1.1 Main Program NACOM ...............

5.1.2 Subroutine MOTION ..... ...........

5.1.3 Function CD ..... ...............

5.1.4 Subroutine RATES ................

5.1.5 Subroutine BALANCE ...............

5.2 Input Data Format ....... ..............

5.3 Output Data Format ..... ...............

6. VALIDATION OF THE NACOM CODE ..... ...........

Droplet

7

7

9

9 . .. . . . 12 . .. . . . 14 . .. . . . 16 . .. . . . 17 . .. . . . 21 . .. . . . 21 . .. . . . 23 . .. . . . 23 . .. . . . 24

. .. . . . 25

. .. . . . 25 . .. . . . 25 . .. . . . 26 . .. . . . 26 . .. . . . 26 . .. . . . 28 . .. . . . 28

. .. . . . 34 . .. . . . 35 . .. . . . 35

. .. . . . 40

. .. . . . . 41

. .. . . . 42

. .. . . . 44

. .. . . . 46

. . . . . . . 53

. . . . . . 6. 65

6.1 Validation of the Model Describing-Droplets' Motion

6.2 Validation of Single Droplet Combustion Model . . .

6.3 Code Validation by LTV Jet Tests ..............

7. SUMMARY AND CONCLUSIONS ....... .................

ACKNOWLEDGMENTS ............ .......................

REFERENCES ..... .................... . ........

APPENDIX A: THE PHYSICAL PROPERTIES ..................

APPENDIX B: NACOM SIMULATION OF LTV JET TESTS .........

APPENDIX C: SAMPLE PROBLEM ....... .................

APPENDIX D: NACOM CODE LISTING ....... ..............
LIST OF FIGURES

Figure Title Page

1 Schematic of a Burning Sodium Droplet 11

2 Dependence of Evaporation Constant K (at Different

Temperatures) upon Mole Fraction of Oxygen Y 11

3 Mass Burning Rates with and without Air Stream Turbulence.

Fuel: n-Butyl Alcohol 15

4 Mass Burning Rate as a Function of Sphere Diameter and

Air Stream Velocity. Fuel: n-Butyl Alcohol; Air 15

Stream Temperature: 26-400C

5 Mass Burning Rate as a Function of Air Stream Velocity.

Fuel: Ethyl Alcohol (95.5 Per Cent by Weight); Sphere Diameter: 0.635 cm; Air Stream Temperature: 18-310 C 15

6 Correlations of Burning Rate Data 15

7 Schematic of Sodium Spray Combustion in a Vessel 19

8 Flow Chart for the Main Program 27

9 Flow Chart for Subroutine MOTION 27

10 Flow Chart for Function CD 27

11 Flow Chart for Subroutine RATES 29

12 Flow Chart for Subroutine BALANCE 29

13 Comparison of Final Velocity between Predictions and

Al Experimental Data 37

14 Comparison of Fraction of Droplet Burned between

Predictions and AI Experimental Data 37

15 Sodium Jet Tests in the Large Test Vessel 37

16 NACOM Prediction of Pressure History for LTV

Jet Test No. 1 47

17 NACOM Prediction of Gas Temperature History for

LTV Jet Test No. 1 47

18 NACOM Prediction of Pressure History for LTV

Jet Test No. 2 47

- Vi -
LIST OF FIGURES (Cont'd)

Figure Title Page

19

20

21

22

23

24

25

26

27

28

29

30

31

32

NACOM Prediction

LTV Jet Test No.

NACOM Prediction

Jet Test No. 3

NACOM Prediction

LTV Jet Test No.

NACOM Prediction

Jet Test No. 4

NACOM Prediction

LTV Jet Test No.

NACOM Prediction

Jet Test No. 6

NACOM Prediction

LTV Jet Test No.

NACOM Prediction

Jet Test No. 7

NACOM Prediction

LTV Jet Test No.

NACOM Prediction

Jet Test No. 8

NACOM Prediction

of

2

of

of

3

of

of

4

of

of

6

of

of

7

of

of

Gas Temperature History for

Pressure History for LTV

Gas Temperature History for

Pressure History for LTV

Gas Temperature History for

Pressure History for LTV

Gas Temperature History for

Pressure History for LTV

Gas Temperature History for

Pressure History for LTV

Gas Temperature History for

47

49

49

49

50

50

50

50

52

52

52

63

63

63.

LTV Jet Test No. 8

Sample Problem Output - NACOM Prediction of Wall

Temperature History for LTV Jet Test No. 8

Sample Problem Output - NACOM Prediction of Spray

Burning Rate for LTV Jet Test No. 8

Sample Problem Output - NACOM Prediction of Oxygen

Mole Fraction for LTV Jet Test No. 8

- vii -
LIST OF TABLES

Table Title Page

1 LTV Sodium Jet Test Summary 38

2 Comparison Between Experimental

Data and Computational Results

for AI Jet Tests 39

- viii -
NOMENCLATURE

Symbol Definition

A Total cell surface area

B Transfer number defined in Equation (4.6)

C Molar Density

Cd Drag coefficient

Cf Empirical constant defined in Equation (4.8)

Cp PGas mixture heat capacity

Cvg Specific heat of the gas at constant volume

Cv,w Specific heat of the walls

D Droplet diameter

DVolume mean diameter

Dd Diffusion coefficient

Di Initial droplet diameter

Dmax The largest group size

Dmin The smallest group size

ý,g Gravitational acceleration

hfg Heat of evaporation

h Heat transfer coefficient at the walls

Hc Heat of combustion

i Stoichiometric ratio

k Gas mixture thermal conductivity

K Burning rate coefficient or evaporation constant

IDroplet mass burning rate

f Falling droplet mass burning rate

m Total mass of gas inside a containment cell

g

m Sodium leak rate

m sSpray mass burning rate

m wTotal mass of the walls

- ix -
-NOMENCLATURE (Cont'd)

Symbol Definition

mz' Rate of sodium mass crossing the z plane

N Total number of droplets

Nu Nusselt number

P Cell pressure

Pr Prandtl number

qg Rate of heat transfer from a single droplet to the gas

Qg Rate of heat transfer from the sodium spray to the gas

Qw Rate of heat.transfer from the gas to the walls

R Universal gas constant

Rv Volume fraction of spray which contains droplets of diameters

smaller than D

Re Reynolds number

Sc Schmidt number

t,t' Time

Tf Flame temperature

T - Average gas temperature

T s Droplet temperature

Tw Wall temperature

V Volume of the cell

V f Droplet falling velocity

VH Reaction rate constant for water vapor reaction

V0 Reaction rate constant for oxygen reaction

Y Ambient oxygen mole fraction

z Coordinate measured vertically downward from the ceiling
NOMENCLATURE (cont'd)

Greek Symbol Definition

p Density

pg Density of the gas

PNa Density of sodium

- xi -

1. INTRODUCTION

Sodium spills and fires in the primary and secondary systems of a liquid

metal fast breeder reactor (LMFBR) pose a potential threat to the safe operation of the plant. In current LMFBR designs, engineered safety features, such

as inerted primary system cells, nitrogen flooding system, are provided to prevent leaking sodium from reaching flammable combustion. However, in the event

of large-scale sodium spills, pressure and temperatures in an inerted cell may

increase substantially because of a large amount of sensible heat contained in

the leaking sodium, even though there is no flammable combustion. In oxygenenriched atmospheres, the leaking sodium will chemically react with oxygen and

release heat of combustion, resulting in pressure-temperature transients in contairnent cells.

Of the two basic types of sodium fires, i.e., spray and pool fires, spray

fires are generally considered to be more severe than pool fires in terms of

equipment cell thermal transients. This is due to the fact that a sodium spray

always burns at a higher rate than a sodium pool containing the same amount of

sodium because the spray burns in a highly divided state, namely, droplet form.

Sodium spray fires are often postulated to result from pipe breaks. The

sodium coming out of the break is usually assumed to eject upward, impinging on

the ceiling of a contairnment cell. A liquid film will form on the ceiling and

then break up to form droplets. The falling droplets form a sodium spray. The

spray will chemically react with oxygen in the cell atmosphere, transferring the

heat of combustion to the cell gas. This leads to pressure-temperature transients in the cell. It is necessary to assess the severity of the equipment

cell thermal transients in order to determine whether adequate structural margins are provided for the cell. To assess the transients, a reliable analytical

tool is required.

- 1-
Sodium spray fires involve complicated combustion and transport processes

which are not yet fully understood. For example, the effects of droplet interaction; oxygen depletion in the spray zone, and water vapor on spray burning remain largely unknown. The conventional approach to modeling sodium spray fires

starts with the modeling of single droplet heat transfer and combustion. The

burning rate of a single droplet is predicted by using a vapor-phase combustion

theory. The spray is usually visualized as a cluster of droplets and hence the

spray burning rate is the sum of the individual droplet burning rates. In determining the spray burning rate, the effects of droplet interaction, nonuniformity of gas temperature across the spray zone, and depletion of oxygen inside the spray zone are usually neglected.

To date a number of computer codes have been developed to analyze sodium

spray fires. Of all these codes SPRAY(') has been widely used in the United

States. The early version of SPRAY was designed to deal with spray fires in

low oxygen concentrations (less than two volume percent*). The latest version

of the code, SPRAY-3A(2), introduced adjustable parameters in the burning

rate equations. The reaction rate constant V was used for oxygen reactions

and the reaction rate constant VH for water vapor reactions. The values of

V0 and V H were selected by fitting the code's calculational results with experimental data obtained from 16 Atomics International (AI)sodium spray tests. As

a result of this best fit, the values of V0 and VH were chosen as 85 and 1500,

respectively. Even with the introduction of these two parameros 'I PRAY 3

predictions of the Al experiments in the intermediate oxygen concentrations

between 2 to 5% are poor.

Throughout the text the indicated percentage of oxygen designates volume percent.

- 2-
Another frequently used sodium spray fire code is SOMIX.(3) SOMIX-1

basically retains the SPRAY vapor-phase combustion model, with a major improvement in the cell gas circulation model. It seems that SOMIX-1 has experienced

difficulties in predicting spray fires in high oxygen concentrations similar to

the difficulties experienced in the early development of SPRAY. Instead of

using the vapor-phase combustion model, SOMIX-2 adopted Krolikowski's diffusion

model(4) for calculating the sodium burning rate in an air atmosphere. In

SOMIX-2, sodium burning was based on the rate at which oxygen diffuses to the

burning zone. Krolikowski's model does not consider sodium vapor diffusion to

the burning zone, and therefore underestimates the sodium burning rate.

Both SPRAY and SOMIX seems to have difficulty in predicting spray fires in

high oxygen environments, where the accuracy of the combustion model is important. SPRAY attempted to overcome this difficulty by means of adjustable parameters, while SOMIX reverted to the early developed Krolikowski's model in order

to obtain better agreenent with experimental data. It is, therefore, imperative

to develop a sodium spray fire code with a reliable combustion model.

A sodium spray fire analytical model., NACOM, was recently developed at BNL.

NACOM uses an established single droplet vapor-phase combustion theory, which

is different from those used in SPRAY and SOMIX. The theory is well established

for combustion of hydrocarbon fuel droplets. It is expected to be equally applicable to combustion of sodium droplets because the combustion of both hydrocarbon fuel and sodium droplets follows the "D2" law.(5)

The SPRAY code uses the surface mean drop size, which is derived from the

volume mean drop size and a log-normal drop size distribution, to compute the

droplet burning rate and heat transfer from the droplets to the cell gas. Analysis with SOMIX has shown that the use of only one drop size could lead to

- 3-
considerable error in the prediction of the pressure rise. In contrast, NACOM

employs a drop size distribution to calculate the spray burning rate and is

therefore expected to yield better results.

Both SPRAY and SOMIX assume that sodium droplets burn in the vapor phase

immediately after they appear at the ceiling. The preignition phase of the

droplets has been ignored. The neglect of preignition combustion will overestimate the droplet burning rate and pressure. In contrast, NACOM includes a

preignition model developed earlier at BNL.( 6 ) These improvements and other

features of the NACOM code will be discussed in the following sections.

- 4-
2. CHARACTERISTICS OF SODIUM COMBUSTION

Sodium is a soft silvery metal, which melts at 980C. Sodium burns readily

in an air atmosphere, especially in the presence of water vapor, forming various

oxides. Only two oxides, namely, sodium monoxide and peroxide, are found to be

abundant in the reaction products. Sodium monoxide, Na2 0, melts at 1,132%C

and decomposes at 1,950*C and may be formed in the following chemical reaction

2Na + 1⁄202 - Na2 0. (2.1)

During this exothermic reaction 2,195 cal/g of combustion heat is released.

