NUREG/CR-4534

SAND86-0419

R3

Printed August 1987

Analysis of Diffusion Flame Tests

J. E. Shepherd

Prepared by

Sandia National Laboratories

Albuquerque, New Mexico 87185 and Livermore, California 94550

for the United States Department ofVEnergy ~1

under Contract DE-AC04-76DPOO789 (I

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NOTICE

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United

States Government nor any agency thereof, or any of their employees, makes any warranty, expressed or implied, or assumes any

legal liability or responsibility for any third party's use, or the

results of such use, of any information, apparatus product or process disclosed in this report, or represents that its use by such

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Superintendent of Documents

U.S. Government Printing Office

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and

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NUREG/CR-4534

SAND86- 04 19

R3

ANALYSIS OF DIFFUSION FLAME

TESTS

J. E. Shepherd

Printed August 1987

Sandia National Laboratories

Albuquerque, NM 87185

Operated by

Sandia Corporation

for the

U. S. Department of Energy

Prepared for

Division of Reactor Accident Analysis

and

Division of Engineering

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555

Under Memorandum of Understanding DOE 40-550-75

NRC FIN Nos. A1246, A1336

Abstract

This report discusses the results and analysis of hydrogen diffusion flame tests

conducted at the Nevada Test Site by EPRI and the U. S. NRC. Those tests were

designed to simulate the effects of hydrogen combustion inside a nuclear power plant

containment following a degraded-core accident. Test initial conditions and sample

data plots are given for 16 tests. Mixing and ignition phenomena are discussed in

terms of the source parameters and igniter location. A simple model is developed for

simulating the heat transfer and computing convective heat transfer coefficients from

experimental pressure measurements. Convective heat transfer coefficients are reported

for four tests. The effect of stagnation-point heat transfer is estimated.

iii-iv

Contents

1 Introduction 2

2 Test Conditions5

2.1 Overview.............................................5

3 Injection, Mixing and Ignition 1.1

3.1 Slow Ignition and Diffusion Flame Burning.................... 11

3.2 Fast Ignition and Diffusion Flame Burning..................... .17

3.3 Deflagration and No Diffusion Flames........................ 17

3.4 No Ignition at All .. .. .. .. .... .... .... .... .... .... .... ...... 19

4 Modeling 20

4.1 Transport Model .. .. .. .... .... .... .... .... .... .... .... ..... 20

4.2 Combustion Model .. .. ..... .. .. .. .... .... .... .... .... ...... 22

4.3 Thermal Model .. . ... .. .. .. .... .... ...... .... .... ...... .... 23

4.4 Approximate Solution . .. .. .. .. .. .. ........ .. .. . .27

4.5 Example: Test C3 .. .. ........ .. .. .. .. .. .. .... ...... ....... 30

4.6 Inverse Model. .. .. .. ................... ...... 36

4.6.1 'Model Formulation. .. .. .. .............. .... .... 36

4.6.2 Data Handling .. .. .. .... .... .... .... .... .... ......... 37

4.6.3 Example: Test C3. .. ..... .. .. .. .... .... ...... .... .... 39

5 'Results 43

5.1 Sprays and Fans.. .. .. .... .... .... ........ .. .. ....... .. ..... 43

5.2 Nozzle Size Effect. .. .. .. .. .... .... ...... .... ........ . .... ... 44

5.3 Stagnation-Point Heat Transfer. .. .. .. .. .... ...... .... .... .... 47

6 Summary 50

A Data Plots A-iL

B MOL for Conduction Equation B-iL

v
List of Figures

1 Configuration of flame jet or plume and induced flow inside the vessel . 3

2 Coordinate system used to define locations in the dewar. . ..... .. .... 6

3 Gas Pressure in test C3. .. .. .. .... .... ...... .... .... .... .... 13

4 Sequence of events observed in stable mixing. .. .. .. .... ...... .... 14

5 Motion of the interface between mixed and original fluid .. .. .. .. .... 16

6 Gas pressure for test CN3.. .. .. .. ..... .. .. .. .... .......... .... 18

7 Gas pressure for test CS6 .. .. .. .. .I. .... .... .... .... .... ....... 18

ý8 Hydrogen concentrations for test C9 .. . .... .. . ..... .. .. .... .... 19

9 Measured (P102) and computed gas pressure for test C3 .. .. .. .. .... 32

10 Measured (T118) and computed gas temperature for test C3. .. .. ..... 33

11 Measured (T121) and computed vessel wall temperature for test C3. . . 34

12 Computed total heat flux for test C3. .. .. .. .. ...... .... .... .... 35

13 Raw data and spline fit for test C3 pressure signal. .. .. .. .... ...... 38

14 Measured (T118) and computed (inverse method) gas temperature for

test C3. .. .. .... .... .... .... .... ......... .. .. .. .... ...... 39

15 Measured (T121) and computed (inverse method) wall temperature for

test C3.. .. .. .... .... ...... ...... .. .. .. .... .... .... ...... 40

16 Computed (inverse method) total wall heat fluxes for test C3 .. .. ..... 41

17 Computed (inverse method) convective heat transfer coefficient for test

C3. .. .. .. .... .... .... .... .... .... .... ...... .... .... .... 42

18 Gas pressures for tests C1, C2, and C3 .. .. .. .. ... I. .... ....... ... 43

19 Gas pressures for tests C1, CN1, and CS1. .. .. .. .. .. .... .... .... 45

20 Gas pressures for tests C3 and CN1 .. .. .. .. .. .... ...... .... .... 47

21 Nondimensional heat transfer coefficient .. .. .. .. .... .... ......... 48

A-i Test CI, gas pressure P102. .. .. .. .. .. .... ........ .. .. ....... A-2

A-2 Test C2, gas pressure P102. .. .. .. .. .. .... .... .... .... ....... A-2

A-3 Test C3, gas pressure P102. .. .. .. .. .. .... .... ...... .... ..... A-3

A-4 Test C3, wall temperatures T120, T121 .. .. .. .. .. .... .... ....... A-3

A-5 Test C3, gas temperature T101l.. .. .. .. .... .... .... .... ....... A-4

A-6 Test C3, gas temperatures T114, T118 .. .. .. .. .... .... .... ..... A-4

A-7 Test C5, gas pressure P102. .. .. .. .. .. .... .... .... ...... ..... A-5

A-8 Test C7, gas pressure P102. .. . ..... .. .. .. .... .... .... ....... A-5

A-9 Test C8, gas pressure P102. .. .. . ..... .. .. .... .... ...... ..... A-6

A-10 Test C8, wall temperatures T120, T121 .. .. .. .. .. .... .... ....... A-6

A-li Test C8, gas temperature T101l.. .. .. .. .... .... .... .... ....... A-7

A-12 Test C8, gas temperatures T114, T118 .. .. .. .. .... .... .... ..... A-7

A-13 Test CILO, gas pressure P102 .. .. .. .. .. .... .... .... .... ....... A-8

A-14 Test CII, gas pressure P102 .. .. .. .. .. .... .... .... .... ý.......A-8

A-15 Test CNl, gas pressure P102 .. .. .. .. .. .. .... ...... .... ....... A-9

A-16 Test CN2, gas pressure P102 .. .. .. .. .. .. .... ...... .... ....... A-9

Ai
A-17 Test CN3, gas pressure P102 .. . . . . . . . . . .... . . .... ... .. A -10

A-18 Test CN3L, gas pressure P102 .. .. .. . .. ... .. .. . ... .. .. ..... A-10

A-19 Test CSI, heat flux H503. .. .. .. .. .. .... .... .... ...... ....... A-li

A-20 Test CS1L, wall temperatures T120, T121 .. .. .. .. .. ......... .. ... A-li

A-21 Test CSI, gas temperature T101.. .. %. .. .. .. .... .... .... ....... A-12

A-22 Test OSiL, gas temperature T102 . .... .. .. .. .. .. .... .... ....... A-12

A-23 Test CS1, gas temperature T118.. .. .. .. .. .. ......... .... .. ... A-13

A-24 Test CS2, gas pressure P102. .. .. .. .. .. ...... ...... .... .. . ... A-13

A-25 Test CS5, gas pressure P102 .. .. .. .. .. .... .... .... .... ....... A-14

A-26 Test CS5, total heat flux H503.. .. .. .. .. .... .... ...... .. .. ... A-14

A,27 Test CS5, gas temperature T118. .. .. .. .. .. ............. A-15

A-28 Test CS5, wall temperatures T120, T121 .. .. .. .. .. .... .... ..... A-15

A-29 Test CS5, gas temperature T101l... .. .. .. .. .... .... .... ....... A-16

A-30 Test CS5, gas temperature T102. .. .. .. .. .. .... .... .... ....... A-16

A-31 Test CS6, gas pressure P102 .. .. .. .. .. .... .... .... .... ....... A-17

vii
List of Tables

1 Test Matrix .. .. .. ..... .. .. .... .... .... ............ 7

2 Initial Conditions. .. .. .. .. .... .... .... .... ...... .... ........ 8

3 Signal Quality for the Hydrogen Behavior test series .. .. ...... .. .... 9

4 Signal Quality for the Equipment Survival test Series .. .. .. .. .. .... 10

5 Source Parameters. .. .. .. .... .... .... .... .... .... ...... .... 12

6 Initial Conditions for Test C3. .. .. .. .. ...... .... .... .... ...... 30

7 NTS Vessel Parameters.. I.. .. .... .... ...... .... .... .... ..... 31

8 Model Parameters for Test 03 .. .. .. .. .. .... .... ...... .... .... 31

9 Inverse Model Results.. .. .. .. .... ...... .... .... .... .......... 46

A-i Instrument Locations.. .. .. .. .. .... .... ........ .. .. .. ....... A-i

viii
Acknowledgment

I would like to thank the personnel of EG&G, particularly Richard Thompson, for

their cooperation and for providing an atmosphere that made Sandia participation in

these tests successful. 0. B. Grump, Jr. (Sandia) was responsible for constructing and

installing the Sandia instrumentation in the dewar. Art Ratzel (Sandia) undertook

the massive task of organizing and analyzing the data from the premixed tests. Loren

Thompson (EPRI) was the program manager and driving force that made the test

plan a reality. Jack Haugh (EPRI) has performed the difficult task of completing the

analysis and test documentation. Sandia participation was supported by the U. S. NRC

Hydrogen Behavior and Mitigation and Prevention research programs; John Larkins

(NRC) and Pat Worthington (NRC) were program managers.

Dedication

To the memory of Loren Thompson.

ix

Executive Summary

This report discusses some results and a partial analysis of the diffusion flame -tests

conducted at the Nevada Test Site by EPRI and the U. S. NRC.I Those tests were

designed to simulate the effects of hydrogen combustion inside a nuclear power plant

containment following a degraded-core accident. Testing was performed during the

years 1983-1984 inside a spherical vessel (an abandoned liquid hydrogen dewar) that

was 2048 M3 in volume.

. 16 tests were performed, 4 tests have been extensively analyzed, 4 more have been

examined briefly and the remaining 8 are either not suitable for analysis or insufficient data were available. For the 4 tests that were extensively analyzed, gas pressure,

temperature and wall heat flux measurements are presented. Only gas pressure measurements are provided for the other tests.

-Mixing and ignition processes have been examined as a function of source parameters and igniter locations. The source Froude number has a profound influence on the

degree of mixing during the injection process. The lack of multiple deflagrations and

the phenomena of nonignition can be explained on this basis. Tests using a buoyant

plume source (low source Froude number) probably have a strongly stratified initial

hydrogen concentration and a distinct moving front between mixed and unmixed fluid.

As the source Froude number increases, the Vessel contents become better mixed. Tests

using jet-like sources (large source Froude numbers) will exhibit good mixing and a

distinct front will not form.

A control-volume thermodynamic model is used to simulate the tests and also to

infer the convective heat transfer coefficients from the measured gas pressures. For

tests in which the gas is well stirred, the control volume model yields good agreement

with all measurements except wall temperature. Stratification in the vessel atmosphere

and stagnation-point heat transfer are examined as possible effects that can explain

the nonuniform vessel wall temperatures.

1
2 2 1 INTRODUCTION,

1 Introduction

This report documents some test results and a partial analysis of the continuous

injection (CI) or diffusion flame portion of the hydrogen combustion tests performed

at Test Cell "C" of the DOE's Nevada Test Site (NTS). These tests were carried out

in 1983-84 as part of a program jointly sponsored by the Electric Power Research

Institute (EPRI) and the U. S. Nuclear Regulatory Commission (NRC). The program

was designed to study hydrogen-air-steam combustion in a large-scale facility under

conditions postulated to occur during hypothetical degraded-core accidents in nuclear

power plants. The test program and results are described in detail by Thompson et

al.' '

Two types of tests were performed. Both were carried out inside a spherical vessel

(an abandoned liquid hydrogen dewar) that was 2048 M3 in volume. The dewar was

modified for H2 and steam injection, water sprays, and an air-purge system. Instrumentation was installed throughout the dewar and four IR-sensitive video cameras were

used to observe the combustion events. Gas pressure, gas temperature, wall temperatures, and heat fluxes were recorded as a function of time by a digital data acquisition

system. The dewar modifications, instrumentation and test operations were performed

by personnel of EG&G, Las Vegas.

A series of 24 separate deflagration tests were performed in which mixtures containing 6-13% H2, 0-40% steam, and the remainder air were ignited by glowplugs.

These tests and the associated analysis performed by Sandia National Laboratories,

Albuquerque (SNLA) are described in Ref. 2. Readers interested in a more in-depth

discussion of the experiment and instrumentation should consult that report and Ref.

1. The terminology used in the present report is identical to that used in Refs. 1 and

2 for the labeling of instruments and location of key equipment.

Another 16 tests were performed in which a H2-steam mixture was continuously

injected into a vessel initially filled with an air-steam mixture. The present report is

concerned with those tests.

Igniters were "powered on" during the injection and usually a propagating flame

would be produced that would burn back down to the injection point and form a

stable diffusion flame over the jet or plume of H2-steam. The energy release rate

associated with these flames was from 1-4 MW. Nozzles of 0.038, 0.13 and 1.0 m

diameter were used in these tests. If the flowrate was held constant, the flame would

burn continuously until the 02 concentration fell below the limiting value of 5-8%

required to support combustion. The flame and gas flow configuration inside the vessel

is shown schematically in Fig. 1.

Above the flame, there is a plume or jet of hot products that impinges on the top

of the vessel at a stagnation point. Heat transfer rates from the gas to the vessel are

highest at this point. The impinging gas flows radially outward from the stagnation

point as a "wall jet"; heat transfer rates decrease continuously with increasing distance

from the stagnation point. Entrainment of the surrounding atmosphere by the flame
3

and downstream flow induces 'a general circulation inside the vessel. This circulation

(and the stirring motion of the fans in some te 'sts) provides the turbulence level and

mean flow that determines the heat transfer rate from the hot combustion products to.

the vessel surface outside the stagnation flow region.

Fire in a Closed Vessel

Stagnation Point

Bulk Gas

Vessel Wall

Wall Jet

Plume or Jet

Flame

f~

Figure 1. Configuration of flame jet or plume and induced flow inside the vessel

The rate of convective heat transfer is the most significant unknown in the analysis

of these experiments. For this reason, the data analysis in this report concentrates on

the determination of the convective heat transfer coefficient from the limited measurements that were made. The issue of scaling up to nuclear plant containment building

dimensions is briefly addressed.

The structure of the report is as follows. The data are presented in Section 2 and

Appendix A. An overview discusses the initial conditions, instrumentation and signal

quality for all 16 tests. Individual data plots are presented in Appendix A for selected

instruments in each test. Only pressure plots are given for the 12 tests that were not

analyzed at SNLA. Injection, mixing and ignition behavior are discussed in Section 3.

Heat transfer modeling is discussed in Section 4. Examples of a test simulation and
4 1 INTRODUCTION

the inverse' method of determining heat transfer rates from data are given using test

03. A summary of the reduced data and convective heat transfer coefficients is given

in Section 5. Speculations are made about the possible scaling laws applicable to the

heat transfer coefficients. The report is summarized in Section 6.
5

2 Test Conditions

2.1. Overview

Sixteen CI tests were performed. 'the source type, flowrates, igni ter location(s), and

fan/spray options are given for each test in Table 1. Initial conditions, gas pressures,

gas temperatures, steam mole fractions, and burn durations are given in Table 2.

The geometry of the vessel and associated equipment is shown in Fig. 2. The

H2 - steam mixture was injected at the bottom of the vessel as a jet or plume directed

vertically upward. The source was located slightly oiff the centerline and about 2 mn (7 ft)

from the bottom of the vessel. The vessel was equipped with a variety of instruments

to measure gas pressure, gas temperature, gas concentration, wall temperature, and

total and radiative heat flux. These instruments and their placements are described in

detail in both the EPRI report' and the report 2 on the premixed test data analysis.

The locations of the instruments discussed in the present report are given in Table 1

of Appendix A.

In general, there were only a limited number of calorimeters included in the Hydrogen Behavior tests. Further, the data sets provided for each test of this series were

limited typically to only the -signals from SNLA-provided instrumentation. For the

Equipment Survival tests, significantly more calorimeters were included, and Sandia

was provided with these data and with additional gas and wall thermocouple data.

An assessment of the instrumentation for which data were provided to Sandia (on

computer tapes) from the continuous-injection combustion tests was performed following preliminary data processing. This processing was used to reduce the EPRI-provided

data sets from 3000-4000 time-signal pairs to a more reasonable set of 200-600 pairs

by elimination of redundant data and some data smoothing. Tables 3 and 4 provide

this assessment of signal'quality for the tests of the Hydrogen Behavior and Equipment

Survival series, respectively. Assessment of radiative calor 'imetry signals for these tests

have been omitted given the problems with processing these data (described in Ref. 2).

In general, there are few data available to SNLA for analysis of the Hydrogen

Behavior tests. Wall and gas thermocouple data were provided for only 2 of the 12

tests; only one pressure signal is available for 5 of the 12 tests. The only tests which

can be analyzed in any detail are NTSCO3 and NTSC08. There are fairly complete

data sets available for the 4 tests of the Equipment Survival Series. The two tests, CS1

and CS5, that had constant-flowrate sources have been analyzed.

Plots of the data are given in Appendix A for selected signals from each test. Only

a pressure signal is given for most tests.
6 2 TEST CONDITIONS

W6

10'

6V

0a

0' -

Figure 2. Coordinate system used to define locations in the dewar. These are rectangular cartesian coordinates, (x, y, Z), with the origin (0,0,0) at the center of the

vessel. The z axis is vertical , x and y axes are in the horizontal plane as shown. These

dimensions are given in feet for consistency with Refs. 1 and 2.
2.1 Overview7 7

Table 1L. Test Matrix

Test Date Gas Injection Rates Igniter an or

H2 H20 Location(s)c Spraysb Sourced

(kg/mmn) (kg/min)

Hydrogen Behavior Series

Cl

C2

03

05

07

C8

09

010

Cli

CN1

CN2

CN3

8-25-83

8-26483

8-30-83

8-23-83

9-8-83

9-8-83

9-12-83

9-13-83

9-13-83

9-19-83

9-20-83

9-22-83

2.1

2.0

1.8

1.6

0.4-2.7e

1.4

1.9

1.8

.1.8

1.9

1.8

1.8

28

28

29

0.0

0-55e

75

10.

63

.63

27f

0-15'

45f

T,3E

T,3E

3E

T,3E

T,C,B

T,3E

B

3E

3E

T,3E

T,3E

B

S

F

F,S

F,S

D

D

D

D

D

D

D

D

.N

N

N

Equipment Survival Series

051

052

OSS

CS6

1-3-84

1-5-84

1-10-84

1-24-84

1.8

3.6

1.8

0.4-1.30

'28

0-27e

9

9-23

T,3E

T,3E

1E

B

S

S

S

S S

'Fans operative (F).

'Sprays' operative- (S).

'Igniters near top (T), 3 or 1 on wall at Equator (3E, 1E), at.

center (C) or near bottom below source elevation (B). dVertical injection through a diffuser (D, diameter 1 in), nozzle

(N, diameter 12.7 cm), or sonic nozzle (S, diameter 3.8 cm).