With excess oxygen at 238 to 400DC, the monoxide is oxidized to sodium peroxide,

Na2 02. Sodium peroxide melts at 674'C and decomposes at about 1,6270C. The

peroxide formation may be represented by

2Na + 02 - Na202. (2.2)

During this reaction, 2,500 cal/g of combustion heat is released.

In the presence of water vapor in air, sodium hydroxide may be formed by

the following reaction

2Na + 2H2 0 - 2NaOH + H2 . (2.3)

Sodium does not react with nitrogen at all known temperatures. However, in

the presence of electric discharge, sodium may react with nitrogen to form the

nitride or the azide.

Sodium fires are characterized by flames and dense clouds of white smoke.

The sodium in a fire is not entirely consumed to form smoke; most of the sodium

remains as residue in the form of sodium oxide and unreacted sodium. Reaction

-5-
products in the residue and smoke contain both sodium peroxide and monoxide. In

excess oxygen, the sodium peroxide is the principal reaction product; in excess

sodium, the sodium monoxide predominates; between these two extremes, substantial quantities of both oxides could be formed.

At oxygen concentrations higher than 5%, sodium spray fires are characterized by incandescence, dense smoke, and rapid pressure increase. At or below 5%

oxygen, there is insufficient oxygen to sustain a flammable combustion or incandescence. However, the smoke occurs at oxygen concentrations down to 0.1%.

- 6-
3. PREVIOUS WORK ON SODIUM SPRAY FIRES

3.1 Sodium Spray Fire Experiments

In 1952 Mangold and Tidball(7) reported sodium spray fire tests conducted in

a semi-cylindrical chamber. In the tests, 14.5 to 88.9 kg of sodium at 454°C were

forced through a nozzle and driven into the chamber. The tests were performed

in various oxygen concentrations ranging from 2.75 to 21%. A maximum chamber

pressure rise of 0.48 atm was measured in 21% oxygen.

Hines and Kelley(8) have reported tests in which 4540 C sodium was sprayed

into a 532 k container. They found that the maximum pressure decreased with decreasing initial oxygen concentrations. In these tests, a maximum pressure rise

of 2.59 atm was obtained in an air atmosphere.

In 1958 Humphreys(9) performed a small-scale experiment in which 3990 C

sodium was driven into a sealed vessel filled with air. A peak pressure rise of

5.78 atm was recorded.

Subsequently, Gracie and Droher(10) performed sodium spray experiments in

a rectangular chamber at low oxygen concentrations. A maximum pressure rise of

0.12 atm in 2% oxygen was measured.

Charak and Smith( 1 1 ) have reported a series of sodium spray tests in which

1-2 grams of sodium at 649 0C were injected into an air-filled chamber. The maximum pressure rise found in the tests was -5.44 atm.

Krolikowski(4) injected 10 g of sodium at 413 0C into a chamber filled with

N2-O2 mixtures. A maximum pressure of 3.06 atm was recorded.

More recently, Atomics International conducted a series of sodium spray

tests.(12) Commercial spray nozzles were mounted on top of a spray test vessel.

Pressure rises in the test vessel were recorded for sodium spray in various

oxygen concentrations. Subsequently, a series of sodium spray dispersal tests I

- 7--
were conducted in the Large Test Vessel(13) (LTV). In the tests, sodium sprays

were formed by directing sodium jets upward against an impact plate. Large

sodium drops were produced in the tests. A maximum pressure of -0.27 atm in

5% oxygen was recorded in the tests.

3.2 Single Sodium Drop Tests

(5) Richard et al. performed stationary sodium drop burning experiments in

various oxygen concentrations, with initial droplet diameters of 1, 2, and 3 mm.

He found that the burning of the sodium drops follows essentially the "D 21, law

that has been established for the combustion of hydrocarbon fuel droplets, i.e.,

the square of the droplet diameter decreases linearly with time during combustion.

Subsequently, Atomics International conducted both stationary and falling

drop tests in the Laboratory Drop Modeling (LDM) test apparatus.(14) In the

stationary drop tests, the droplet burning rates for 6-7 mm droplets were

measured. In the falling drop tests, the distance at which the droplet reaches

full burning and the fraction of droplet mass burned in a 14.73 meter fall distance

were recorded.

-8-
4. MODELING OF SODIUM SPRAY FIRES

In this section, the physical models that are used in the NACOM code to

simulate combustion of a sodium spray in a vessel will be discussed. The sodium spray is formed by directing a sodium jet upward against an impact plate

situated at the top of the vessel. The spray contains numerous sodium drops.

Therefore, the formulation of this sodium spray combustion problem must start

with formulation of the combustion of single sodium droplets. It is a conventional practice to derive the spray combustion rate by sunmning up all the burning rates of the individual droplets. The Spalding single droplet vapor-phase

combustion theory will be discussed first. Then the modification factor for the

burning rate equation in forced convection experienced by a falling droplet will

be introduced. Subsequently, Section 4.3 will be devoted to the discussion of

the drag coefficient and solution to the equation of droplets' motion, With the

introduction of a drop size distribution the spray combustion will be formulated

in Section 4.5. Finally, the energy conservation equations for the walls and

the gas inside the vessel will be discussed in Section 4.6.

4.1 Combustion Model for a Spherical, Stationary Droplet

Figure I shows the combustion of a stationary droplet in its final stage,

i.e., steady state. The droplet is surrounded by a burning zone or flame zone.

The sodium vaporizing from the droplet surface diffuses toward the burning zone

from the surroundings. Both sodium vapor and oxygen burn instantaneously and

stoichiometrically in the burning zone. The heat released by the combustion is

fed back to the droplet surface and contributes to the vaporization of the

sodium, thus sustaining the vapor-phase combustion.

-9-.
In the conventional vapor-phase droplet combustion theory, it is often

assumed that a single stationary, spherical, burning droplet is surrounded by

a spherical, symmetrical burning zone. It is further assumed that all the fuel

reaching the burning zone is burned instantaneously under steady state conditions. It follows that the burningrate of the fuel is controlled by the rate

of evaporation of the liquid droplet, which, in turn, is determined by the rate

of heat transfer to the droplet.

The mass burning rate, m, of a droplet may be related to the rate of decrease in droplet size by

m- d D 3 P)

dt- 6 P) (4.1)

where p is the density of the droplet, and P is the droplet diameter. Equation

(4.1) may be rewritten as

2 d) _ 4! (4.2)

dt irpD

It has been shown in numerous hydrocarbon fuel drop combustion experiments that

the square of droplet diameter decreases linearly with time. The proportionality

d(D 2) constant, K, which is defined as K -, -D2 , is termed the burning rate coefficient or evaporation constant. Recently, Richard et al .(5) has experimentally

verified that the combustion of sodium droplets also follows the "D2'' law. The

evaporation constant obtained by Richard et al. for three furnace temperatures

is shown in Fig. 2. It is seen from Fig. 2 that the evaporation constant is a

linear function of the oxygen mole fraction. The mass burning rate may therefore

be expressed in terms of K as

m = 4 pD (4.3)

and the linear relationship between D22 D and t, namely,

2 Di2 - Kt (4.4)

is called the "D2 '' law.

- 10 -
A/3500C

E

C

0

C

0

0

CL

4.10"2

3.10"2

2.10.2

2500 C

3000 C

N

I XPROFILE TEMPERATURE

I.

Figure 1. Schematic of a Burning Sodium

Droplet

a

/

.1 .2 .3 4.5

oxygen mole fraction

Figure 2. Dependence of Evaporation Constant K (at Different Temperatures) upon

Mole Fraction of Oxygen Y

- Ii -
At present there are a number of quasi-steady-state vapor-phase droplet

combustion theories. In general, these theories follow the "D21, law. One of

the established theories proposed by Spalding(15) gives

K =8k Rn (1I+B) (4.5) C pp

where k is the gas mixture thermal conductivity, C.p is the gas mixture heat

capacity, and the transfer number, B, is defined as

B C (Tg T T) +- L (4.6)

hfgI

Equation (4.5) has also been proposed at Atomics International during its early

stage of model development effort.

4.2 Combustion Model for a Free-Falling Droplet

To apply the preceding theory to a free-falling droplet, the effect of

forced convection on the droplet burning rate must be taken into account. The

forced convection will cause the flame to deviate from spherical symmetry and

increase the burning rate. It is very difficult to analytically obtain the

droplet burning rate in forced convection. Therefore, most of the burning rate

expressions for falling droplets are either empirical or semi-empirical correlations.

Both SPRAY and SOMIX assume that sodium droplets burn in the vapor phase

immediately after they appear at the ceiling. The preignition phase of the

droplets has been ignored. In the preignition period, a coarse film (or scale)

of oxides is formed on the droplet surface by the surface oxidation process.

Heat generated by the oxidation process is fed back to the droplet surface more

easily than it is transferred to the gaseous atmosphere. This results in a

rapid increase of the droplet temperature. Ignition of the droplet occurs

- 12 -
when the droplet ignition temperature is reached. A preignition oxidation model

has been developed by Tsai.(6) In the model, the Ranz-Marshall correlation was

used to predict oxygen diffusion to the droplet surface. The oxidation of sodium

at the droplet surface will generate heat which is partly absorbed by the droplet and partly transferred to the cell gas. A governing equation was obtained

by making an energy balance on the droplet, which was then solved for time and

distance at which the droplet is ignited to reach full burning. The calculated

droplet fall distance to reach full burning as a function of droplet diameter

was found to be in good agreement with the LDM falling sodium drop test data.(6)

The sodium droplet burning rate during preignition may be obtained from the oxygen flux and the stoichiometric ratio as

irCD dYD 1/2 1/3

mf - i (2 + 0.6 Re Sc ). (4.7)

After the droplet is ignited, the droplet is burned in.the vapor phase.

The burning rate for a stationary droplet burning in the vapor phase may be obtained from Equations (4.3) and (4.5). For a free-falling droplet, this burning rate should be modified by a multiplication factor that accounts for the

forced convection effect. It has been found by various investigators that,

on the basis of their experimental data, the droplet burning rate in forced convection may be related to the stationary droplet burning rate by

1/2 1/3

mf = m (l + CfRe Pr (4.8)

The empirical constant Cf has been given values ranging from 0.24 to 0.81 by

different investigators experimenting with different fuels. In the present

analysis a value of 0.3 selected by Ranz and Marshall( 1 7 ) is used.

- 13 -
The reason for choosing this value is that it correlates very well the data on the

distance for a falling sodium drop to reach full burning during its preignition

phase.(6) Substituting Equations (4.3) and (4.5) into Equation (4.8), we have

mf Dc (1+CfRe1⁄2 Prl/3) Yn (l+B). (4.g)

Agoston(18) used 0.31 and 0.22 as the values of the constant Cf for ethyl alcohol

and n-butyl alcohol droplets, respectively. The agreement between Equation (4.9)

with the chosen Cf values and experimental data is shown in Figs. 3 through 6.

An evaluation of physical properties that appear in Equations (4.7) and.

(4.9) is given in Appendix A.

4.3 Droplets' Motion

The equation of motion of an evaporating droplet differs from that of a

rigid sphere by a term which accounts for the inertial force contributed by the

mass flux effusing from the surface of the droplet. This affects the drag force

on the droplet. When vapor effuses from the droplet surface, the skin drag decreases due to the thickening of the momentum boundary layer. In addition, combustion gases swept into the low pressure region within the wake of a burning

droplet also reduce the form drag.

Considerable data on the steady-state drag coefficient for a rigid sphere

are available, but very little data on the drag coefficient for an accelerating

sphere exist. At high Reynolds numbers, it has been observed that flattening

of the droplets causes an increase of the drag coefficient.

Due to the lack of reliable data and correlations, the mechanisms discussed

above that affect the motion of a free-falling droplet will not be considered.

Instead, the drag coefficient for a rigid sphere(1) is used in the present model

of droplet motion, and may be written as

- 14 -
26 LINES IEPRES3EW1 N0ýT71JU ;32 Ui.ET 3.

14 - Co;DilI0-6 0, -:

0o

-22

0- Ad

160

1I4

1 2 /P o O

S6 -

z

- A D, OX5 24 - C.0.

ZO 0 0,0

E eV I --- • 16 - 0

z3 ,' 0 o 

4.

o, 20 -0 60 so C>- lzo 1o .60 -SO

AIR STREt" VELOCITY 1c/•-1-M

Figure 4. MassBurning Rate as a Function

of Sphere Diameter and Air Stream Velocity.

Fuel: n-Butyl Alcohol; Air Stream

Temperature: 26-40*C

0 2C

SPH ERE

DI-ETIE

a 0.315

0.63S 0.935

S0.1,12

o 6.02

* 1.32

40 60 80

AIR STREAM VELOCI

1 ULI'LENCE TU;•i

R IKENSiTY ,

(5&)

S.F I 10. 3.0

54.0 S.11 I

20.