'Blowout test, variable flowrates.

f Steam flowrate oscillated, mean value given.
8 8 2 TEST CONDITIONS

Table 2. Initial Conditions

Test P- T. XH2 '0 Til tl- tof At

(kPa) (K) '(K) (s)- (s) (s)

Hydrogen Behavior Series

C1 120.7 346 ;0.29 383 170 700 530

C2 100.7 328 0.15 390 210 600'2 .380-980"

C3 107.6 346 0.32 393 292 706 .414

C5 106.2 344 0.30 348 170 1030 860

C7 100.7 341 0.27 388 145 12 20 ' _b

.C8 110.4 344 0.29 408 365 720 355

C9 110.4 344 0.29 383 --- C _C

C10 109.0 344 0.29 413 1250 600 350

C11 134.5 356 0.39 408 330 650 320

CNM .106.9 344 0.30 398 250 705 455

CN2 100.0 329 0.16 413 140 good 2 10 ,4 00 d

CN3 110.4 326 0.11 400 390 1240 850

Equipment Survival Series

C1 106.9 343 0.29 403 306 900 594,

CS2 106.9 343 0.29 393 100 535e 135,315e

CS5 93.1 325 0.15 403 246 900' 654

CS6 91.0 321 0.12 373 -f' -f -f

'Erratic burning after 600 s.

bVaxiable fiowrate, erratic burning

CDeflagration after 1000 s, see text. Designation changed to P8.

dVariable flowrate, two burns.

'Variable fiowrate, two'burnis.'

f Deflagration at 4050 s.
2.1 Overview9 9

Table 3. Signal Quality for the Hydrogen Behavior test series

Instrument Test

05 C1 0 2 03 07 08 010 011 CMi 0N2 0N3

Pressure Trasducers

P102 U U U G U G

P105 G G G M B B

Total Slug Calorimeter

H104 G G G G G G

Total Thin-Film Gauge

H*232 G G G M G G

Total Gardon Gauge

H*106 G G G U R R

Wall Thermocouples

T120 U U U G U G

T121 U U U G U G

Gas Thermocouples (3-mil)

T101' U U U G U G

T105 U U U G U G

Gas Thermocouples (32-mil)

T114 U U U G U G

T118 U U U G U G

U

B

U

B

U

B

U

B

U

B

G G G G G

G C G G G

R. R R R R

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

U

a Pressure sensor P104 inoperative for all tests.

VU - Signal not provided by EPBI (i.e. "unavailable")

'R- H1106 was reconfigured as a radiative gauge

'G- Signal quality"good"

W- Signal quality "marginal"

'T' - Signal quality "bad"
10 2 TEST CONDITIONS

Table 4. Signal Quality for the Equipment Survival test Series

Instrument Test

O81 052 CS5 OS6

Pressure Transducersa

P101

P102

P103

Total Slug Calorimeter

H104

Total Thin-Film Gauge

H232

Flat-Plate Gauge

T501

T502

T503

U

G

U

U

G

U

U

G

U

G

G

G

G G G G

G G B G

G

G

G

G

G

M

M

M

G

G

G

G

G

G

Aluminum Cube

T504

T505

Total Schmidt-Boelter Gauges

H502

H503

H504

H506

H507

Wall Thermocouples

T120

T121

Gas Thermocouples (3-mil)

T101

T102

T105

Gas Thermocouples (32-mil)

T118

T151

M

G

M

M

B.

M

G

G

G

G

G

G

M

M

B

G

G

G

G

G

G

M

G

B

B

B

M

G

G

G

G

G

B

G

G

G

B

G

M

M

M

B

M.

,G

*G

G

G

G

B

G

G

a P104 and P105 inoperative for all tests

'U' - Signal "unavailable"

'G' - Signal quality "good"

'M- Signal quality "marginal"

'B' - Signal quality "bad"
11

3 Injection, Mixing and Ignition

Four distinct types of ignition behavior were observed in the tests. These are: (1)

slow ignition and diffusion flame burning; (2) fast ignition (deflagration) followed with

diffusion 'flame burning; (3) deflagration and no diffusion flames; (4) no ignition of any

kind. The dominant behavior was of type (1), slow ignition followed by a diffusion

flame. The other three behaviors were singular events that were observed in only one

test each out of the entire program of testing. Despite the exceptional nature of these

events, it is possible to understand these phenomena and the circumstances under which

they might occur. The ignition behavior is determined by two factors: the fluid motion

induced by the H2-steam source and the location of the igniter.

The fluid motion in the vessel during injection depends crucially on the source

characteristics. For subsonic jets and plumes, the relevant dimensional quantities are

the source diameter, fluid density, and velocity. These are listed in Table 5 together

with two nondimensional quantities, the Froude number Fr and the Reynolds number

Re:

oW_ UD

Fr = Re =Re= gApD'V

where U is the source velocity; p the source density; D the source diameter; Ap the

source-atmosphere density difference; g the gravitation acceleration; v the kinematic

viscosity of the jet fluid.

The Froude number characterizes the most important aspect of these sources, the

relative role of inertial and gravitation forces. All tests with the diffuser source (D=1

m) are characterized by very low Froude numbers, Fr -0.1, indicating that buoyancy

forces dominate the plume flow above the source. The nozzle sources (D=0.13 m)

have intermediate Froude numbers, Fr -- 5 X 103 104o, and the gravitational and

inertial forces are comparable. The sonic sources (D =0.038 m) have very large Froude

numbers, Fr > 10', and the jet flow above the source is dominated by inertial forces.

The influence of the Froude number on the mixing is discussed below.

3.1 Slow Ignition and Diffusion Flame Burning

This was the behavior observed in the majority of tests. At the start of all tests,

the igniters were turned on and the flow of H2 and steam started. There was a delay

of 100 to 400 seconds between the start of injection and the formation of a diffusion

flame at the source. No pressure pulses or deflagrations were observed and the diffusion

flame appeared (from IR video cameras inside the dewar) to be ignited by a very weak

flame propagating from the igniter(s) back to the source. Depending on the igniter

location(s) and the source characteristics, ignition could occur relatively quickly (2-10

s) or take place over a longer time of several minutes.

For this dominant ignition sequence, the gas pressure and temperature rises within

the vessel were produced entirely by the diffusion flame. An example of the gas pressure
12 12 3 INJECTION, MIXING AND IGNITION

produced by test C1 is shown in Fig. 3. The slow initial rise in the pressure is due

to the compression of the original gas in the vessel by the injected H2-steam mixture.

After a period of 170 s, the hydrogen concentration has increased to the point (- 4-.5%)

where the igniter at the top of the vessel initiates combustion in the surrounding gas.

The combusting region then slowly propagates downward toward the source and causes

the ignition of the entire plume.

Table 5. Source Parameters

Test U p Fr Re

(m/s) (kg/in3 )

Hydrogen Behavior Series

C1 1.35 0.456 0.10 4.7x 104

C2 1.64 0.376 0.15 4.6 x104

C3 1.55 0.396 0.13 4.5 x 104

C5 0.52 0.074 0.0019 3.9x 103

C8 4.55 0.535 1.76 1.8 x101

C9 0.55 0.070 0.0024 4.0x X 10

C10 2.94 0.467 0.60 9.7x10

C11 2.'36 0.584 0.40 9.8X I04

CN1 98.4 0.389 4.0 x10 3 3.5 x101

CN3 136 0.233 9.5 x103 5.7 X10 5

Equipment Survival Series

CSPa 439 - --

C556 531 ---

a Sonic jet.

This burning plume or diffusion flame has a power output of about 3 MW that

causes the large increase in gas pressure at this point. As the combustion products

are mixed with the vessel contents and the energy is absorbed by the vessel walls, the

rate of pressurization decreases. The diffusion flame persists until 700 s when the 02

concentration in the vessel falls below -'~8%. At this point, the flame goes out and the

pressure decreases as heat is continually absorbed by the vessel walls. Eventually the

pressure begins to rise again due to compression by the injected gas.

This ignition behavior is consistent with the formation of a stable layer of hydrogen

at the top of the vessel. The layer is supplied with hydrogen by the jet or plume formed

above the source and the depth of the layer increases steadily with time. Although there
3.1 Slow Ignition and Diffusion Flame Burning 113

were insufficient measurements of hydrogen concentration made to show this in detail,

the phenomena of stable stratification is well known and has been observed in many

similar types of mixing experiments. The basic sequence of events was first described

by Baines and Turner3 and is illustrated in Fig. 4.

The first phase of the process is the development of the jet or plume above the

source. This process has been investigated by Turner" for impulsively started buoyant

sources with negligible momentum, i.e., Fr << 1. He found that the transient flow

could be approximated by a vortex flow at the head and a steady plume flow behind.

The head travels at a speed equal to about 0.6 of the local centerline velocity for the

equivalent steady plume. From the start of injection to impingement on the vessel top,

the entire process takes about 10 s for the sources used in the NTS tests.

0

9

0.0 250.0 500.0 750.0 1000.0 1250.0

time (s)

1500.0

Figure 3. Gas pressure in Test C1. This exhibits. the signal characteristic of slow

ignition followed by diffusion flame burning.
14

i4 3 INJECTION, -MIXING AND IGNITION

(a)

(b)

I(C)

(d)

Figure 4. Sequence of events observed in stable mixing. (a) Transient development

of the plume or jet flow. (b) Impingement of the jet on the top of the vessel and the

formation of a stable layer. (c) Growth of the stable layer. (d) Asymptotic approach

of the bottom of the layer to the source level.
3.1 Slow Ignition an~d Diffusion Flame Burning 115

The second phase of the process is the impingement of the plume and development

of a stable layer. The vertical motion of the fluid in the plume is converted to a radially

outward motion along the top of the vessel. Th is radial motion is frequently referred

to as a "wall jet." Since the fluid in the wall jet is lighter than the vessel contents,

eventually the fluid will separate from the wall and turn inward toward the jet. This

occurs when the momentum of the fluid in the wall jet decreases below a critical level

and the upward buoyancy forces dominate.

Fluid separated from the wall spreads out horizontally to form a stably stratified

layer. This fluid consists of the original source fluid and vessel fluid entrained by both

the plume and the wall jet. A nearly planar horizontal interface separates the lighter

fluid at the top of the vessel from the original vessel contents. In the third phase of

the process, the interface moves downward toward the source elevation. There is'a

slow circulation within the stable layer and the motion of the vessel contents below is

primarily horizontal due to entrainment into the plume. For a very-low-momentum

plume, the circulation within the stable layer can be quite weak and stratification occurs

within the layer. In this situation, the interface remains planar and only asymptotically

approaches the source elevation; this is the fourth phase.