23.

32.

60.

2iiN.tS01OPIC 7Tt,.1FULFNCE

t00 120 140

TY 1-1-0e¢)

LULE NO AIR STREAM

CALE TEUP.RA TURE

(-j (1c

t60

0.10

0.10

0,0

0.310

1.3

1.3

37

12

39

3.,

.4ý

22

25

24

Figure 3. Mass Burning Rates with and

without Air Stream Turbulence.' Fuel:

n-Butyl Alcohol

0

.f N7ATURAL 0 0 0

0 0 o . C O N V E C O 1I N 0 o 0 o 00 

6 -- 0

00

21-

M 20 40 60 80 500 120

CIR 5IREAM VELOCITY (cmn/sec)

Figure 5. Mass Burning Rage as a Function

of Air Stream Velocity. Fuel: Ethyl

Alcohol (95.5 Per Cent by Weight); Sphere

Diameter: 0.635 cm; Air Stream Temperature: 18-31°C

o!

-' " I ... . O' ,.3

Figure 6. Correlations of Burning Rate

Data

- 15 -
24/Re Re < 0.1

2.6 + 23.71/Re 0.1 < Re < 6

Cd =

18.5/Re 0 "6 6 < Re < 500

4/9 Re > 500. (4.10)

The equation of motion of a burning droplet may be written as

dVf 3pgVf 2Cd

dt 4pD (4.11)

Upon substitution of Equation (4.10) into Equation (4.11), the latter can be

integrated to yield Vf, which can then be used in Equations (4.7) and (4.9) to

evaluate the falling droplet burning rates.

The Runge-Kutta method is used to solve Equation (4.11). The motion of the

droplets is divided into equal time intervals. To avoid numerical instability

at the beginning of droplets' motion, an asymptotic solution of Equation (4.10)

at time zero is used in the initial phase of the motion, when the drag force is

less than one hundredth of the gravitational force. The asymptotic solution is

obtained from Equation (4.11) by letting Vf approach zero.

4.4 Drop Size Distribution

SPRAY uses a log-normal drop size distribution(1) to compute the surface

mean drop diameter from the volume mean drop diameter. The surface mean drop diameter is then used to comput 1te droplet. burning rat The use of oly one drop

size could lead to substantial error in computing the spray burning rate.(19)

The log-normal drop size distribution used in SPRAY was first considered in

the present.analysis. However, it was found that it did not correlate with the drop

- 16 -
size distribution data obtained from Atomics International Jet Test No. 4 very

well. Later, the Nukiyama-Tanasama correlation(19) was used, which seems to better

correlate with the AI experimental data. The Nukiyama-Tanasama correlation

may be written as

dP 5 D exp 3.915Dl

(3.9 / 12 ex (4.12)

Equation (4.12) is now used in the present version of NACOM. We note however

that the NACOM code is not restricted to the use of the Nukiyama-Tanasama

distribution. Other distributions can be accommodated.

4.5 Spray Combustion

The formulation of single droplet combustion is very straightforward.

However, for a spray of liquid droplets, the parameters that affect spray combustion, such as the actual distribution of drop size, local number density of

droplets, local oxygen concentration, and interaction between droplets are generally unknown. Due to depletion of oxygen in the spray zone, the oxygen concentration within the spray zone is lower than that outside the spray zone. However, the gas temperature is higher inside the spray zone than outside the

spray zone because of heat released by combustion inside the spray zone. At

present, the combustion model adopted in the NACOM code does not consider the

variation of oxygen concentration over the spray zone. An average gas temperature is used in the code instead of assuming a temperature distribution over

the spray zone. It is further assumed that there are no interactions among

burning droplets, i.e., the combustion of each individual droplet in the spray

is not affected by its neighboring droplets. Under this assumption, the single

droplet combustion theory introduced in Sections 4.1 and 4.2 can be used to form

the basis of the present spray combustion theory.

- 17 -
Consider sodium leaking with a mass flow rate m, (t) into a cell of height

H as shown in Fig. 7. It is assumed that the leaking sodium first impinges on

the ceiling and then rains down to form a spray. The spray is assumed to consist of droplets obeying the Nukiyama-Tanasaira drop size distribution. The

droplets will burn away their mass during descent with the burning rate of the

spray being the sum of the burning rates of all the droplets. There are two

methods to formulate the spray burning rate. One is the Eulerian method and

the other is the Lagrangian method. In the Eulerian method, a determination

is made of the total burning rate of all the droplets which occupy an elemental

volume in the spray zone at time t. A summation of all the contributions from

all the elemental volumes is made to obtain the spray burning rate. It is difficult to implement this method to the present problem because the population

of a group of droplets having a specific size changes from one elemental volume

to another as a result of droplets' combustion. To circumvent this difficulty,

the Lagrangian method keeps track of each group of droplets from the ceiling to

the floor. The population of each size group is computed from the sodium leak

rate and the Nukiyama-Tanasama size distribution. . Since the method keeps track

of every size group from its first appearance at the ceiling, the population

of each group will not change during its descent although its average size will

change because of combustion. The average size of each group at the time of

interest is computed from the burning rate and its size at the last time step.

The spray burning rate is the sum of the burning rates of all the droplets,

namel y,

is(t) =f ]' f (D (Di, t-,t), Vf (Di,t-,t)) d2N (4.13)

-i

- 18 -
Figure 7. Schematic of Sodium Spray

Combustion in a Vessel

- 19 -
d2 N is the number of droplets having diameters between D and D + dD, and having elevations between z and z + dz at time t. These d2N droplets are originated from the ceiling at time t-, having initial diameters between Di and

Di + dDi. Since the Lagrangian method is used to follow a specific size

group all the way from its appearance at the ceiling to the elevation z, the

population of the group d2N does not change with time until the whole group

is completely burned up. Therefore, d 2N can be derived from the sodium leak

rate and the drop size distribution as

d2N d m N (t) dR ddt- dDi

Di 3 a dDi

6 i 3Na

(4.14)

Equation

Tanasama

have

(4.14) can take any form of drop

correlation, Equation (4.12), is

m2 Nt() 3 .9 15 D 5

Di PNa

The drop size D at time t can be computed

rate at the last time step. The velocity

needed to compute the burning rate mnf, is

Equation (4.11).

size distribution. When the Nukiyamasubstituted into Equation (4.14), we

exp 3.915 Di dt'dDi. (4.15)

D

from Equation (4.1) and the burning

of a droplet at time t, which is

obtained from the solutions of

During the preignition period, the preignition oxidation model , namely,

Equation (4.7), is used to compute the burning rate rf. After the droplets

reach full burning, the vapor-phase burning rate expression, namely, Equation

(4.9) is used. At any instant the distances to reach full burning are computed for different drop sizes using the method described in Reference 6 with

the additional consideration of heat transfer from the droplet to the gas.

- 20 -
To evaluate Equations (4.13) and (4.15) numerically, a constant time step,

At', and a constant range of drop size, ADi, are selected. The range of integration with respect to drop size is chosen by determining the largest and

smallest drop sizes. The largest and smallest group sizes, Dmax and Dmin,

are determined by equating the total volumes of droplets in the two groups to 1%

dR _dR = .1•dR

of the volume of the mean size group, i.e., I D=Dm- = 0.01 -

D=Dmax D=Dmin D .

The droplets between the groups which have the largest and smallest average drop

sizes are divided into eleven groups. The integration is then approximated by

the sum of the burning rates of all groups locating at different elevations,

i.e.,

ms fmf ANi (4.16)

where the i sunmnation sums over all the size groups and the j summation over all

the elemental volumes inside the spray zone.

4.6 Heat Transfer

4.6.1 Heat Transfer to the Gas

The combustion of the sodium spray will release heat of combustion to the

surrounding gas. In the case of low oxygen concentrations in which combustion

is insignificant, the sodium spray will transfer its sensible heat to the gas.

When the spray is in vapor-phase combustion, it transfers part of the heat of

combustion to the droplet surface to vaporize sodium and the remaining part of

the heat to the surrounding gas. When sensible heat transfer is the dominant

mode of heat transfer in low oxygen environments, the spray transfers heat to

the gas simply by decreasing its temperature.

- 21 -
During the preignition period, the rate of heat transfer from a sodium

droplet to the gas may be evaluated from the Ranz-Marshall correlation(17) as

k1

(2 + 0.6 Re' Pr3 ) (T - T ). (4.17)

After the droplets are ignited, the droplets are burning in the vapor-phase.

The heat of combustion is the primary heat source. Part of the heat of combustion is fed back to the droplet surface and the remaining part is transferred to

the gas. Therefore, the rate of heat transfer from a burning droplet to the gas

may be written as

q=21Tk D 1-203

2•p D (1 + 0.3 Re1⁄2 PrT) (Hc hfg)

Zn (1+B). (4.1:8)

In Equation (4.18), it has been assumed that heat transfer inside the droplet is

negligible. This assumption has been supported by experimental observations

that the droplet is at the boiling point during most of its vapor-phase combustion period.

The heat transfer from a sodium spray to the surrounding gas is the sum of

the total heat transferred from the droplets to the gas. Therefore, the total

heat transfer rate from the spray to the surrounding gas may be written as

Qg =f!fq 9 d2 N (4.19)

Similarly, Equation (4.19) can be approximated by the summation of q9's cver

all the size groups and elemental volumes, namely

Q q9 AN. A (4.20) i j L

- 22 -
4.6.2 Heat Transfer to the Walls

Heat transfer from the gas to the walls of a containment cell depends on

the gas and wall temperatures and gas circulation inside the cell. To determine

the gas circulation flow field, one has to solve a set of conservation equations

including the momentum, energy and mass transport equations. In typical sodium

spray fires, the spray duration is usually very short. During this short period

of time, heat transfer to the walls is insignificant in most cases. Since the

gas circulation has an effect on heat transfer to the walls only, it was decided

to use an empirical value for the heat transfer coefficient rather than resort

to elaborate numerical schemes for solving the conservation equations.

The heat transfer rate at the walls may be expressed in terns of the heat

transfer coefficient as

= h A (Tg - TW). (4.21)

The value of h for typical containment cell walls is 0.000054 cal/cm2.s

(1 Btu/ft2 sec) as proposed by Shire.(20)

4.6.3 Heat Balance on the Gas

Heat transfer from the droplets to the cell gas will increase the gas temperature and pressure. The gas temperature inside the spray zone will be higher

than that outside the spray zone. A knowledge of the average gas temperature is

adequate for determining the cell pressure rise and only one average gas temperature is therefore used in the present model. Conservation of energy dictates

that the increase of the internal energy of the gas must be equal to the net

heat transfer to the gas. The energy equation for the cell gas may be written

as

mC dT

mgCv'g Idt =g Q w- dt 9 (4.22))

- 23 -
where mg is the total mass of the gas inside the containment cell, Cv,g is

the specific heat of the gas at constant volume. Assuming that the gas is an

ideal gas, the gas pressure may be evaluated from the ideal gas law

P = C R T . (4.23)

g

The molar density decreases with time because of oxygen consumption. The oxygen

consumption rate is computed from the droplet mass burning rate. Then the oxygen mole fraction and the molar number of oxygen are, in turn, obtained from the

oxygen consumption rate at the last time step. The molar density is then computed from the total molar number of the gas mixture.

4.6.4 Heat Balance on the Walls

Heat transfer to the walls is primarily due to convective heat transfer

from the gas to the walls and therefore only convective heat transfer is considered. In application to LMFBR containment cells, it is reasonable to assume

that the wall temperature, Tw, is uniform and all the outer walls of the cells

are thermally insulated. Under these assumptions, the energy equation for the

walls becomes

dT

mwCv,w dt w Qw (4.24)

where m. is the total mass of the walls, and Cv,w is the specific heat of

the walls.

- 24 -
5. THE NACOM COMPUTER PROGRAM

Using the physical models described in the previous sections, the NACOM

computer programhas been developed to simulate sodium spray fires postulated

to occur in LMFBR containment cells. NACOM performs calculations of the single

droplet and spray burning rates, heat transfer from the spray to the gas and

heat transfer from the gas to the walls. The code calculates the gas and wall

temperature rises, gas. pressure, oxygen mole fractions, spray burning rate, etc.

The program is written in the FORTRAN language for use on the CDC 7600/6600

computer system. The entire listing of the code is given in Appendix D. In

this section, the code structure along with the input and output. formats will be

discussed.

5.1 Code Structure

The code consists of the NACOM main program, the MOTION, RATES and BALANCE

subroutines, and the CD function subprogram. The main program reads input data,

initializes constants, computes drop size distribution, and prints outputs. The

MOTION, RATES and BALANCE subroutines perform droplet dynamic, combustion, and

heat and mass transfer calculations, respectively. They are called by the main

program. The CD function subprogram calculates the drag coefficient. In the

following discussion, flow charts will be used to illustrate the computational

procedures in each component of the code.