As discussed in Baines and Turner, a simple solution can be obtained for the interface motion in phases 3 and 4 if the source is a low-momentum plume. This solution

neglects the initial mass flowrate in the source and equates the rate at which the

original vessel fluid below the interface is being consumed dM1 /dt to the plume mass

entrainment rate A1k.

d

-M1 +M~ =0

dt

The first term is computed as

dA= p,,A (z) dY

where the original vessel fluid density is pu, the interface height is Y, and the vessel

area perpendicular to the plume is A(z). An idealized similarity solution is used for

the plume entrainment

=CmPV (W ) 2/5(YZ5/

where Cm. 0.21, zo is the origin of the plume and W is the buoyancy flux, defined as

W =f g,&pU27rr dr

This integral is an invariant for a plume in a uniform atmosphere and can be computed

at any elevation; it is simplest to do the computation at the source where all the

conditions are known.
.16 3 INJECTION, MIXING AND IGNITION

I have computed the motion of the interface inside a sphere for a point source located

0.7 radii below the center and on the vertical axis of symmetry. This approximates the

geometry of the NTS experiments. The results are shown in Fig. 5; these were obtained

by numerical integration. The interface motion is described with normalized variables

Y=Y/RI and r = tITET,, where X. is the vessel radius and TET is the characteristic

filling time. The filling time is given by

TET = ,

which is approximately one-third the time required to entrain the entire contents of

the vessel through the plume once. These filling. times are given in Table 5 for all tests

with low Froude number.

bc

10

6

N

40

10- 1-1 0

10

time, 7-

101

Figure 5. Motion of the interface between mixed -and original fluid. Solution for a

sphere with the source at -0.7R on the vertical axis. Solution for the equivalent cylinder

is also shown.

The simple picture discussed in previous paragraphs changes dramatically with

increasing jet Froude number. This has been demonstrated in small-scale experiments'

using jets of brine into fresh water. As the Froude number is increased, the interface
3.2 Fast Ignition and Diffusion Flame Burning 117

between mixed and unmixed fluid breaks down and at very high Froudel- numbers,

a large-scale circulation is set up within the vessel. This circulation eliminates any

stratification within the mixed layer and efficiently mixes the container fluid with the

jet fluid. The mixing occurs throughout the vessel and extends to regions usually not

touched in low Froude number flow, i.e., the stagnant region below the source elevation.

Experiments in a right circular cylinder suggest that the transition between stable and

unstable mixing occurs at a source Froude number of -~ 3000.

3.2 Fast Ignition and Diffusion Flame Burning

This ignition sequence was observed in one test, CN3. The ignition source was near

,the bottom and a jet with intermediate Froude number was the source. At intermediate

Froude numbers, a front is present between the mixed and unmixed fluid. This front

moves much more rapidly than in the low Froude number cases and there is much more

circulation within the mixed region, i.e., stratification does not develop. When the

front reaches the ignition source near the bottom, the resulting flame can propagate

through a large portion of the mixed fluid. This produces the pressure spike at the

beginning of the burn that is charac teristic of a deflagration. This pressure spike can

be observed in Fig. 6 at a time of 390 s. Following the spike is an almost linear increase

in pressure due to the diffusion -flame. The slope is much smaller than in previous'

examples due to the -enhanced heat transfer caused by the fluid motion induced by

the fans and sprays and also, the thermal sink effect of the water evaporated from the

sprays.

3.3 Deflagration and No Diffusion Flames

Prior to the actual testing, most computations suggested that this behavior was

expected to dominate. In fact, a very special set of circumstances had to be arranged to

observe this behavior in the last test, CS6; and only one small deflagration was observed

near the end of the test. Deflagrations, either multiple or single, were exceptional

cases. The pressure trace for CS6 is shown below. Note that the first four spikes in

the pressure signal are not burns but rather the result of purging the water from the

lines connecting the transducers to the vessel. A single deflagration occurs at 4000 s.

A very low flowrate, was combined with water sprays and bottom ignition to achieve

this effect.

Like test CN3, the source Froude number was in an intermediate regime. This

results in a mixed layer above the igniter, although some stratification is still possible.

There is a long delay until the hydrogen concentration at the igniter reaches -4% and

then the resulting flame propagates throughout the vessel. This deflagration produces

the pressure spike at 4000 s.
18 -3 INJECTION, MIXING AND IGNITION

CJ

pli

05. 0.0. 0. 5. 00. 200 10.

tim (s

Fiue6 a rsur o etCI oe h pk u0ote elgaina h

beinn ftedfuso lm giin pry n as0r ot ndrn h et

ac

00

0

9

0.0 1000.0 2000.0 3000.0 4000.0

time (s)

Figure 7T. Gas pressure for test CS6. Note that the first four spikes are artifacts. A

deflagration occurs at 4500 s. Sprays were on during the test.
3.4 No Ignition at All 119

3.4 No Ignition at All

This behavior was observed in Test C9 which was later designated P8 after operator

intervention resulted in a deflagration. The flow above the source was a plume with

very low Froude number, Fr -0.002. This flow produced a stable mixing layer which

never got any lower than the source elevation. Since the igniter was --1 m below the

source, no ignition was observed as long as the atmosphere was quiescent. Due to

concerns about the buildup of hydrogen, the source flow was turned off at about 720 s.

Igniters were left on, the fans were turned on at 975 s, and ignition took place at 1060

s. A deflagration propagated through the vessel, producing a peak pressure of -400

kPa. This pressure is in good agreement with the adiabatic, constant-volume value

for a mean hydrogen concentration of 11.1%, the amount computed by integrating the

flowrate.

The hydrogen concentration profiles shown in Fig. 8 provide a nice confirmation of

the simple Baines and Turner theory of stable mixing. A delay of 300 s is observed

between the detection of hydrogen at +10 ft and -10 ft. According to the simple theory,

the characteristic filling time is 149 s and the delay should be approximately 250 s.

25100

H001

0 500time (S)

Figure 8. Hydrogen concentration for test C9. Sensor H001 located at +10 ft

(z/R = 0.38); sensor H003 located at -10 ft (z/R = -0.38).
20 20 4 'MODELING

4 Modeling

The modeling and analyses performed for the CI tests are primarily based on thermodynamic considerations and ignore the details of the fluid flow and spatial variation

of gas temperature and wall heat flux. The injected fluid and combustion products

are also assumed to instantaneously mix with the fluid that is already present in the

vessel. This type of treatment is appropriate considering the rather crude nature of

the measurements and our lack of knowledge about these processes. For tests in which

mixing is strongly driven by a high-momentum jet or fans within the vessel, this type

of modeling is very successful. For low-momentu~m plume fires, we cannot expect as

much from the model and as discussed below, the stratification produced by buoyancy

can be quite important.

One aspect of these tests that will always require consideration of the local flowfield

is the plume or jet flow above the fire and the resulting stagnation point at the ceiling

of the vessel. While no specific data on this region were obtained in the NTS tests, the

results of other investigations and previously developed models can be utilized. In this

manner, the peak heat transfer rates at the stagnation point and the spatial variation

of the vessel wall temperature can be estimated.

The plan for this section is to first develop the general model and illustrate the nature of the results with approximate analytical solutions to the model. The application

of the model to a single test (C3) will then be given. Following this, the inverse version of the model will be derived and the computation of the convective heat transfer

coefficient given for test C3. The problem of stagnation-point heat transfer and wall

temperature variation will be examined and methods for estimating the peak fluxes

and temperature profiles discussed. Finally, the effects of stratification and buoyancy

will be discussed.

4.1 Tr~ansport Model

The transport model is based on the integral version of the transport theorem for

a single volume fixed in spaces6

d tf ( )f P2f~ (1)u

where V is the vessel volume, A is the vessel area available for heat transfer, Aj~ the

area over which injection occurs, e the fluid specific internal energy, h the fluid specific

enthalpy, p the fluid density, u the fluid velocity, q the heat flux to the vessel and Q

the total heat transfer rate from the gas to the vessel.

The flow inside the vessel is subsonic (except possibly near the jet exit) and the

kinetic energy 02 /2 can be neglected compared to the internal energy, enthalpy and

heat transfer terms. In addition, the gas flowing into the vessel will be assumed to be
4.1 Transport Model 221

in a sufficiently uniform thermodynamic state that average values for h can be used,

so that

IAid, puhdA = - jet (2)

where the sum is over all components (species) entering the vessel through the jet or

plume and Mf is the mass fiowrate of species j into the vessel.

The energy integral E can be rewritten in terms of the energies ei and masses M

of the individual species of gas within the vessel

E f pedV = E Miei.(3

vessel

The time derivative of the energy can then be split into two terms

dE =_1 dM, i Meg dT (4)

dt vessel dt d

where M = MA' is the total mass within the vessel. On the RHS, the first term

represents changes in energy due to mass addition and chemical reaction within the

vessel. The second term represents the change in energy due to changes in temperature.

The symbol cg denotes the average (mass-weighted) constant-volume specific heat of

the gas within the vessel

cg =>yicv, (5)

where yj is the mass fraction of species s

With these approximations and definitions, the complete energy equation can then

be written as

Me ~ -T -ei ->E1Mhj=-Q. (6) Mcg~+vessel jet

This result can be further simplified by utilizing the thermodynamic identity

h = + E(7)

where p denotes gas pressure. Applying the ideal gas law p = pRT and assuming that

the jet or plume pressure is identical to the vessel pressure (valid for all but sonic or

supersonic jets) we obtain the final version of the energy equation

dT dM, Mcg - = ~et vEse dei + MietR~jet - Q (8)

where Mjet is the total mass fiowrate of injected gas.
22 22 4 MODELING

This form of the equation clearly shows the different processes that cause changes in

the temperature of the gas within the vessel. The first two terms on the RHS represent

energy changes due to either i) differences in the composition and thermodynamic state

of the gas in the jet and in the vessel or ii) chemical reaction between the different

species within the vessel. Note that if the jet and vessel gas have the same composition

and temperature and there is no chemical reaction, the sum of these terms vanishes.

The third term represents the compression work done by the injected jet fluid on the

gas within the vessel. The fourth term represents the energy change due to the sum of

the heat transfer processes that result in a transfer of energy from the gas to the vessel

walls.

4.2 Combustion Model

In keeping with the spirit of the transport model, a very simplified description of

the combustion process is used. The diffusion flame is treated as an energy source

and any hydrogen entering the vessel while the fire is burning is completely consumed.

The time periods during which combustion occurs .are specified as input data to the

computation. The magnitude of the energy release term is determined by assuming

that a stoichiometric proportion of oxygen is burned, with the incoming hydrogen to

produce only water as a product.

One complication that can occur is that hydrogen may be present in the atmosphere

inside the vessel. This can be due to the initial transient phase during which injection

is taking place but ignition has not occurred or, if the flowrate is varied during the

test, the flame may extinguish and later reignite. The concentration of hydrogen in

the vessel atmosphere is usually lower than the limit value (4%) for flame propagation

when ignition takes place and a deflagration does not occur. One exception to this rule

is when a low-momentum (plume) source of hydrogen is used and the ignition source

is placed near or below the elevation of the source. This situation and the possibility

of stratification and resulting defiagrations was discussed earlier in this report. Deflagrations are not included in the present model but a number of other researchers have

considered this problem and many different types of models are presently available.