5.1.1 Main Program NACOM

The main program is the primary controlling program. It reads input data,

initializes constants, computes drop size distribution, and prints outputs. Two

options are available for reading sodium leak rate data. One is to use average

sodium leak rate, where IP must be set to zero. The other is to use the variable leak rate table. There are also two output printing options. One is to

- 25 -
print out detailed combustion and heat transfer information and the other is

to omit it completely. More detailed output discussion will be given in

Section 5.3. The MOTION, RATES and BALANCE subroutines are called by the main

program to perform droplet dynamic, combustion, and heat and mass transfer calculations. The flow chart for the main program is given in Fig. 8.

5.1.2 Subroutine MOTION

This subroutine is designed to perform droplet dynamic calculations. The

Runge-Kutta method is used to solve the droplets' equation of motion. The

velocity and distance travelled by a falling droplet are computed at discrete

times t n for eleven initial drop sizes. For convenience, a constant time stepAt

is adopted, which can be adjusted by specifying a value for the time step reduction parameter, X. Because of high acceleration at the start of droplet

motion, a large time step may lead to numerical instability. A time step re-

'duction parameter of 2 is recommended as a result of compromise between accuracy

and computer time. To avoid numerical instability, an asymptotic solution of

the equation of droplets' motion is obtained for the initial stage of the motion.

The subroutine flow chart is given in Fig. 9.

5.1.3 Function CD

The function CD uses the Reynolds number from the MOTION subroutine to

calculate the drag coefficient, which is then fed back to the subroutine to

compute the drag experienced by a sodium droplet falling in a gas stream.

The flow chart for the function CD is given in Fig. 10.

5.1.4 Subroutine RATES

This subroutine computes the spray burning rate, heat released by the

spray combustion, heat transferred to the droplets, and heat transferred to the

gas from the spray. The number of drops in a specific size group, created in

a At spray duration, is first computed using the volume fraction of the group

- 26 -
Figure 8. Flow Chart for the Main

Program

Figure 10. Flow Chart for Function CD

Figure 9. Flow Chart for Subroutine

Motion

- 27 -
and the sodium leak rate. The average drop size, elevation, velocity, and burning rate of the group are then computed. Heat released by droplet combustion,

and heat transferred to the droplet surface and the gas are, in turn, computed

from the burning rate. The spray burning rate and heat transferred from the

spray to the gas are simply the sum of the contributions from all the burning

droplets. Finally, the drop size, number of drops and droplet temperature of

each group are recomputed at the next time step. The flow chart for the subroutine RATES is given in Fig. 11.

5.1.5 Subroutine BALANCE

This subroutine does heat and mass balances. The gas and oxygen molar numbers at the next time step are computed from the amount of oxygen consumed within the present time step. The oxygen mole fraction at the next time step is

then computed from the gas and oxygen molar numbers. 'The gas and wall temperature rises at this time step are computed from the heat transfer rates, which

are input from the RATES subroutines. The flow chart for the subroutine BALANCE

is shown in Fig. 12.

5.2 Input Data Format

The first card in the input deck is the title card. The title of the case

run starts from the second column and less than 70 characters are allowed. The

first column is set to 1 for detailed combustion and heat transfer data outputs.

The following data cards are read subsequently in the main program.

- 28 -
NIIILING

A COMPUTE INITIALIZE PARAMETERS PREIGNTON AT START BURNING YES RATES, COMUT

OF DROPLETS' HEAT TRANSFER GASPAND

MOTION RATES J GAS AND .• l ,•-• ' I O XYGEN

COMPUTE 

MOLE FRACTIONS

S VAPOR-PHASE FOR NEXT

BURNING ITIME STEP

MRATES,S

R 

iGAS AND

TRATE S FE

_9 HEATWALL 

TEMP.

FOR 

NEXT

TIME 

STEP

B U R N I N GR E T U R N

HEAT FERFigure TRAN 12. Flow Chart for Subroutine

RATES

COMPUTEOMPUTEC

DO 20 RGAS 

AND

J=IDRJLE 2.TEMLTE 

P ATO NEXT

TTIME STEP

BRNINTE AES

- 29 -
Card No. Symbol Col umns Format Definition

Card No. Symbol Columns Format Definition

2

2

2

2

2

2

3

3

3

3

3

3

4

ALl

H

VOL

DME

FNA

TSI

PI

TG I

YOI

TMAX

TEND

X

NA202

1-12

13-24

25-36

37-48

49-60

61-72

1-12

13-24

25-36

37-48

49-60

61-72

1-12

13-24

25-36

37-48

F12.4

F12.4

F12.4

F12.4

F12.4

F12.4

F12.4

F12.4

F12.4

F12.4

F12.4

F12.4

F12.4

F12.4

112

112

Total cell wall area (m2 )

Cell height (m)

Cell volume (m3 )

Volume mean droplet diameter (cm)

Mean sodium leak rate (g/s)

Initial sodium temperature (*C)

Initial cell gas pressure (atm)

Initial cell gas temperature (°C)

Initial oxygen mole fraction

Maximum problem time (s)

Spray duration (s)

Time step reduction parameter

Fraction of peroxide in the

reaction products

Product of wall specific heat

density and thickness (cal/cm2 °K)

Print interval

Number of pairs of data used

in the leak rate table (•540)

4 CPS

NPRT

IP

4

4

Card No. 4 is followed by the following leak rate table, which is optional.

Card No.

5

6

Leak Rate Table

Time (s)

(Columns 1-12)

TL(1)

TL(2)

Leak Rate (g/s)

(Columns 13-24)

AML(1)

AML(2)

IP + 4 TL(IP) AML(IP)

The data deck prepared according to the input data format described above will

have the following outlook:

- 30 -
Card No.

1 Title Card

2 ALl H VOL DME FNA TSI

3 PI TGI YOI TMAX TEND X

4 NA202 CPS NPRT IP

5 TL(1) AML(1)

6 TL(2) AML(2)

IP + 4 TL(IP) APL(IP)

5.3 Output Data Format

Flexibility has been considered in the code output. The print interval can

be adjusted to suit specific need by adjusting the parameter NPRT. The option

of printing the detailed combustion and heat transfer information is available.

A sample probelm output is given in Appendix C. The printout appears in the

following order:

1) The title of the case run

2) Input Listing

All the data used for the input parameters are printed out.

3) Leak Rate Table

The variable leak rates at discrete times are printed out.

4) Droplets' Motion

The solutions to the equation of droplets' motion, namely, distance

travelled and droplet veloc-ity at discrete times for each size group

are printed out.

5) Volume Fraction of Spray

The volume fraction of the spray per unit diameter for each size

group is printed out.

- 31 -
6) Detailed Combustion and Heat Transfer Information (Optional)

This option prints out the drop size, drop population, droplet temperature, Reynolds number, burning rates and heat transfer rates for each

size group. Also printed out are the spray burning rate and the total

heat transfer rate to the gas. The printout of these parameters is

requested by assigning numeral "I" to the first column of the title

card.

7) Thermal Transient

The cell pressure rise, gas temperature, wall temperature, oxygen mole

fraction, spray burning rate, etc. are printed in a specified time

interval.

Output Parameters

The definitions and units used for the output parameters are given below:

I = Size group number

DI = Initial diameter of size group i (cm)

TF = Droplet travelling time (s)

Z = Distance travelled by a droplet at time TF (cm)

VF = Droplet velocity at time TF (cm/s)

RD = Volume fraction of sodium spray per unit diameter, occupied by droplets in a

size group (cm-1)

TIME = Time elapsed (s)

P = Cell pressure rise (atm)

TG = Average cell gas temperature (°C)

TW = Cell wall temperature (°C)

YOC = Oxygen mole fraction

SRS = Sodium spray burning rate (g/s)

SBR = Total amount of sodium burned (g)

- 32-
Q = Rate of heat transfer from sodium spray to gas (cal/s)

SQ = Total amount of heat transfer from sodium spray to gas (cal)

QW = Rate of heat transfer from gas to walls (cal/s)

SQW = Total amount of heat transfer from gas to walls (cal)

MOLO = Molar number of oxygen (g-mole)

MOLG = Molar number of gas (g-mole)

SML = Total amount of sodium leakage (g)

There are also optional printout of combustion and heat transfer data. The definitions of these output parameters are given below:

D = Instantaneous droplet diameter (cm)

DN = Number of droplets in a size group

TS = Droplet temperature (OC)

RE = Droplet Reynolds number

BRF = Falling droplet burning rate (g/s)

QIN = Rate of heat transfer to droplet (cal/s)

QC = Single droplet combustion heat release rate (cal/s)

QG = Rate of heat transfer from' droplet to gas (cal/s)

- 33 -
6. VALIDATION OF THE NACOM CODE

In order to ensure that the code adequately predicts pressure and temperature

rises resulting from sodium spray fires, validation of the physical models employed

is required. Specifically, the models describing droplets' motion and the droplet

combustion will be compared to AI experimental data.

6.1 Validation of the Model Describing Droplets' Motion

A determination of the adequacy of data on droplet velocities is crucial to

the accurate determination of droplet burning rates. The droplet velocities are

obtained by solving the droplets' equation of motion, namely, Equation (4.11). The

single droplet burning tests(22) conducted at AI may be used for validation purposes. In these tests, the final velocities of sodium droplets with diameters

ranging from 1.5 to 7 mm were measured. A case was run with NACOM to simulate the

falling of sodium droplets through a distance of 14.73 m in the test vessel. Within

this distance, the sodium droplets will all reach their terminal velocities. The

final velocities measured in the tests are shown in Fig. 13 together with the NACOM

and SPRAY-3A (2) predictions. Figure 13 shows that the final velocities predicted

by both NACOM and SPRAY-3A are in good agreement with the test data for droplets

larger than 4 mm. However, for small drops both NACOM and SPRAY-3A predictions of

final velocities are below the test data, with the NACOM predictions a little closer

to the experimental values. The discrepancy between the calculated and experimental values is due to the fact that the effect of droplet burning on the drag

coefficient has not been adequately taken into account. The effect is to decrease

the drag coefficient and hence increase the final velocity of the droplet.

- 34 -
6.2 Validation of Single Droplet Combustion Model

The single droplet combustion model is the basis for the formulation of

spray combustion. The model becomes important in high oxygen concentrations.

Therefore, it is necessary to validate the model in an air atmosphere. The

single droplet burning tests(22) in air conducted at Atomics International can

be used for validation purposes. In the tests, the droplets were released

from the top of the test vessel, and the masses of droplets at the 14.73 meter,

distance from the top were measured. The diameters of the droplets used in the

tests were from 1.5 to 7 mm. The NACOM calculation of the case discussed in

the preceding section gives the final masses of the droplets at the 14.73 meter

distance. The fraction of droplet mass burned is then computed from the initial

and final masses of a droplet. The measured fraction of droplet mass burned

is shown in Fig. 14 together with the NACOMrand SPRAY-3A(2) predictions. The

fraction of droplet mass burned decreases linearly for droplets larger than

0.3 cm. For droplet diameters less than 0.2 cm, the fraction of droplet burned

is close to one that means that droplets smaller than 0.2 cm will be totally

burned in the 14.73 meter travelling distance. AI attempted to correlate its

data by drawing a straight line through the data points for large drops. However, the linear relationship no longer holds for droplets smaller than 0.3 cm.

The NACOM prediction compares well with the experimental data while SPRAY-3A

underpredicts the fraction of droplet burned. The largest discrepancy is partly

due to the underprediction of droplet velocities by SPRAY-3A and partly due

to the inaccurate single drop combustion model used in the code.

6.3 Code Validation by LTV Jet Tests

Atomics International has conducted a number of sodium spray dispersal tests

in the Large Test Vessel, 7.62 m (25 ft) high by 3.05 m (10 ft) diameter. A

2.54 cm nozzle was centered on top of the vessel with its open end 11.43 cm

- 35 -
below the stainless steel impact plate as shown in Fig. 15. Sodium ejected from

the nozzle at velocities 3 to 6 m/s was directed upward to impinge on the impact

plate. The sodium moved radially on the plate and then rained down forming a

sodium spray. The sodium spray contained droplets of mean droplet diameters

ranging from 0.37 to 0.53 cm. The tests were conducted in atmospheres containing 0-21% oxygen.

To date, seven LTV Jet Tests have been performed. A summary of the LTV

Jet Tests(21,22,23) is given in Table 1. It should be noted that test data obtained from Tests No. 1 and No. 2 are incomplete. In these two tests, the mean

droplet diameters and resulting oxygen depletion were not recorded. To simulate

these two tests with NACOM, the mean droplet diameters produced in the tests are

needed as input parameters. To overcome the difficulty, estimated mean droplet

diameters are used in the simulations. In Jet Tests No. 3 through No. 8, the

monoxide-peroxide ratio in the reaction products was not measured. According

(12) to AI STV test results1, in low oxygen environments, the primary reaction

product is sodium monoxide. Consequently, NACOM simulation of Jet Tests No. 3

through No. 8 will assume 100% Na2 02 in the reaction products.

The summary of NACOM simulations of AI Jet Tests is shown in Table 2. In

Table 2, the calculational results and experimental data on the maximum pressure

rise, oxygen consumed, and sodium consumed for seven LTV Jet Tests are compared.

It is seen that NACOM has better predictions of the maximum pressure rise than

SPRAY-3A except for Jet Tests No. 3-and No. 8. In 21% oxygen, NACOM predicts higher

burning rates and hence NACOM is more conservative than SPRAY-3A in terms of the

pressure rise.

For more detailed information on the NACOM calculational results for the

LTV Jet Tests, see Appendix B.

- 36 -
12

10

03

-J

* 3

/0

- NACOM PREDICTION

--- SPRAY-3A PREDICTION

o AI EXPERIMENTAL DATA

.2 3 4 5 6

INITIAL DROPLET DIAMETER (mrm)

7 8 10

1.0

0.9

E

E

-0.7

0

c0.6

I-

,, 0.5 -J

0cr0 0.4

LL.

0

z 0.3

(-)

a: 0.2 U0.1

Figure 13. Comparison of Final Velocity

between Predictions and Al Experimental

Data

I I I I ; I I

0

0

- NACOM PREDICTION 8

0 AI EXPERIMENTAL DATA a

A SPRAY-3A PREDICTION

Figure 15. Sodium Jet Tests in the Large

Test Vessel

I I I I I I I

0 0.1 0.2 0.3 OA 0.5 0.6 0.7

INITIAL DROPLET DIAMETER, Di(cm)

Figure 14. Comparison of Fraction of

Droplet Burned between Predictions and

Al Experimental Data

0.8

- 37 -
Table 1. LTV Sodium Jet Test Summary

w

I 2 3 4 6 7 8

Initial Oxygen Concentration (Vol %) 21 21 1.5 0 4.8 0.8 0.8

Initial Gas Temperature (°C) 23.9 23.9 20 23.9 23.9 23.9 23.9

Initial Gas Pressure (atm, gauge) 0.099 0.099 0.099 0.099 0.099

Ambient Pressure (atm) 0.97 0.97 0.97 0.97 0.97 0.97 0.97

Initial Humidity (ppm vol) 7400 8000 4400 4400 530 1100 48

Sodium Drive Pressure (atm) 17 20.7 0.83 0.83 0.83 0.83

Initial Sodium Temperature (°C) 538 538/593 532 532 529 538 538

Sodium Jet Velocity (m/s) 15.2 30.5 5.88 3.08 3.23 2.68 3.02

Sodium Release (kg) 1.72. 2.40/2.45 4.08 5.62 5.58 2.36 2.72

Resulting Pressure Rise (atm) 0.22 0.8 0.053 0.039 0.29 0.046 0.033

Resulting Oxygen Depletion (vol %) 0 0 0.7 0 0

Strike Plate Temperature (°C) 1093 471 604 443 449

Sodium Drop Temperature at Floor (0C) 67 527/116 316/82

Final Humidity (ppm vol) 3500 85 66 90

Fallout Mean Size (pm) 0.18 0.21 0.16 0.145 0.145

Reaction Products (% Na2 02 ) 100 91-96

Burning Efficiency 0.26 0.66

Peak Aerosol Concentration (jim Na2O/cc) 7.2 17.1 0.1 0.13 4.8 0.18 0.07
TABLE 2

Comparison Between Experimental Data and

Computational Results for Al Jet Tests

I

Ij

Initial 02 Maximum Pressure Rise (atm.) 02 Consumed (mol. %) Na Consumed (mol. %)

Concentration

Test No. (mol. %) Test NACOM SPRAY-3A Test NACOM SPRAY-3A Test NACOM SPRAY-3A

J-1 21 0.22 0.23 0.20 0.41 0.15 26.0 40.7 31.8

J-2 21 0.80 0.68 0.60 - 1.15 0.54 66.0 85.1 70.9

J-3 1.5 0.051 0.043 0.044 0 0.02 -.0 - 1.20 0.60

J-4 0.015 0.040 0.041, 0.045 0 0.005 00 0.009 0.48

J-6 4.8 0.29 0.11 0.10 0.7 0.12 0.04 4.8 2.5

J-7 0.8 0.048 0.031 0.030 0 0.008 0.003 - 0.88. 1.12

J-8 0.8 0.034 0.043 0.038 0 0.012 0.004 - 0.87 1.12
7. SUMMARY AND CONCLUSIONS

The NACOM code has been developed to simulate sodium spray fires that are

postulated to occur in LMFBR equipment cells. NACOM performs droplet dynamic,

combustion, and heat and mass transfer calculations. The code calculates the gas

pressure, gas and wall temperatures, oxygen mole fraction, spray burning rate, and

heat transfer rates. The code computes the spray burning rate from the single

droplet burning rates. The single droplet burning rates are, in turn, predicted

by the Tsai (6) preignition oxidation model and the Spalding(15) vapor-phase combustion theory. In arriving at the spray burning rate, no adjustable parameters

such as those used in SPRAY are utilized to fit spray fire experimental data. In

contrast, SPRAY uses two adjustable parameters whose values are determined by curve

fitting of AI experimental data. Consequently, NACOM is more reliable than SPRAY

when applied to large-scale spray fires in LMFBR equipment cells and containment

building.

The code has been verified by comparison with the AI single droplet burning

tests. The droplet final velocities predicted by the code agree well with the Al

experimental data and are somewhat better than those predicted by SPRAY-3A at small

droplet diameters. The fraction of droplet mass burned predicted by NACOM for falling droplets has been found to be in good agreement with the AI experimental data

while it is underpredicted by SPRAY-3A.

Further experimental verification of the code is provided by the NACOM simulation of the LTV Jet Tests. The NACOM predictions of the pressure rise are more

accurate than the SPRAY-3A predictions in most cases. It appears that NACOM is

more conservative than SPRAY-3A in terms of the pressure rise because SPRAY-3A

underpredicts the single droplet burning rate. The code has been verified for

oxygen concentrations ranging from 0 to 21%. Therefore, the code is applicable

to sodium spray fires in the secondary sodium system as well as the primary sodium

system of an LMFBR.

- 40 -
ACKNOWLEDGMENTS

The author would like to thank Dr. R. A. Bari and Dr. W. T.

Pratt for helpful discussions and for providing constructive comments

on the manuscript. Thanks are also due to Dr. R. J. Cerbone for

reviewing the draft copy.

- 41 -
REFERENCES

1. P.R. Shire, "SPRAY Code User's Report," HEDL-TME 76-94, March 1977.

2. P.R. Shire, "SPRAY Code Modification and Verification with Experimental Test

Results, SPRAY-3A Version," HEDL-TI-75293, February 1978.

3. M.P. Heisler and K. Mori, "SOMIX-1 Users. Manual for the LBL CDC 7600

Computer," N707TI130045, Atomics International, June 1976.

4. T.S. Krolikowski, "Violently Sprayed Sodium-Air Reaction in an Enclosed

Volume," ANL-7472, Argonne National Laboratory, September 1968.

5. J.R. Richard, R. Delbourgo, and P. Laffitte, "Spontaneous Ignition and

Combustion of Sodium Droplets in Various Oxidizing Atmospheres at Atmospheric

Pressure," Twelfth Symposium (International) on Combustion, pp. 39-48, 1969.

6. S.S. Tsai, "Surface. Oxidation Process Prior to Ignition of a Sodium Droplet,"

Trans. Am. Nucl. Soc., 27, 524, 1977.

7. F.L. Mangold and R.A. Tidball, "Sodium Fire Studies," NP-3812, April 1952.

8. E. Hines and J.K. Kelley, "Determination of the Maximum Pressures Attained

During the Reaction of Sodium with Air in Closed Systems," Detroit Edison

Report 55-C-80, February 1956.

9. J.R. Humphreys Jr., "Sodium-Air Reactions as They Pertain to Reactor Safety.

and Containment," Proceedings of Second International Conference on Peaceful

Uses of Atomic Energy, Geneva, Vol. 22, p. 177, 1958.

10. J.D. Gracie and J.J. Droher, "A Study of Sodium Fires," NAA-SR-4383, Atomics

International, October 1960.

11. I. Charak and F.A. Smith, "Preliminary Evaluation of a Technique to Study

Expulsion of Sodium into Air," Proceedings of Conference on Safety, Fuel

and Core Design in Large Fast Power Reactors, ANL-7120, Argonne National

Laboratory, p. 868, October 1965.

12. "Quarterly Technical Progress Report, LMFBR Safety Programs, January-March

1971," AI-AEC-12992, Atomics International, May 1971.

13. "Quarterly Technical Progress Report, LMFBR Safety Programs, January-March

1972," AI-AEC-13026, Atomics International, May 1972.

14. "Quarterly Technical Progress Report, Nuclear Safety, Characterization of

Sodium Fires and Fast Reactor Fission Products, July-September 1975,"

AI-ERDA-13161, Atomics International, November 1975.

15. D.B. Spalding, "Some Fundamentals of Combustion," Butterworths, London,

England, 1955.

16. "Annual Technical Progress Report, LMFBR Safety Programs, GFY 1971,"

AI-AEC-13006, Atomics International, September 1971.

- 42 -
17. W.E. Ranz and W.R. Marshall, Jr., "Evaporation from Drops, Part II," Chem.

Eng. Progr., Vol. 48, No. 4, pp. 173-180, April 1952.

18. G.A. Agoston, H. Wise and W.A. Rosser, "Dynamic Factors Affecting the

Combustion of Liquid Spheres," 6th Symposium (Int.) on Combustion, Reinhold,

New York, p. 708, 1957.

19. E. Mayer, "Vaporization Rate Limited Combustion in Bipropellant Rocket

Chambers," ARS Journal, July 1959.

20. P.R. Shire, "A Combustion Model for Hypothetical Sodium Spray Fire Within

Containment for an LMFBR," M.S. Thesis, University of Washington, 1972.

21. L. Baurmash, et al., "Test Report - Sodium Fires Experiment, Jet Tests No. 6,

7 and 8," TR-707-130-002, Atomics International, May 1972.

22. R.P. Johnson, et al., "Test Report for the Sodium Drop Burning and Velocity Tests for SOMIX," N-707-TR-130022, Atomics International, September 1977.

23. L. Baurmash, et al., "Test Report - Sodium Fires Experiment, Jet Tests

No. 3 and 4," TR-707-130-001, Atomics International, March 1972.

24. L. Baurmash, et al., "Summary Report for Laboratory Experiments on Sodium

Fires," TR-707-130-007, Atomics International, August 1973.

- 43 -
APPENDIX A

THE PHYSICAL PROPERTIES

The transport properties of the gas mixture surrounding a sodium droplet

vary substantially with the gas composition and the gas temperature. An accurate

determination of the properties is difficult because the gas composition and the

gas temperature vary considerably from the droplet surface to the burning zone

and from the burning zone to the surroundings. Therefore, mean values of the

transport properties must be used. In the code, the arithmetic mean of the droplet temperature and the gas temperature is used to compute the transport properties of the gas mixture. The variation of the transport properties with the gas

composition is less pronounced. It is a good approximation to assume that the

gas is 100% N2 in the evaluation of the transport properties since the gas mixture is predominantly nitrogen.

For the droplets' motion, however, the oncoming properties of the gas

stream are used, which were found to be in better agreement with experimental

data.

In the code, the physical properties are considered as functions of temperature and pressure only. The following formulas are used to compute the

physical properties. In the formulas, the unit of temperature T is °K and the

unit of pressure P is atmosphere.