The combustion model we use assumes that no deflagration occurs and the hydrogen

present in the vessel atmosphere is consumed within the diffusion flame only. The rate

at which the atmospheric hydrogen is consumed depends on the rate at which the

vessel atmosphere is being entrained into the diffusion flame. The entrainment rate is

primarily a function of source momentum. For jet-like sources with high momentum,

approximately three times the jet mass flowrate will be entrained.' For plume-.like

sources with low momentum, up to 15 times the plume flowrate will be entrained.'

The actual rate of atmospheric hydrogen combustion will be somewhat lower than the

entrainment rate since not all entrained fluid will enter the high-temiperature portions of

the diffusion flame. The computation simply takes the mass burning rate of atmospheric

hydrogen to be some constant a (given as an input parameter) times the source mass
4.3 Thermal Model 23

flowrate.

Based- on the simple model described above, the combustion analysis reduces to

a prescription for computing the time derivatives of the mass of each species within

the vessel. These derivatives are then used to evaluate the second term of the energy

equation (8) given above. For the simple ýmodel in which the fire is either on or off,

there are two separate situations.

Fire off:

dMH2 = MMf2 ; (a

dt (a

dMH2 O =_ H;(b

dt -M 2 ;(b

dMo2 - 0; (9c)

dt

d 2 = 0. (9d) dt

Fire on:

dMH, aHMJt la = aHMd 1a

dt

dMH2O WH20 ' dMH,' M H2 0+ kH M 1 + d '(lob)

dt W112

dM021 W 0 2 kH2+ dM2(l0c)

dt .2 W1 2 \dt/

dMN2 =(ld

dt

The symbol Wi represents the molecular weight of the ith species.

A quantity that frequently arises in the course of the computations is the equivalent

heat release rate of the fire, Qf. This is the rate at which energy would have to be

added to the gas externally as heat to produce the same gas temperature rise as the

combustion process. Since the convention is that Qf is a positive quantity, it is defined

to be the difference of the two terms on the RHS of the energy equation (8)

Qf dM,

jet Vessel d

4.3 Thermal Model

.Heat transfer from the mixture of hot combustion products and vessel atmosphere

fluid occurs through the'combined actions of convection, radiation and condensation. In
24 24 4 MODELING

the NTS tests, the vessel interior surfaces were usually hot enough so that condensation

was negligible. For this reason', condensation is not, considered in the present model.

Models developed for defiagrations usually include a condensation submodel that could

be applied to the present problem. The processes of convection and radiation are

obviously coupled and a correct treatment of this mixed-mode heat transfer process is

a complex undertaking. Consistent with the other simplifiocations used in this model,

the two processes will be approximated as being uncoupled but simultaneously occuring.

Standard engineering approximations will be used to compute the rate of heat transfer

for each mode and the individual rates will be summed

Q =Qrad + Q00on1

to obtain the Q term on the RHS of the energy equation (8). Each process is discussed

separately below.

Convection

Convection is computed using Newton's law of cooling

Q =on AnM.l (Tg -Tm) (12) sur faces

where the sum is over all the surfaces m that are exposed to the gas inside the vessel.

For each surface, a constant value of the convective coefficient lm is used. Temperatures

'Used in this formula are Tg, the mean temperature of the gas inside the vessel and Tm,

the mean temperature of the front of each surface. For the NTS experiment, the only

surface of any importance is the vessel wall itself so that m 1 and the front surface

temperature T, will be denoted T,.

Obviously, the success of this approach depends on the appropriate value of N being

chosen. There are a number of existing heat transfer correlations that can be used to

estimate )I and comparison of simulation results with measured data can be used to

improve these estimates. Estimation formulas have been not been used in the computation directly since no correlations exist, for the type of. mixed (forced-free) convection

that actually exists in the experiments. Unfortunately,;,,many inappropriate textbook

correlations have been applied in the past to this problem leading to misleading and

erroneous results. By not providing correlations, the user of this model will be forced

to contemplate the crudeness of the present technique and will hopefully realize the

very approximate nature of the model results.

One technique that can be used to icircumvent this ignorance of the correct correlation is to use the experimental data and a variation on the present model to infer

the convective heat transfer coefficient for each test. This will be referred to as the

',inverse"~ version of the model and the details are given later. The problem of scaling

and extrapolating the limited data from the present tests is also considered in later

sections of this report.
4.3 Thermal Model 225

Radiation

Radiation heat transfer is handled by an approximate enclosure model using an

effective beam length to compute a mean gas emittance. Nonuniformity of the gas

composition and temperature are not included since these have not been quantified

for the NTS tests. The majority of the radiant exchange is between the combustion

products (steam) mixed into the vessel atmosphere and the cooler vessel walls. A small

fraction of the radiant exchange is directly from the very hot products in the flame zone

itself to the cooler vessel walls with some absorption by the intervening atmosphere.

The net radiant heat transfer rate from the gas to the vessel can be expressed as

Qrad --= Ae~ff a (T 4 - Tn' 4 x (13)

where a- is the Stefan-Boltzmann constant.

The first term represents the bulk-gas/vessel radiant exchange. The effective emittance Eff is computed using Hottel's furnace model'

1 =1 +1-1 (14)

Cef f 69 6,

where the e. is the gas emittance and c,, is the emissivity of the vessel wall. The gas

emittance is a function of the gas composition y, thermodynamic state p, T, and the

path length C2 over which radiative transfer occurs

IEg = E (y, p, T, 12.(15)

The emittance is computed using the approximate, but fairly accurate exponential

wide-band model of Edwards1 0 and the known gas composition and thermodynamic

state. The path length used for this computation is known as the mean beam length

L2 and is based on the engineering estimate1 1 of

123.5-A'

which is 1.17R for a sphere of radius R.

The second term in Eq. (13) is the direct exchange between the fire and the wall.

This is an empirical expression that has been deduced from experimentation. The

fraction of energy radiated directly from the fire is X which ranges between 0.05 and

0.15 for hydrogen diffusion flames in air.",'1 The higher values of X are for plume-like

fires, the lower are for jet-like fires.

No data are available for steam-diluted flames so I have assumed that the fraction

is unchanged. The transmission by the atmosphere r is computed with the exponential

wide-band model using an adiabatic flame temperature and black body distribution

for the radiation source and the bulk gas temperature and properties for the absorbing

gas. A typical value of r is 0.7.
26 26 4 MODELING

Conduction

In the one-surface model of the NTS vessel, -the conduction model is greatly simplified. Since the vessel atmosphere is considered to be well-mixed and spatially uniform,

only conduction transverse to the vessel surface has to be considered. In actuality, the

assumption of uniform heat transfer to the vessel Walls is the least realistic feature of

the present model. The disagreement of the model results with the experimental data

is discussed more completely in sections to follow.

A crude but greatly simplifying assumption is that the vessel walls are thermally

thin and that the temperature within the wall is uniform. In that case, the energy

equation for the vessel wall is

dTV

dt

where c, is the heat capacity of the wall and M, is the total mass of Wall material.'Unfortunately, the walls of the NTS vessel are made of relatively low' thermal conductivity

stainless steel. The characteristic conduction time

t2

tcondis fairly long, about 85 s for the 19 mm thick stainless steel vessel shell. This-means

that the thermally thin assumption is only valid if the transients occur on time scales

much longer than this.

A better model is a one-dimensional transient conduction process in a slab with

an insulated back boundary and a given flux at the front surface. The temperature

distribution inside the wall is determined by solving the conduction equation

aT - a2T (7

with the boundary conditions of

ka T" (18)

and

-k (9, O. (19)

ax 1~

Note that the computation involves an implicit solution for the front surface temperature since it also appears in the expressions for computing the flux. This implicit

problem can cause instability of the numerical solution method if not handled properly. This is due to the stiffness of the radiation condition, i.e., the flux is very sensitive

to changes in the surface temperature when the system is close to equilibrium. The

technique used to avoid this problem is described further below.
4.4 -Approximate Solution 227

Summary

The complete expression for the heat flux from the gas to the vessel wall is

Q AM1 (Tg - T,,) + Ae~fu (T g T + TXQf. (20)

This expression is used in the energy equation for the gas (8) and the boundary condition (17) for the vessel wall conduction solution. These two equations must be simultaneously solved together with the equations for the mass of each species within the

vessel.

The partial differential equation (16) governing the vessel wall temperature is reduced to a set of ordinary differential equations by approximating the, spatial derivative

by a finite difference expression. If there are N spatial mesh points then the conduction

equation reduces to N coupled ordinary differential equations for the temperatures at

each mesh point. The details of this solution method are discussed in Appendix A.

The reduction of the conduction equation to a set of N ordinary differential equations .allows the use of existing subroutine packages to obtain the solution to the total

of N + 5 differential equations that make u p the complete system. A, fully implicit

predictor-corrector method based on the Adams-Bashford-Moulton algorithm was used

to perform this task. The package implementing this method, subroutine DEABM of

the SLATEC mathematical library, 14 uses a built-in step-size selection technique based

on maintaining user-specified error tolerances. The implicit nature of the method and

the built-in error control eliminate any tendency toward instability and assure a converged solution with minimal computational effort.

A simple FORTRAN program was written to read the input conditions, call the

integration routines and output the results. The thermodynamic properties of the

gas were evaluated using the CHEMKIN subroutine library 1 5 which is based on the

ideal-gas equation of state and a 4th-order polynomial fit to the specific heats. Gas

thermodynamic properties computed by this method are very accurate and represent

the smallest source of uncertainty in the model.

4.4 Approximate Solution

Under certain conditions, terms in the model equations can be approximated and

an analytic solution found to the approximate set of equations. This analytic solution is

very useful in understanding the behavior of the numerical solutions to the full model.

The approximations used to simplify the model are:

1. Thermally thin vessel wall. Neglect conduction and treat the wall as a lumped

mass. No other heat sinks present.

2. Convection heat transfer only. Neglect radiation.

3. Constant gas specific heat. Neglect differences between species.
28 4 MODELING

4. Neglect the increase of gas mass inside the vessel during the burn. M=0.

With these assumptions, the set of model equations becomes:

dt - Q1 (t) Q Cg Meg

dt~

Cvd"= C =c MVcV (21) dt

Qf (t) = Q(t) f + RTje~tMj.t (t); Qý= A)1 (Tg -T.) .

This is a pair of coupled, linear ordinary differential equations for Tg and T" and

can be solved by a change of variables that uncouples the equations. In general the

equivalent heat release rate Qf is an arbitrary function of time that wIill be different

for each experiment. The general solution can be written in terms of Qf as

AT= f t exp(- t. ) dt' (22)

and

CgTg + C"1T" Q(0 di-. (23)

If Qf is described by relat~ively simple functions of time, the integrals can be evaluated analytically to obtain explicit expressions for T' and T,. A practical example that

can be used to construct solutions for the NTS tests is the constant-strength fire. The

solution for AT is

AT = AT,,,.: [1 - exp(-t/ti)] (24)

where the time constant t1 is given by

C 1 1 1

the maximum temperature difference is

ATmlax = A)1 C,

and the total energy (gas and vessel) in the system is

CgT, + C.1 = Qft.
4.4 Approximate Solution 229

Physically, these solutions indicate that following a transient period of duration t1,

the gas-wall temperature difference reaches a constant value. A constant temperature

difference implies a constant convective flux. For vessels like the NTS dewar, the total

heat capacity of the wall is much larger than the total heat capacity of the gas and

C/C9 ý- 1. Therefore, the rate of heat transfer out of the vessel almost exactly balances

the heat input from the fire.

From the energy integral, we can see that the gas and wall temperatures will increase

linearly with time after the initial transient. The gas is essentially passive and serves

primarily to pass the energy released by the fire directly to the wall. Despite the

simplistic nature of the approximate model, the solution qualitatively reproduces the

test data trends. In comparing this model with the tests, there are three phases of each

test that must be considered:

1. Precombustion. This is the initial period during which the source is turned on

and hydrogen is accumulating in the vessel but not combusting. The hydrogen

levels near the igniters are below the flammability limit. The effective heat release

rate ýf is very small and is due only to the compression work by the source. This

results in the linearly increasing pressure observed at the beginning of each test

performed at NTS. The gradual linear increase can be thought of as a "baseline"

level onto which the effects of combustion are superimposed.

2. Combustion. A standing diffusion flame exists at the jet or plume exit. The

effective heat release rate is the sum of the chemical energy released in combustion

and the compression work by the source. The combustion phase can be subdivided

into two stages:

(a) Transient. For a time t, following ignition, the gas temperature (and pressure) rises faster than the wall temperature until a significant amount of

heat transfer begins to occur.

(b) Steady-State. After the transient stage, the gas-wall temperature difference reaches a constant, a constant amount of heat is transferred out of the

gas into the vessel and the vessel and gas temperatures rise linearly with

time. The rate of temperature increase is much larger in this stage than in

the precombustion stage since the chemical energy release by combustion is

much larger than the compression work.

3. Postcombustion. After the fire has been burning for some time, the oxygen content of the vessel atmosphere will be depleted below some critical level (between 5

and 8% by volume) and the fire will be extinguished. The rate of energy addition

and the vessel-wall temperature difference will decrease to the precombustion

level. This transient will also occur on a timescale of ti and can be observed in

the experimental pressure traces as the "tail" at the end of the burn. If injection
30 30 4 MODELING

is continued after the fire is out, the tail will merge with the gradual increase due

to the compression work.

The most unrealistic feature of the analytic model is the neglect of radiative heat

transfer. Comparison of numerical solutions of the full model with test data indicate

that 40-60% of the heat transfer can be through radiation. The next most unrealistic

feature is the assumption of instantaneous mixing that is used in the original model

formulation. The actual transient stage of the combustion phase is much longer than

predicted because of the finite time required to mix the combustion products with the

atmosphere inside the vessel. Finally, as mentioned earlier, the test data indicate a

very nonuniform rate of heat transfer depending primarily on the elevation within the

vessel. This is due both to the plume or jet impingement and stratification in the

atmosphere.

Despite these failings, this sort of analytic approach is very useful to obtain insight

into the qualitative behavior observed in CI tests. It is possible to generalize the model

to treat thermally thick surfaces,: such as the concrete walls in actual nuclear plant

containments. The main conclusion that the gas-wall temperature difference reaches a

constant following an initial transient remains unchanged. However, the gas and wall

surface temperature increase as Vt rather than linearly in the quasi-steady stage.

4.5 Example: Test C3

The previously developed model was applied to test C3 of the hydrogen behavior

series performed at NTS on Aug. 30, 1983. This test was performed with the fans on

and the large diameter (1 m) plume source. Hydrogen and steam injection rates were

constant during the entire test. The plume ignited at 292 s after the start of injection

and burned continuously until it extinguished at 706 s due to insufficient oxygen. The

initial conditions for the test are given in Table 6

Table 6. Initial Conditions for Test C3

H2 flowrate MH2 0.03 kg/s

H20 fiowrate MH2 0 0.45 kg/s

Gas temperature Yo 344 K

Gas pressure P.0 107.6 kPa

Steam fraction XH2 0 0.30

Jet temperature T, 393 K

Burn start tn 292 s

Burn end t011f 706 s

The vessel itself was modeled using data supplied by EPRI. The vessel was constructed of type 304 stainless steel and consisted of an inner shell 19 mm thick separated
4.5 Example: Test C3 331

by -. 1 mn of insulation (perlite) from an outer shell. The inner shell was treated as

either a lumped mass or a one-dimensional slab with an insulated rear boundary. The

approximate nature of the model. and poor comparison of measured and computed

model temperatures indicates that the lumped-mass thermal model is adequate at

the present level of sophistication. Dimensions and thermophysical data used in the

computation are given in Table 7.

Table 7. NTS Vessel Parameters

Interior volume 2085 In3

Interior radius 7.92 mn

Shell thickness 19 rmii

Shell mass 1.19x i05 kg

Thermal conductivity 17.3 W/m-K

Specific heat 460. J/kg-K

Density 8.0Ox 103 kg/in 3

Thermal diffusivity 4.7 x 10-6 M1 /s

Emissivity 0.6

Model parameters used in or derived from the computation are given in Table 8.

Equivalent heat release is computed from the given fiowrates and Eq. 11 above. The

actual value computed by the numerical model varies slightly during the test as the

vessel atmosphere composition changes and the gas heats up; the value given in Table 8

is an average. The convective coefficient shown was determined by trial and error using

a natural convection correlation as an initial guess. Gas emittance and transmission

were computed from the EWB model using an average gas temperature determined

from the data plots. A direct radiation fraction of 0.15 was chosen since that had been

previously measured 1 2 ,

1 3 for plume fires of hydrogen in air.

Table 8. Model Parameters for Test C3

Equivalent heat release rate Qf 3.7 MW

Heat transfer coefficient )1 20 W/m-K

Gas emittance Cg 0.50

Direct radiation fraction X 0.15

Gas transmittance to fire radiation T 0.70

Transient time scale tj 136 s

Steady-state temperature difference AT 212 K

Results of the numerical simulation using the parameter values given in Tables 7-8

are shown in Figs. 9-12. Note that the simulation is compared with actual data for all

signals except total heat flux; those gauges were not operational in this test. For the
32 32 4 MODELING

particular value of )I chosen, 20 W/m-K, there is good agreement between measured

and computed gas pressure and temperature. Agreement is much poorer for vessel wall

temperature. This is apparently due to both stratification and the stagnation-point

heat transfer at the top of the vessel.

P102

Cr)

0.0 200.0 400.0 600.0 800.0 1000.0

time (s)

Figure 9. Measured (P102) and computed gas pressure for test C3.
4.5 Example: Test C3 333

0

0

0

0

00 2.000.0 400.0'60. 800.0 1000.0

time (s)

Figure 10. Measured (TI18) and computed gas temperature for test C3.
34 34 4 MODELING

0

6

If)

~m4

"mu)

0

6

0

0*

0

If)

Ct,

0*

0

0

Ct,

0.0 200.0 400.0 600.0 '800.0- 1000.0

timeý (s)

Figure 11. Measured (T121) and computed vessel wall temperature for test C3.
4.5 Example: Test C3 35

............. 1 odel

0

S 00 0. 00.600 80010.

cme(s

Figure 12. Computed total heat flux for test C3.
36 36 4 'MODELING

4.6 Inverse Model

In the previous section, test C3 was discussed and it was demonstrated that fairly

good agreement between the model and data could be obtained if the appropriate value

of the heat transfer coefficient )I was used. In order to determine M1, a trial and error

method was used. While this could be used for all pf ,Ihe.tes~ts, a better technique is

available.

Previous work on premixed combustion 2 ,

16 ,1 7 ,18 has demonstrated that the measured

pressure signals can be used to infer the total heat fluxes. If the total flux is known and

the radiative portion can be estimated, then it is-poss ible to compute the convective

flux by subtraction. Knowing either the measured or estimated gas temperature, the

convective heat transfer coefficient can then be computed. This powerful "inverse"~

technique has been used to reduce data from numerous experiments in cluding the

premixed tests at NTS.

It is possible to extend the inverse method to continuous-injection tests, compute

average total fluxes, and estimate convective heat transfer coefficients.'as a function of

time. That extension is discussed below.

4.6.1 Model Formulation

The inverse method is based on using the pressure signal and its derivative to

determine the mean gas temperature and temperature derivative. Writing the ideal

gas law as

pV =NRT

where N is the number of moles and.I is the universal gas constant (8314 J/kg mol-K).

Consequently, the time derivative of gas temperature for a constant-volume system is

07_TT(ldp 1idN\ 25

di p-dt -N dt ) (

In terms of the constituent species masses M, and the molecular weights W,, the

total number of moles can be expressed as

N= Z A (26)

and the time derivative is

dN __(27)

Using this expression to' compute the temperature derivative', the previously derived

gas energy equation can be used to compute the rate of heat loss from the gas
4.6 Inverse Model 3

37

Q Qf MRTict IC g dt (28)

The gas thermodynamic state can be used to estimate the radiative heat transfer

rate from Eq. 13. Convective heat transfer. rates are computed as

Q cony = Q - Qrad

A convective heat transfer coefficient can then be calculated as

Qon

A(T - T.)

In order to est imate Qrad and compute N1,the vessel wall surface temperature must

be known. This means that the wall energy equation must be solved simultaneously

with the gas energy and species equations, just as in the direct version of the model.

4.6.2 Data Handling,

The key to successful use of the inverse model is computing sufficiently smooth, but

realistic-, derivatives of the pressure signals. It is well known that computing derivatives

from discrete and possibly noisy data is an ill-posed problem. That is, the answer does

not depend on the initial data in a unique and well-behaved fashion. Some care is

needed to eliminate this problem without smoothing the initial data excessively.