Nitrogen

Specific heat (cal/g-K)

C = 0.2316 + 4.61 x 10-5T

p

Absolute viscosity (g/cm-s)

1 = 4.2 x 10-6 T066

- 44 -
Thermal conductivity (cal/cm-s.K)

k 1.05 x 10 6 T

0 .71852

Mass Transfer

N2-0 2 binary diffusion coefficient (cm 2/s)

D = 1.849 x 10- T1 "64 5

P

Product of molar density and binary diffusion coefficient (g-mole/cm-s)

CD = 2.25 x 10- 7T0 .645

Sodium

Density of the liquid (g/cm3

p = 0.949 - 2.23 x 10- 4 (T-273) - 1.75 x 10-8 (T-273) 2

Specific heat of the liquid (cal/g-K)

Cp= 0.34324'- 1.3868 X 10-4 (T-273) + 1.1044 x 10-7 (T-273) 2

The heat of combustion Hc and the stoichiometric ratio i depend on the composition of the reaction products. When the fraction of Na202 present in the

reaction products, f, is known, the fraction of unit mass of sodium that reacts

with oxygen to form Na202 is

S = 1.3478f/(1.6957 - 0.3479f)

The heat of combustion may be expressed in terms of S as

Hc = 2195 (I-S) + 2500 S (cal/g)

and the stoichiometric ratio may be written as

S + (1-S g of 02_ 1.4375 2.875 g of Na

- 45 -
APPENDIX B

NACOM SIMULATION OF LTV JET TESTS

B.1 Jet Test No. 1

In this test, 1.72 Kg of sodium at 538 0C were injected at 15.2 m/s into a

21% oxygen atmosphere. Since the mean droplet diameter was not measured, a mean

droplet diameter of 2 mm, estimated by Shire (2) using a correlation of jet' velocity and drop size, was used in the NACOM simulation of the test.

The NACOM calculational results for the test are shown in Figs. 16 and 17.

It is seen from Fig. 16 that a maximum pressure rise of 0.23 atm is reached at

2.2 seconds. The NACOM prediction of the maximum pressure rise is about 5%

higher than the experimental value, while the SPRAY-3A prediction is about 9%

lower. The NACOM-calculated maximum gas temperature is 88 0 C. The NACOM-predicted

burning efficiency (amount of sodium consumed/amount of sodium leaked) is 41% which

is about 57% higher than the experimental value. The discrepancy may be due to

the inaccurate estimate of the mean droplet diameter.

B.2 Jet Test No. 2

In this test, 2.4 kg of sodium at 538 0C were injected at 30.5 m/s into a

21% oxygen atmosphere. An estimated mean droplet diameter of 1 mm(2) was used

in the NACOM analysis of this test.

The calculated cell pressure rise and gas temperature are shown in Figs. 18

and 19, respectively. The calculated maximum pressure rise is 0.68 atm at 2.2

seconds as compared to the experimentally observed maximum pressure rise of 0.8 atm

at 2 seconds. The calculated maximum gas temperature is 214 0 C. A burning efficiency of 85% is predicted, which is about 29% higher than the experimental result.

The SPRAY-3A predicts a lower burning efficiency and hence a lower pressure rise.

It appears that NACOM is more conservative than SPRAY-3A in an air atmosphere,

because NACOM has a higher single droplet burning rate.

- 46 -
U 0.2

(n 0.1

In

Io.

V)

Z;)o

• 80

: 60 Idi

Q.

w 40

I---

" 20 Csz

I I I I I I I

0 5 10 15 20 25 30 35 40

1 TIME (s)

45

TIME (s)

Figure 16. NACOM Prediction of Pressure

History for LTV Jet Test No. 1

Figure 17. NACOM Prediction of Gas Temperature History for LTV Jet Test No. 1

300

1.2

.I.0

8

0.8

0.6

o Q4 'U

a- /- NACOM PREDICTION

0 AI EXPERIMENTAL DATA

0

a: 200

I'-

n,-

(_

Lj 100

U.•.

f• I I I ; ; I I I N I A I I I I I I

0 5 IO 15 20 25 30 35

TIME (s)

40 45 0 5 10 15 20 25

TIME (s)

30 35 40 45

Figure 18. NACOM Prediction of Pressure

History for LTV Jet Test No. 2

Figure 19. NACOM Prediction of Gas Temperature History for LTV Jet Test No. 2

- 47 -
B.3 Jet Test No. 3

4.08 kg of sodium at 532°C were injected into a 1.5% oxygen atmosphere at

5.88 m/s over a 2.7 second period. The measured mean droplet diameter was 0.457 cm.

The pressure rise and gas temperature predicted by NACOM are shown in Figs. 20

and 21, respectively. The pressure reaches its peak of 0.043 atm at 4 seconds.

The maximum pressure rise predicted by NACOM is about 16% lower *than the observed

value and is about the same as that predicted by SPRAY-3A. The low pressure rise

predicted is mainly due to high humidity (0.8%) in the atmosphere since the water

vapor is almost consumed after the test. The NACOM prediction of the maximum gas

temperature is 30 0 C, compared with the experimental value of 33 0 C.

B.4 Jet Test No. 4

In this test, 5.62 kg of sodium at 532 C were injected into a zero oxygen

atmosphere at 3.08m/s over a 5.7 second period. The measured mean droplet diameter

was 0.533 cm. The NACOM calculational results for this test are shown in Figs. 22

and 23. The maximum pressure rise predicted by NACOM is 0.041 atm reached at 6.6

seconds, compared with the measured value and SPRAY-3A prediction of 0.04 atm and

0.045 atm, respectively. This shows that the heat transfer models used in NACOM

are better than those used in SPRAY-3A. The NACOM prediction of the maximum gas

temperature is 35 0 C, which is the same as the experimental value.

B.5 Jet Test No. 6

In this test, 5.58 kg of sodium at 5290C were injected into a 4.8% 02

atmosphere at 3.23 m/s over a three second period. The measured mean droplet

diameter was 0.406 cm. The NACOM calculational results for this test are shown

in Figs. 24 and 25. The maximum pressure rise predicted by NACOM is 0.11 atm

reached at 6.8 seconds, compared with the measured value of 0.29 atm and SPRAY-3A

prediction of 0.10 atm. The large discrepancy between experiment and predictions

- 48 -
w

(f)

w

w

x~

0.05

0.04 LJ

zA

E 0.03

I i a:

35 40 45 0) 0.02

Uj

a- 0.01

SNACOM PREDICTION

OAl EXPERIMENTAL DATA

0

0 5 10 15 20 25 30

TIME (s)

Figure 20. NACOM Prediction of Pressure

History for LTV Jet Test No. 3

0 5 10 15 20 25 30

TIME (s)

35 40 45

50

LIJ

w

a--

LIU)

I-L

(.9

40

___ - V I- T T . F I Figure 22. NACOM Prediction of Pressure

History for LTV Jet Test No. 4

30

0 5 0 15 20 25 30

TIME (s)

35 40 45

Figure 21. NACOM Prediction of Gas Temperature History for LTV Jet Test No. 3

- 49 -
50

0

w

aLU

C_

0 5 10 15 20 25

TIME (s)

30' 35 40 45

60

1v)

2 60

IS40

20 I i I i i i

Figure 23. NACOM Prediction of Gas Temperature History for LTV Jet Test No. 4

S 5 Kt) 15 2T 2M 30 3s 5 40 TIME (s)

45

0.5

,, 0.4

0.3

0.2

L I

a- 0.I1

Figure 25. NACOM Prediction of Gas Temperature History for LTV Jet Test No. 6

0 5 0 15 20 25 30

TIME (s)

35 40 45

Figure 24. NACOM Prediction of Pressure

History for LTV Jet Test No. 6

- 50 -
is because the effect of water vapor on sodium burning is very pronounced in

this test. The effect has not been considered in the present version of the

NACOM code. The sodium injection resulted in 0.7% oxygen consumption, compared

with the NACOM and SPRAY-3A predictions of 0.12% and 0.04%, respectively. The

maximum gas temperature predicted by NACOM is 540C, compared with the experimental value of 1030C.

B.6 Jet Test No. 7

In this test, 2.36 kg of sodium at 5380C were injected into a 0.8% 02 atmosphere at 2.68 m/s over a 3.3 second period. The measured mean droplet diameter

was 0.356 cm. The NACOM calculational results for this test are shown in Figs.

26 and 27. The maximum pressure rise predicted by NACOM is 0.03 atm which is

about 38% lower than the experimental value. Again, in this test water vapor

plays an important role in increasing sodium burning rate and hence increasing

pressure rise. The maximum gas temperature predicted by NACOM is 320 C, compared

with the experimental value of 37 0 C.

B.7 Jet Test No. 8

In this test, 2.72 kg of sodium at 5380 C were injected into a 0.8% 02 atmosphere at 3.02 m/s over a 3.3 second period. The measured mean droplet diameter

was 0.369 cm. The NACOM calculational results for this test are shown in Figs.

28 and 29. NACOM predicts a maximum pressure rise of 0.043 atm at 4.8 seconds

while SPRAY-3A predicts a maximum pressure rise of 0.038 atm. In comparison, the

measured maximum pressure rise is 0.034 atm. This test is essentially the same

as Jet Test No. 7 except that the amount of sodium injected is higher and humidity

is lower in this test. The lower humidity leads to lower pressure rise observed

in this test even though the amount of sodium injected is higher in this test.

The maximum gas temperature predicted by NACOM is 360C, which is 12% higher than

the experimental value.

- 51 -
OO• On i I I I-A 

LUj

(I,

LJ

0.05

0.04

0.03

0

ý_F - NACOM PREDICTION

0 AI EXPERIMENTAL DATA

I I - I. I

Ui

u-I

40

3-

S30

I i I I I I I

K

0.02

0.01

II 2( 0 5 10 15 20 25 30 35 40. 45

TIME (s)

Figure 26. NACOM Prediction of Pressure

History for LTV Jet Test No. 7

0 5 10 15 20 25 TIME (s)

30 35 40 45

Figure 27. NACOM Prediction of Gas Temperature History for LTV Jet Test No. 7

0.06

E

in

LU

0.

0.

TIME (s) TIME (s)

Figure 28. NACOM Prediction of Pressure

History for LTV Jet Test No. 8

Figure 29. NACOM Prediction of Gas Temperature History for LTV Jet Test No. 8

- 52 -
APPENDIX C

SAMPLE PROBLEM

- 53 -
A detailed description of the code structure, and the input and output

formats is given in the previous sections. For illustrative purposes, a sample

problem will be solved by use of the NACOM code. The problem selected for these

purposes is AI Jet Test No. 8(21) in the Large Test Vessel (LTV). In this test,

2.7 kg of 538 0 C sodium were injected into the LTV filled with 0.8% 02. The LTV

is a right circular cylinder, 9.14 m long and 3.05 m in diameter. The measured

volume mean diameter of the droplets is 0.369 cm.

The input data deck for this sample problem is given as follows.

0 AI JET TEST NO.8-SODIUM SPRAY IN LTV.

93.5863 7.62 62.2971 0.369 824.6 537.8

1.07 23.9 0.008 46. 3.3 2.

0. 0.586 250 8

0. 0.

0.5 1556.8

1.0 1354.3

1.5 1183.4

2.0 1107.5

2.5 1069.5

3.0 601.2

3.4 0.

The first column in the title card has been set to zero for the option of

omitting the detailed combustion and heat transfer outputs. These outputs can be

obtained by setting the first column to one. The code outputs for this sample

problem are given on the following page. The major output parameters of interest

are the pressure rise, gas and wall temperatures, oxygen mole fraction, and spray

burning rate. The histories of these output parameters are shown in Fig. 28

through 32.

54 -
AT JET TEST NO.8 - SODIUM SPPAY IN LTv.

SDING

ALl= .9359E*1. H- .7620E+01 VDLv .6230W+02 DMEc .3690E40n FNAm .84246E+03 TSI= .53781.03

P1= .10TOE101 TGI= .2390E+02 YnVu .8000E-02 T7IAy= .4600o.02 TEND= .3300E.01 X= .2000E#01

TIME (S) 0. " *5000E100

.loooEO|

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.3400E+01

ttPSm saoý6t+66 NppIt=- 250 1 p

FLOW RATE(G/S}

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TF

IF

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IF

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IF

TF

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.2276E+03

.3l2bLE03

.54601+03

.75046+03

.790CE#6 2

.*911L*03

.4 7?9E.+n3

.r51•.l.•3

.Rlf!1lE.03

.,174E*03

.3093E#03

.49176E03

.6597E*03

.8104E+03

.9421E*03

.1055E+04

.1200E*00

.3200E+00

.52006,00

.T720E*00

.9?OOE*00

.6268E401

.4716E#02

.1258E*03

.2401E.03

.3T726E03

.5636F#03

.1174E403

*309RE.03

.4935E403

.6642E403

.8189E+03

.1368E*03

.3281E+03

.5092E+03

.6756E+03

.8244r*03

.9542E*03

.1563E#03

.3467E+03

.5265E#03

.6913E*03

.8383E*03

.9661E#03

.1756E*03

.3653E*03

.5437E*03

.7069E+03

.8519E*03

.)9778E*03

.14006.00

.3400CE+~00

* 540 CE . C

.7400E600

.9400E+00

.1140tio0

.8616E*01

.5336E*02

.13STE503

.2534E+03

,4035E*03

.5827E+03

.1369E+03

.32866E03

.5112E603

.6804E403

.8334E*03

.968;5.63

.1600EO00

.3600E*00

.5600E*00

.7600E400

.9600E400

.116DE.01

.113S6.02

.5993E*02

.1459Ei03

.2670E#03

.4202E+03

.60216*03

,1563E*03

.3473E,03

.5288E#03

*6965E403

*8477E*03

.89106E03

. 1800E600

.3800E+00

.5800E*00

.7800E400

.9800E+00

1448E*02

,6687E+02 .1565E403

:2809E+03

.4372E403

.6217E+03

.1757E603 .3660E#03

:5462E+03

.7I24E*03

.8619E#03

TF

IF

T F

IF

I F

36

T F

z

z

z

V F

V F

VF

V F

0.