The data were recorded as a set of time-value pairs at fixed time increments. Quite

often the data contained a number of redundant points since the sampling rate was

far from optimal for most of the test. The first operation on the data was to remove

the redundant points and reduce the size of the data set. Following this step, from

200-700 data points remained. These remaining points were fit to a cubic spline with

the least-squares routine EFO from the SLATEC mathematical library. 1 4

A spline is a continuous function composed of individual polynomials joined together

at points known as knots. Depending on the order of the spline, the function and

the first n derivatives of each polynomial on either side of a knot must match when

evaluated at the knot point. This insures the "smoothness" of the resulting curve. By

using a large number of individual polynomials (i.e., knots), splines can also fit rather

arbitrary data quite well. The polynomial coefficients are determined by using a linear

least-squares fitting procedure and the given constraints at the knot points.

Using from 20 to 30 knots, the pressure data were fit with a cubic spline, i.e., a

spline composed of 3rd-order polynomials. The derivative of the spline was computed

analytically and the resulting expression evaluated to obtain the time derivative at

any point. Standard B-spline evaluation routines were used to perform this task. In

order to obtain a good fit near the beginning and end of the burn, where kinks occur

in the pressure signals, a higher concentration of knots was used and multiple knots

were placed at the kinks. A multiple knot relaxes the requirement of continuity of the
38 4 MODELING

highest-order derivative at that point and makes sharp changes in the signal derivative

easier to fit. A simple interactive program was written to facilitate performing this

task and an example of the data together with a spline fit is, shown in Fig. 13.

C,)

C=)0

W0

0.0 200.0 400.0 600.0 800.0

time (s)

1000.0

F igure 13. Raw data and spline fit for test C3 pressure signal
4.6 Inverse Model 339

4.6.3 Example: Test CS

An example of the application of the inverse method is given for test C3. Model

parameters and test conditions are as given above for the direct simulation. Although

the main product of the inverse method is the heat transfer rate and convective heat

transfer coefficient, the gas thermodyna miic sta te is also computed. Results are shown

in Figs. 14-17.

C)

0

6

CO

CC.
40 404 ýýMODELING

0o

I'l

0)

0o

n

0

0

0

0.0 200. 0 400.0 600.0 ..800.0 1000.0

time (s)

Figure 15. Measured (T121) and computed. (inverse metho'd) -wall temperature for

test C3
4.6 Inverse Model 4

41

C

I-tot al

radiat2 (

........... I

0.0 200.0 400.0 6010.0 800.0 1000.0

time(s

Figure. 16. Computed (inverse method) total wall heat fluxes for test C3
42 42 4 :MODELING

0O

N

10

09

0-

0

0

00

0-

CI)

-4-

0

0

6 I I

0.0 200.0 400.0 1600.0 800.0 1000.0

time. (s)

Figure 17. Computed. (inverse method) convective heat transfer coefficient for test

C3
43

5 Results

This section compares test results in the framework of the model presented in the

previous -section and discusses the results of the inverse modeling for heat transfer.

First, the effect of fans and sprays are discussed. Second, the effect of varying the nozzle

size on the average heat transfer coefficient is discussed. Third, the nonuniformity of

the heat transfer is discussed and the magnitude of the stagnation-point heat transfer

rate is estimated.

5.1 Sprays and Fans

Three tests were conducted with nearly identical source parameters: C1 is the

baseline case, no fans or sprays; C2 is the spray case; C3 is the fan case,. All tests were

conducted with the 1 m diameter diffuser source and nominal fiowrates of 1.8 kg/mmn

hydrogen and 27 kg/mmn steam. A comparison of the gas pressures for all three cases

is shown in Fig. 18.

0Q

-~' 0

C13

CflO 0)6

0

6

0

0.0 200.0 400.0 600.0 800.0

time (s)

1000.0 1200.0

Figure 18. Gas pressures for tests C1, C2, and C3.

Sprays are clearly the most effective in enhancing the heat transfer. Peak pressures

and temperatures were lower in test C2 than in either C1 or C3. Fans significantly

increase the heat transfer coefficient, consequently the peak temperature and pressure

for test C3 are lower than those. observed in test C1. A clear region of "quasi-steady"

heat transfer is observed in C3, this region does not appear in C1.
44 44 5 RES ULTS

5.2 Nozzle Size Effect

Three tests were carried out with almost identical flowrates of hydrogen and steam

and three different source diameters. D: C1, D = 1 mn; ONi, D = 0.13 m; CS1, D

= 0.038 mn. Flowrates were nominally 1 ý9 kg/mmn hydrogen. and .28 kg/mmn steam.

The effect of nozzle diameter is quite -apparent in the comparison shown in Fig. 19.

Decreasing the nozzle diameter at a fixed flowrate has the effect of increasing the heat

transfer coefficient. This is due to the increase in the importance of the initial jet

momentum as the nozzle diameter decreases, i.e., the Froude number increases. The

momentum injected into the vessel by the source results in increased bulk gas motion

(circulation) and increased dissipation in the boundary layer regions near the vessel

walls. Both processes increase the heat transfer coefficient.

A simple model can be used to predict the change in heat transfer coefficient with

source parameter variations. This-moidel uses the extended Reynolds' analogy between

Stanton number St and skin friction coefficient Cf:

PUCp 2PU2

For laminar flow," 9 the analogy is:

Cf

St 2Pr2I3)

where Pr is the Prandtl number. For turbulent flow, 1 9 a useful empirical correlation is

Ka'rma'n's formula

St=2Pr0 4 (T)4

where T,, is the wall temperature and T, is the freestream temperature. In order to

use these analogies between heat and momentum transfer, I will assume that all of the

momentum injected into the vessel is dissipated at the walls of the vessels. Since I am

only interested in obtaining a scaling relationship, the simpler laminar formula will be

used.

The analysis is particularly simple for jet-like sources which have a constant momentum flux J. Plumes require a more sophisticated analysis since the momentum

flux increases due to the effect of buoyancy accelerating the source fluid. For a jet,

the initial source momentum is J = pU2 Aj and the shear stress at the wall rw, can

be estimated as J/AW, where A,,, is the heat transfer surface area of, the. vessel wall.

Substitution into the extended Reynolds' analogy- yields the following expression for

the heat transfer coefficient M1

M Cp.J

uwAW
5.2 Nozzle Size Effect 45

where u,,, is the characteristic circulation'velocity in the vessel. A simple estimate for

u,, is u,, L/T where L is the height of the vessel and T is the turnover time. Turnover

time can be estimated as the total mass in the vessel M,, divided by the total plume

or jet entrainment rate Mf, 6 T -MtI/M6 . The value of the time T is typically an order

of magnitude smaller than the time TET computed for a nonburning plume in Section

3 above.

If a jet entrainment law is used, i.e., Me L~-Y the heat transfer coefficient is

approximately

)hp VP7,J. L

For a fixed mass fiowrate and vessel size, this implies that the heat transfer coefficient

scales as M-A 1 /

2 -D- 1 . While'there are not enough data points to confirm the

exact power of D in this relationship, a dependence on the inverse power of D is clearly

indicated by the data. In order to check the relationship between source momentum

and average heat transfer coefficient more closely, I have analyzed additional tests with

the inverse model. The results are given in Table 9.

104

00 200.0__400.0___ 00.0__00.0__1000.0

tim (s

Fiue1.Gs rsue ortssC,1NadC1
46 46 5 RES ULTS

Table 9. Inverse Model Results

Test

Quantity C3 08 CS1 CS5

Computed Peak. Values

Q1 (MW) 3. 5 2.8 3.6 3.6

q (kW/M2 ) 4.6 4.5 4.6 4.6

h (W/M 2 -K) 23; 60 50 22

2'g (K) 490 410 440 500

Ti, (K) 375 372 388. 370

Measured Peak Values

q4 (kW/m 2 ) - - 17 10

Tgl (K) 623 490 475 580

TO (K) 463 425 415 500

T~d (K) 433 398 395 430

a'Heat flux gauge H503

bGas thermocouple T101

' Wall thermocouple T120

d Wall thermocouple T121

Notable are the following points: The maximum heat transfer rates predicted by

the inverse computations are lower by a factor of two or three than those measured

by the Schmidt-Boelter gauge H503. This is an indication of the nonuniformity of

heat transfer. This observation is supported by the difference between calculated and

measured wall peak temperature. The differences between the two measured wall temperatures are due to the wall jet and its influence on the heat transfer (see the following

discussion on stagnation point heat transfer).

The heat transfer coefficients inferred from the inverse technique indirectly support

the scaling hypothesis discussed above. Although test CN1 was not analyzed, comparison of the pressure data with those for test C3 (see Fig. 20) show that the results

for the two tests are almost identical. Since the source parameters and initial conditions are identical, the heat trans *fer coefficients should be the same, W1 -23 W/m 2 -K.

The coefficient for test CS1, which has corresponding initial conditions and the same

source parameters as CN1 except the nozzle diameter is'smaller by a factor of 3.3, is

50 W/m 2-K. The ratio of heat transfer coefficients is 2.2 vs 3.3 for the inverse source

diameter ratio. The Agreement is probably satisfactory in view of the idealized nature

of the theory.
5.3 Stagnation-Point Heat Transfer 47

Comparison of tests CS1 and CS5 yields similar support for the scaling hypothesis.

Test CS5 is almost identical to CS1 except the steam fiowrate is 3.0 times lower in

CS5 than in CS1. For a fixed nozzle diameter, the scaling hypothesis implies that

the heat transfer coefficient should vary directly as the mass fiowrate. For test CS5,

M-22 W/m'-K, 2.3 times lower than in test CS1. Again the agreement is probably

satisfactory.. The scaling arguments have not been applied to the plume-like flows such

as test Cl. Two complications arise in these cases: plume entrainment laws must be

used; the role natural convection plays must be assessed.

0Q

U)

U) 0

0.0 200.0 400.0 600.0

time (s)

800.0 1000.0

Figure 20. Gas pressures for tests C3 and CN1.

5.3 Stagnation-Point Heat Transfer

As mentioned above, the peak heat transfer rates occur at the top of the vessel where

the jet or plume impinges. We have chosen not to include this effect in the present

model since few data were obtained in that part of the vessel. It is useful to estimate

the peak heat transfer rates that did occur since they represent limiting conditions for

equipment survival. This effect could also explain the systematic differences between

wall temperature measurements.
48 48 5 RES ULTS

Heat transfer above fires, both jets and plumes, has been studied extensively in the

last two decades. Most investigations2 1

0

'

2 1 1' 2 2 have been concerned with impingement on

fiat ceilings; limited data on jet flows 2 3 and analytical results for laminar flows indicate

that the curvature of the surface will affect the results. This will be neglected in the

discussion below.