.2000E*00

o•4000E+00

.600064o0

..AOOE*O0

.1000F.01

. 1200E.01

0.

.7426+,02

. lbt7E .03

.2962E*03

.4967.E03

.1000E-07

19551E.03

315 2 * 03

.5657E*03

.73 30+0 1

.20006E-C

.2200E*00

S4 200CE. 0

.6200E+00

.A2006E.00

.1020E*6 l

.1220F.01

.1960E.00

.219OE0.2

.81966,02

.1791)E03

.31•,o360

.4744F+03

.66606+03

.1960F.02

.2145k.03

.403116.03

.*F31E.03

.74•(F9*03

.1200t.00

.3200E*00

.5200E.00

.7200E.00

.9200E*00

.11206E01

.6269E.01

.4719F.02

.1260E*03

.2408E*03

.38ORE-0.1

.5670E.03

.1174E.03

.310 1+ . JJ

.4949f -0.4

9,61• F 03

. gP09 .03

.14OOE.00

.3400E+00

.5400E+00

.7400E00

.9400E*00

.1140,E01

.861 TE.01

.5339E602

.1359E+03

.254 1E.03

.4054E603

.5864F.03

.1369E+03

.3290F.03

.5128F40-4

.b844F-03

.16006.O0

.3600E.00

.5600.E00

.7600E400

.9600EO00

.IIAOE*OI

.1136E*02

.5997E*02

.1462E603

.267RE003

.4222E*03

.6060E*03

.15646.03

.3478E#03

.5306F#03

.7007E-03

8556E1.03

.1800DE00

.3800E.00

.o5800E*00

.700OE*00

.9800E*00

.1800I1O

,1448E602

.6693E+02

.1568E#03

.2818F+ 03

.4393E*03

.6259E+03

.1758E+03

.3666E#03

.5482F,*03

.71t,9E*03

.A7nlr '
VF .8845[E03 .R9RSE#03 .Q128E+03 .9267TE03 .9404E*03 .9540E403 .9673EO03 .*qO5F.03 .q936E+03 .1006E+04

VF .1019E*04 .102F+04 .ln44E*04 .1056E404 *106AE4O4 .1080E+04

Rrf .1622E-01 S5S73E+00 oISTuFO*1 .1847E+l1 o1443E[01 oA823E*O0 o457PE.00 .2113E#00 .9931E-o1.3524E-01

DI) o1317E-01

Pa .43158t-nl

Ow oA4013E,03

SM4eL4003E+04

TGz .359]1E.02

SO= .16333E406

i1MEt ,5000E&ol SECONDS

TW= Z•3903E402 YOCz .78p41E-02

rjW= .606ARE403 . SOW= .16326E#04

BRSz .1T475E400

MOLOm .21570E*02

SRR= .29412E*02

MOLG .27358E*04

P= .42405E-01

0=0.

I SML= .34003E#04

TGv .35703E+02

SO= .16351E406

TIMEm .1O00GOE-n SECONDS

TW= .23908E*02 YOCz .78837E-02 HRSwo. SBP= .29502E#02

JWv .59609E+03 SOW= .46415E*04' MOLOO *21569E*02 NOLG= .27358E404

P= .41616E-0I

S•iL= .34003V404

P= .40H42E-nl1

ý= 0.

StIL= .34003E#04

TG= ,3S484E#02

TG: .35269E40?

S(j= .16351EL06

TW= .23014Eý02 YOC= .78A37E-02

(JW= .58474 .E.Oi §nW= tS03j3E#04

TIME= .20000E.fl SEcofiOS

T'q= .*391qEfn2 YOCz .7AR37E-0O

(JW= .57361E#03 So,]= .*04)E#Ob

Rpsto. SBP= .295O2E402

MOL0= .22569E*02 MOLG= .273SAE;64

FRS:O. S9P: .29502E+02

HOLOc .21569E*02 MOLG= .2735SE404

TI'F:. .;"'S0(JE.,f)? SFCONDFS
P= .400f?E-O1 TG= °35058E*02

0=0. So: .16351E*06

SML= o34O03E*04

TW= .23924E#02

ow= .56270E+03

YOC= *7r837E-02

SOW= .13330E*05

BRSZO. SRR= *2950fE*02

MOLO: *2ish9E.02 MOLG= .273S8E*04

I

P= .39337E-01

umO.

SML= .34003E+04

Pa .38605E-01

SMLm .34003E*04

P= .37RT9A-0I

SML= .3400.3E,04

Pr .37184E-01

SML= .34003F.04

TG= .3485)E40?

TO= *34648E*o2

SO: .16351E*06

TG= .j444qt+0?.

SO= .16351E*06

TG= .34254E40?

SO= .163"5IE.O(

TIME= .30000E*02 StCONDS

TW= *23929E*02 YOCz .7Ae37E-02

owz .*SIqq4;03 toWn .16116E*05

TIME% *35000E*02 SECONDS

TW= ,23934E*02 YOC= .78837E-02

OW= .54148E403 SOW- .IR5oE*.Ob

TIME: .4000G0E40 SECANDS

iW= .23039E+0? YOC= .1as31E-02

Ow= ,53117E*03 SOW= .21531E.05

TIME= .45000E*02 SECONDS

Tw= .°3944F'0m YOCm Ti.037E-02

OWz ,52 106E603 SOW= 1 2.4161E*0b

R0S= 0. SAP= .29502E*02

MOL0= .2l569E*02 MOLG= .27359E.04

RRS2O. SBR= .29502E+02

M(1LOO .21569E+02 MOLG= .27358E#04

4kRS=O. SfR= .29S02Et*2

MOLO: *21569E*02 . MOLG= *2735IE,04

OS=0,- SRP= .2950E.02

MOLO= ej1569E.n2 MOLG= .27358E.04
I I I I I I

n 23.94 iLa0.

LJ

'- 23.92

_j

_j

Iz

0

0 5 10 15 20 25

TIME (s)

30

Figure 30. Sample

Prediction of Wall

LTV Jet Test No. 8

Problem Out

Temperature

4 35 40 45

U.

-J

0

put - NACOM 2

History for Z

x

0

0.0081

0.0080

0.0079

0.0078

I I I I I I I

I I I I I I

0 5 10 15 20 25

TIME Is) 30 35 40 45

LU

10

znZ)

CO 5

a-

((1

Figure 32. Sample Problem Output - NACOM

Prediction of Oxygen Mole Fraction for

LTV Jet Test No. 8

0 5 10 15 20 25 30 35 40 45

TIME Is)

Figure 31. Sample Problem Output - NACOM

Prediction of Spray Burning Rate for LTV

Jet Test No. 8

- 63 -

APPENDIX D

NACOM CODE LISTING

- 65 -
PROGRAM NACOM(INPUT.OUTPUT)

C

C NACOM IS A COMPUTER PROGRAM WHICH SIMULATES SODIUM SPRAY FIRES

C IN LMF@k CONTAINMENT CELLS AS A RESULT-OF POSTULATED PIPE RUPTURES.

C

DIMENSION TITLE(7)tnL(2)

COMMON /NMRH/DTt4OLOtflOLGRTG,V8L,YOC

COMMON /NM4R/U (I1) ,FNA9HI IDUL) II ( !)

COMMON /NRfW/AI98PRSP9O

COMMON /Nk/AAMML(40) 0,0DU( 1,600) tDM( 19600) ,ON(I19600) ,HC,

JHFGIP,IO,N,NPRT,RD(11),SgtL,TtTRtTENDTL(40),TS(11,600)tTSI

COMMON /NM/bMF9HPIdd'UL

COMVON /rNi4/,LICPSGl~tTW

RFAL NA2O0

REAL MOLO,MOLG

DATA P/P2.054/gHF6/IO05./

READ 36,ITITLE

C

C READ INPUT DATA.

C

REAU 37,ALI9,HVOL,DMEFNAqTSI

REAb 37,PITGI9YOI,TMAXTENDX

READ 36,NA202,CPSNPPT.IP

C

IF(IF.EQO.0) GO TO 47

00 46 I=1,.IP

46 READ 4cTL(I),AML(I)

47 PRINJ 41,TITLF

PRINT 4?

PRINT 4.3,ALItHVOLOMEtFNATS19PIpTGIYOI ,TMAXTEND.X,

INA202,CPSNPRTIP

IF(IP.EQ.O) bO TO 55

PRINT 51

DO 52 I=1,IP

52 PRINT 53,TL(I),AML(I)

55 DT=0.01*X

ALI=ALI*Inoco.

.4H 0 100.

VOLzVOL.I 000000.

TG=TGI#273.

TB=1154.

PmPI

YOC=YOI

TW=TG

T=O.

NzO

SBR=O.

SQ=O,

SOW=O,

SML=O.

Sz'1.347P4*NA202/C1.6q57--D.3479-NA2O2)

HC=(1.-S)*2194.5#S*2500.

AI=S/].4375+(I.-S)/2.875

RHOL=0.949-2.23E-4*TSI-1*75E-b*TSI**2

A=3.91415/6.*RHOL

IM=TMAX/DT c

C SELECTION OF DROP SIZES. C

DO 200 L=1,2

IF(L.EQ.I) DL(1)=DME*4.

IF(L.EQ.2) DL(2):DME/.,

00 201 M=1920

- 66 -
AB=EXP(3.915*(I.-()L(L)/nME))

F=(UL(L)/DML)**5*Ad-0.Ol

IF(F.LT.I.E-6) GO To 200

FP=(5.*CL(L) *4/OME**5-(DL(L)/DME) *5*3.915/DME) AB

201 DL(L)=DL(L)-F/FP

200 CONTINUF

ID=lo I10=IDl

HI=(DL(1)-DL(2))/IO

DO 120 I=1,IDD

120 D(I)=(I-I)*HI*DL(?)

C

CALL MOTION

00 110 I1=1.10f)

JJ=II(1)

C

C COMPUTE DROP SIZE DISTRIBUTION.

C

R.)(I)=(3.')]S/DMiE)**6O*[(I)**5/120.*EXP(-3.915*D(I)/DME)

C

DO 110 J=1.JJ

TS(IJ)=O.

DN(IgJ)=O.

DM(I@J)=O.,

110 DD(IJ)=O.

PRINT 130

PRINT 100,9(RD(I),1=,IDD)

DO 45 I=1,IM

T=T*DT

N=N*1

IF(N.LT.NPHT) GO TO 300

PRINT Ao,T

300 CALL PATES

CALL BALANCE

SBR=SBR+BRS*DT

SQ=SQ*(I*DT

SQW=SQW*QW*DT

PP=P-PI

TGG=TG-273.

TWW=TW-273.

IF(N.LT.NPRT) GO TO 45

PRINT 90,PPTGGtTwWtYOCBPStSBR•PUSdQWtSQWMOLOMOLGSML

N= 0

45 CONTINUE

36 FORMAT(II,7A10)

37 FORMAT(6F12.4)

38 FORMAT(2F12.4,2112)

40 FORMAT(2F12.')

41 FORMAT(IHi,1•OX7A10///)

42 FORMAT(SOX,"lNPUT LISTING"/)

.43 FORMAT (IOX..ALI=-.EI0.4,3X,'H=",E1O.4,3X,"VOL=".El0.4,

13Xt"DME="lE 10,4,3X,"FNA=",Ei0.4,3X ,"TSI='"tE0.4// 210X •"Pl="9EI O,4,3X,"TGI="t El O. 4,3X;"Y•IP=1"iE 10.4 9,

33X ,"TMAX=",E 10.4, 3X ,"TEND=" ,EI 0,*4, 3X , t'X="tE i0.4//

S41OXXSNA202="IE10.4,3X,"CPS=",E 0 .4,3X,"NPRT=",• 515t3AXltIP="9I51///)

51 FORMAT(15X,"TIME(S) FLOW RATE(G/S)")

53 FORMAT(I1X,9E2.4,6XE12.4)

80 FORMAT (///44X,"TIME=",EI I.,5IX,"SECONDS"/)

90 FORMAT( IOX"P="EE11 ,5,3X,"TG=",E1,5,3X,"TW=",E 11,5,3X,

1'"YOC=",El11.5,3Xe."9RS=S',EII.5,4X,'SBR=IE11./S/IIOXQ=",E11.5.

23X,"SO=..,E 11 .5,3XmQW="9,E 11 .b, 3X "SQW =uE 11 .5,3X "MOLO=",E 11.5

3,3X, -MOLG=-,E11.5//IOX ISML="5Ell.5///)

- 67 -
100 FORMATC OX,"RD",2X,1OEjO.4)

130 FORMATW//)

STOP

END

SUBROUTINE MOTION

C

C THIS SUHROUTINE COMPUTES THE DROPLET VELOCITIES BY INTEGRATING

C THE E(JUATION OF MOTION FOR THE UROPLETS.

C

DIMENSION TF(1,1600),Z(i1,bOb)

COMMON /NM4Rb/DT,?OLOMOLGRTGVOLYOC

COMMON /NMR/D(C1) ,FNAHIIDL),II {(1)

COMMON /MRB/RHOG9GMqVF(ll,60U)

COMMON /NM/UMEHPIRhQOL

REAL MOLOMOLoMU6

MOL6=PIoVOL/(R*TG)

MOLG=MOLG*YOC

Gm:(MOLG-MOLO)*?H.01f6MOLO*J?.

kHO6=GM/VOL

MUG=4.2F-6*7G**0.6b

10 40 I=1I1D'i)

RP=3.*RHOG/(4.*RHOL*D(I))

DRM=n(I) *RHOG/MUG

TF(I1, )=U.

Z(1,1)=O.

NN=O

C

C RUNGE-KUTTA METHOD TO SOLVE THE EQUPTION OF MOTION FOR DROPLET VELOCITY.

C

DO 10 J=1,599

TF(I.J 1)=T (I, J)+L)T

IF(NN.EU.I) GO TO 200

VF(IJ*1)=980.*TF(I.J+I)

Z(IYJ*])=490.*TF(IJ+I)**2

REV=VF(I*J. )*{DRM

DRAG=RP*VF(I,9J I)**2*CD(REV)

IF(DRAG.LT.I.) GO TO 110

NN:I

200 x=vF(I,J)

HEV~x*rOp A

ORAG=RP*X**R*CO(REV)

PI=(980.-()HAG) *fT

X=VF(IJ)+PI/2o

PEV=X*DPM'.

P2:(980.-wP*A**2.*C D(REV))*DT

x=vF(IJ)+P2/2.

REV=X*I)P

P3=(960.-WP4X*A**CU(REV))*f)T

X=VF (I ,J) +P3

PEV=X*DR"i

P4:(980.-PP*X**2*CD(PEV))*D)T

VF(IJ+I)=\F(IJ)+(PI*2.*P2,2.*P3÷P4)/6.

Z(IPJ*I)=ZCI1J)+VFCIJ)*DT

110 IF(Z{I,J.1).GE.H) GO TO 70

10 CONTINUE

70 II(I)J

PRINT 25,I0(CI)

PRINT 30,(TF(T,K).KM=1J)

PRINT 80

PRINT 45(.C(I.K),K=IJ)

PRINT 80

PRINT 60,CVF(I,K),K=19J)

- 68 -
40 CONTINUE

25 FORMAT (//5X,"I="tI3,4X,"DI=",EiO.4/)

30 FORMAT(1OX9"TF"92Xl,0E11 .4)

45 FORMA.T ( IOX,"Z",3XvlOE11 .4)

60 FORMAT (10X9"VF",2XI OEI1 .4)

80 FORMAT(/)

RETURN'

END

FUNCTION CD(REV)

C

C STANDARD DRAG COEFFICIENT CORRELATIONS.

C

C

IF(REV.LT.O.1) Cb=?4./REV

IF(REV.GE.O.I.AND.REV.LT.6.) CD=2.6+23.71/REV

IF(RLV.GE.b..AND.REV.LT.500.) CD=18.5/REV**0.6

IF(RFV.GE.500.) CD=4./9.

RETURN

END

SUHROUTINE PATES

C.

C THIS IS To CALCULATE- THE BUHNINU HATE OF SODIUM SPRAY AND TOTAL HEAT

C RELEASED BY SPRAY COmRUTION.

C

DIMENSION RE(6UU),OJC(bOO)0C,('bOA0)TSS(600)

DIMENSION 8RF(60O),QIN(bo0)

COMMON /NMR9/DT.MOLOMOLGRTGVULtYOC

COMMON /NMR/D(11),FNA9HIIDDvII(11.)

COMMON /NRB/AI9BPSPQ

COMMON /NR/AAML(4O),HDD(llbOO),DM(11,9600) DN(IC1bOO)OHCo

IHFG,1PIQNNPRTRD(11),SMLTTHTENDTL(40),TS(11,AOO),TSI

COMMON /MRP1/HHO(3qGMVF(11,600)

REAL MOLO9MOLGHUG

MOLG=POVOL/(R*TG)

MOLO=MOLG*YOC

GM=(MOLG-MOLU)*26.O16.MOLO*3e.

YO=mOLO*3?./Gm

RHOG=GM/VOL

TA=(TG+TH)/2.

CPG=O.2316j4.b1E-5*TA

AKG=1.0SE-6*TA**0.11852

MIJG=4.2E-6*rO**0.6b

PR=C PG ti uG/ AG

DP=1.849E-5*TA*1.645/P

CDP=2.25F-7-TA**0.645

SC=PUG/(RHOG*OP)

H=HC*YO/HFG/AI*CPG (TG-T13)/HIG

BPS=O.

C

C COMPUTE THE SODIUN LEAK RATE.

C

IF(T.GE.TENU) 60 TO 101

IF(IP.EQ.O) GO TO 100

DO 30 K=1,IP

IF((TL(K)-T).GT.O.) GO TO 40

30 CONTINUE

AM=AML(IP)

GO TO To

40 AM=CAML(K)-AML(K-)I)/CTL(KI-TLCK-)I)*C•TTL(K-1))*AMLCK-1)

(O TO 70

100 AM=FNA

- 69 -
GO TO 70

101 AM=U.

T0 SML=SMLAM*DT

C DO 10 I=I,IDD

DMI=A*D (I)*3

ON (1, 1 ) =AM*R) (CI) *H I/DMI *I)T DD(1,1)=D(1)

IF(AM.LT. I.E-1O) DD(1,1)=0.

C

C COMPUTE THE DROPLET ,lURNING RATLS,HEAT OF COMHUSTIONAND HEAT TRANSFEkRRED.

DO 19 J=lgJJ

TSS(J):O.

RE (J)=n.

RRF(J)=O.

QIN(J),0.

QCC..)=O,

19 oo(j)=o,

.TS(Ig, )=TSI*273.

00 20 J=1,JJ

DM (I ,J)= A*•DF IdJ) **3

IF(CD(I,J).LT.1.F-10) GO TO eO

RE(J)=VF (CJ)*L)[)(IJ)*lHOG/tIUG

At=StURT(RE(J))

DMT-M (I ,J)/lT

IF(TS(IJ).GE.T9) 60 TO hol

HWF(J)=CDP*YOC*3.14159*1)D(1,J)* (2.0.6*AI*SC**0.3333),*32.,/AI

IF (W Fd(J) .GT.DMT) HkF (J).=)flT

OC (J)-=HC*i•RF (C)

OGC(J)=3.141b9*AKGOr)C( I ,J)*•TS(IJ) -T))*(2.,O.6,AIoA2)

QIN (J) =oC (J) - G (J)

GO TO 602

601 {fP=2.*3.14159*DD( IJ)OAKG/CPG*ALCG(1..R)

IF(CLP.LT.1.E-1O) i'=O.

BRF (J)=FHR*(Cl.0.3*A1*A2)

IFC(bRF(J).GT.OMT) HRF(J)=)MT

QIN (J) =HFG*aF (J)

OC(J)=HC*HRF (J)

QG (J) =0C (,J) -01IN (J)

TS ( IdJ) =Tfl

602 IF(J.EO.JJ) GO TO 60i

FRS -- kS.. HF (J) *f)Fj ( I, J)

Q=Q0OG, (J) *fI'j (C idJ)

605 TSS(J)=TS(I,J)-?73.

20 CONTINUE

C

IF(N.LT.NPRT) GO TO 1601

IF(IC.NE.1) GO TO 100]

PRINT 5019I

Pk NT 50pqu, ob(li,J),J=lJJ)

PRINT 503

PRINT 504. ([N(I,dJ) ddJJJ)

PRINT 503

PRINT 515,(TSS(J),J=ljj)

PRINT 503

PRINT 505,(CRE(J)J-d ,JJ)

PRINT S3

PRINT 51 (;ikFd(J),J=1,jj)

PRI,\T 503

PRIINT 506, C((JINýd),O=jdjj)

PRINT 5(,3

- 70 -
PRINT 507,((0C(J),J=1,JJ)

PRINT 503

PRINT 508,C(G(J),J=IJJ)

PRINT 503

1001 CONTINUE

KJ=JJ-1

C

C COMPUTE ODOP SIZEtNUMBFRAND TEMPERATURF AT NEXT TIME STEP.

C

00 120 K=I,KJ

KK=JJ÷ -K

IF(0D(I,KK-I).LT.1.E-I0) GO TO 110

IF(TS(I,KK-1).GE.T6) GO TO 604

CPL=O.34324-1.386RE-4*(TS(It•K-1}-273.)4I.1044E-7*

-lfTs(IKK-1)-273.)**2

81=QIN(KK-I)/(DM(I,KK-1)*CPL)

TS(IKK)=TS(IKK-1)+BI*DT

GO TO 603

604 TS(IKK)=TS(IoKK-l)

603 DOM=HRF (KK-I)*UT

DMODOM(IKK-1)-D0D

IF(UMD.LT.I.E-1O) GO Tu 110

DO(IKK)=(DMD/A)**0..1333

ON(I.KK) ntN (I, KK-])

GO 10 120

110 DD(IKK)=0.

ON(IKK)=O.

TS(1 KK)=O.

120 CONTINUE

10 CONTINUE

501 FORlAT(5X,'I=",I3/)

502 FORMAT(ICOX,")"92X, OEI.4)

503 FORMAT(/)

504 FOPMAT 10XX,'DN",2K,10ELI.4)

505 FORMAT ]OX,"RE",2xIoEI1.4)

506 FORMAT C1OX,("IN",2X, lEII,4)

507 FORMAT OX,0'.C",2X,1OEI1.4)

508 FORMAT ClOXv'OG",2X,0F•1.4)

511 FORMAT (IOx,"BF",2X,1OEI1.4)

sis FORMAT I0X,"TS",2X,1UElI.4)

RETUPRN

ENO

SUBROUTTNE BALANCE

C

C THIS SU3ROUTINE OOES HEAT AND MASS HALANCES.

C

COMMON /NkRIi/DTo LOtMOLGoRTGVOLYOC

COMk'ON /NR4/AIHRSPqU

COMON /mRH/NHOGGMVF.(IIC.bU)

COMMON /NH/ALICPSS,.OQ,Tt

REAL 0OLOMOLGMUG,MRO

F(X*Y)=(J-**(X-Y))*V

F (X$Y) =c * (X-Y) *S

C

C MASS 8ALANCE ON GAS.

C

CPG=O.2316.4.61E-5*TG

CVG=CPG1/.4

MUG=4.2E-6*TG**0.66

AKG=1.05E-6*TG**0.71852

MPOOAl*bS*DT/32.

MOLU=MOtO-MkO

MOLG=4OLG-MRO

- 71 -
YOC 0 MOL. / MOL G

IF(YOC.LT.1.E-1?) YOC:O.

C

C USE OF HEAT RALANCF EQUJATIONS TO EVALUATE GAS AND WALL TEMPERATURES.

C

HH=U.O00054

w=HH*ALI

V=1./(RHOG*VOL*CVU)

S=1./(ALI*CPS)

UW=w*(T6-Tw) C

C USE OF RUNGE-KoFTA rrIETHOD TO SOLVE FOR GAS AND WALL TEMPERATURES.

C

AI=F(TGT4)*UDT

81=G(TG,Tw)*DT

A2=F(TG+Aj/e.,Ivw+Rj/2.)*)T

P2=G(TGAI/2.Tw*,il/2.)*DT

A3=F(TG+A2/2.tTW,2/2.)*0T

1i3=G(TG+A?/2. ,Tw+HZ/2. *DT

A4=F(TG#A39TW4b3)*UT

A4=F(TG+A3vTw+b3) *T

TC,=TG,(AI,2.*•I22.*A3+A4)/6.

TW=Tw+,Cl?.*RB2.2.*P3+R4)/6.

P=MCLG*R*TG/VOL

RETURN

END

- 72 -
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