Plume flows have been extensively investigated. The heat transfer coefficient along

the wall can be expressed as a nondimensional function of the nondimensional distance

X/H where X is the coordinate along the wall and H is the height above the source.

The heat transfer coefficient is given as a normalized quantity h,~ that resembles a

Stanton number based on an idealized plume velocity:

I7 _ QI

-H PCPT~7gH 2

The variation of hc with X/H is shown in Fig. 21 together with the approximate

locations of the wall thermocouples T120 and T121.

0.08

0.06

Ti120

V

T121

V

0.04

0.02

0.00

0.0 0.2 0.4 0.6 0.8 1.0

x/H

Figure 21. Nondimensional heat transfer coefficient h, vs nondimensional wall coordinate X/H. From Sargent.2
5.3 -Stagnation-Point Heat Transfer 49

The magnitude of the actual heat transfer coefficient and the resulting heat flux

have been computed for test C1 assuming a cold wall: Mt = 127 W/m'-K and q, = 8.6

kW/m2 . The value of q~, is appropriate for the beginning of the transient and will

increase with time as the background gas temperature in the vessel increases. Near

the end of the burn, this value could be up to 4 times larger. On the other hand,

the average heat transfer coefficient and heat flux for test C1 must certainly be less

than those values obtained for test C3: M( = 23 W/M 2 -K and q, = 5 kW/m'. This

indicates that the peak stagnation heat flux and heat transfer coefficient can be up

to 5-6 times larger than the average values for tests with low Froude number sources.

Using correlations appropriate for jet flames, 24 similar conclusions are reached for those

tests.
50 50 6 SUMMARY

6 Summary

I have discussed several aspects of the NTS continuous-injection tests and given

a brief sumnmary of the data. Key areas mentioned are: mixing during the injection

process; the role of convective heat transfer in determining the gas pressure and temperature; experimental determination of the average heat transfer coefficient; the effect

of the wall jet and stagnation region on predicting wall temperatures.

The source Froude number has a profound influence on the degree of mixing during

the injection process. The various types of ignition behavior can be related to the

Froude number and. igniter location. The lack of multiple deflagrations and the phenomenon of nonignition can be explained on this basis. Tests using a buoyant plume

source probably have a strongly stratified initial hydrogen concentration and a distinct

moving front will exist between mixed and unmixed fluid. As the source Froude number

increases, the vessel contents become better mixed. Tests using jet-like sources (large

source Froude numbers) will exhibit good mixing and a distinct front will not form.

A simple model for the thermodynamics and heat transfer is proposed. This model

is solved analytically for an idealized case and the results are used to discuss the test

data. Numerical results of a detailed implementation of the model are compared to a

single test, C3. This simulation demonstrates that the model can accurately predict gas

temperatures and pressures if the convective heat transfer coefficient is chosen correctly.

Major conclusions of the model are that the wall-gas temperature difference reaches a

constant value after an initial transient and that the total heat flux depends only on

the fire power, vessel, and atmosphere heat capacities.

The model is inverted and used to infer average convective heat transfer rates to

the vessel. Convective heat transfer is shown to increase with the source momentum

or Froude number. A simple momentum conservation analysis is used to deduce the

scaling of heat transfer with the jet momentum. Heat transfer coefficients determined

by the inverse computation appear to scale as the square root of the jet momentum,

in satisfactory agreement with the simple scaling model.

The data. are compared to measured and estimated stagnation-point heat transfer

rates. These comparisons indicate that the heat transfer rate in the stagnation region

can be up to 5 times larger than the average value. Expected variations in heat transfer

rate near the stagnation point could account for the observed systematic variation in

wall thermocouple measurements.
51

References

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and J. J. Haugh 1985 "Large-Scale Hydrogen Combustion Experiments" EPRJ

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the Nevada Test Site (NTS) Sandia National Laboratories.Report SAND85-0135,

NUREG/CR-4138.

3. W. D. Baines and J., S. Turner 1969 "Turbulent buoyant convection from a source

in a confined region" J. Fluid Mech. 37, 51-80.

4. J. S. Turner 1962 "The 'starting plume' in neutral surroundings" J. Fluid Mech.

13, 356-368.

5. J. E. Shepherd, M. R. Baer, and J. C. Cummings 1984 "Fluid Motion Induced

by Filling Containers" Bull. Am. Phys. Soc. 29(9), abstract EF4.

6. P. A. Thompson 1972 Compressible-Fluid Dynamics, McGraw-Hill, NY, 41.

7. J. Ek Broadwell, W. J. Dahm, and M. D. Mungal 1984 "Blowout of turbulent

diffusion flames," 20th Symposium (Intl.) on Combustion, The Combustion Institute, Pittsburgh, PA, 303-310.

8. E. E. Zukoski, T. Kubota, and B. Cetegen 1980/81 "Entrainment in Fire Plumes,"

Fire Safety Journal 3, 107-121.

9. H. C. Hottel and A. F. Sarofim 1967 Radiative T~ransfer, McGraw-Hill, 460.

10. D. K. Edwards 1976 "Molecular Gas Band Radiation," in Advances in Heat

Transfer 12, Academic Press, NY, NY.

11. R. Siegel and J. R. Howell 1981 Thermal Radiation Heat Tiransfer, 2nd

Edition, McGraw-Hill, 567.

12. E. S. Fishburne and H. S. Pergament 1980 "The Dynamics and Radiation Intensity of Large Hydrogen Fires," 17th Symposium (Intl.) on Combustion, The

Combustion Institute, Pittsburgh, PA, 1063-1072.

13. D. Burgess and M. Hertzburg 1974 "Radiation from Pool Fires," in Heat Tr-ansfer in Flames, Eds. N. H. Afghan and J. M. Beers, Hemisphere, 413-430.

14. K. H. Haskell, W. H. Vandevender, and E. L. Walton 1980, The SLATE C Mathematical Subprogram Library, Sandia National Laboratories Report SAND8O2792.
52 52 6 SUMMARY

15. R. J. Kee, J. A. Miller, T. H. Jefferson 1980 CHEMKIN: A General-Purpose,

Problem-In dependent, Transportable Fortran Chemical Kinetics Code Package

Sandia National Laboratories Report SAND8O-8003.

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ANS/ASME Conference on the Design, Construction and Operation of Nuclear

Power Plants, Portland, OR, Aug. 5-7, 1984.

17. A. C. Ratzel and J. E. Shepherd 1985 "Heat Transfer Resulting form Premixed

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Y. Jaluria, W. W. Yuen, and K. Miyasaka), Publication HTD-45 of the ASME,

191-201.

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CA.

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a
A-1

A Data Plots

This appendix contains plots of selected data from each of the 15 tests. Pressure

data only is given for all tests except C3, C8, CSi, and CS5. Gas and wall temperatures

and some heat flux data are given for these four tests. The test designation and the

instrument identification is given with each plot. Instrumentation locations are given

as a function of the (X, y, Z) coordinates within the vessel in the table below. The

coordinates are defined in Fig. 2 of the main text.

Table A-1. Instrument Locations

Instrument Location

(X1 , Z~,

Gas thermocouple (3-mil)

T101

T102

1,-2,19

-1,-i, 1

Gas thermocouple (32-mul)

T114

Ti118

9,0,21

20,0,0

Wall thermocouple (32-mul)

T120 -2,-3,26

T121 -18.4,1,18.4

Heat flux gauge (total)

H503 i,-2.5,2

Gas pressure transducer

P 102

a Units are feet.

-5,-5,0
A-2 A-2 A DATA PLOTS 0

9

0

L-A

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

0

06

.Figure A-i. Test Ci, gas pressure P102.

0

U3

(Ul ... .. ..... . ........... 'I'll ............ .

0

0;

to

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-2. Test C2, gas pressure P102.
A-3

0

6S

cv

00

En-6

0

6

0.0 250.0 500.0 750.0. 1000.0 1250.0 1500.0

.time (s)

Figure A-3. Test C3, gas pressure P102. 0

0

0

0

0

so

0

6

0

C,,

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-4. Test C3, wall temperatures T120, T121.
A-4 A-4 A DATA PLOTS

q

0

0

0

~40

S

0

0

6

0

C,

0.0 250-.0 500.0 750.0 1000.0

.time (s)

1250.0 1500.0

Figure A-5. Test C3, gas temperature Tiol.

C6

2-4

0

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-6. Test C3, gas temperatures T114, T118.

A
A-5

0

6

04

in~

0.0. 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-7T. Test C5, gas pressure P102. 0

6

0

0

d

kIo

(121

6Q

0

CS 10

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-8. Test C7l, gas pressure P102.
A-6 A-6 A DATA PLOTS

q

0

0

0

U);

0

01

00

0

d

a',

0.0 250.0 500.0 750.0 1000.0

time (s)

Figure A-9. Test C8, gas pressure P102.

1250.0 1500.0

0

0;

;J,

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-10. Test C8, wall temperatures T120, T121.
A-7

C50

-4O

0U

0

0

0

0.0 250.0, 500.0 750.0 ,1000.0

time (s)

1250.0 1500.0

Figure A-11. Test C8, gas temperature T101.

0q

0;

0

0.0 250.0 500.0 750.0' 1000.0 -1250.0 1500.0

time (s)

Figure A-12. Test C8, gas temperatures T114, T118.
A-8 A-8 A DATA PLOTS

0

6;

0

ati

in2

04

0

I',

0.0 250.0 500.0 750.0 '1000.0 1250.0 1500.0

time (s)

Figure A-13. Test CIO, gas pressure P102.

0

0

6-

0

0.0 250.0 500.0 750.0

time (s)

1000.0. 1250.0 1500.0

Figure A-14. Test CII, gas pressure P102.
A-9

0

0

Rq

0q

If;

0

0.0 -250.0 500.0. 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-15. Test CN1, gas 0

6;

0

M

0V

v-4

pressure P102.

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-16. Test CN2, gas pressure P102.
A-10 A-b A DATA PLOTS

C;

0

04,C

6

0

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-17. Test CN3, gas pressure P102.

qV

0

04

0

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-18. Test CS1, gas pressure P102.
A-11

0

6

0Q

C?

k6

0.0 250.0 500.0 '750.0 1000.0 1250.0

A1.time (s) Figure A1.Test CSI, heat flux H503.

1500.0

0

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-20. Test CSI, wall temperatures T120, T121.
A-12 A-12 A DATA PLOTS

0

6

0

0

Q~o

0

0

6

0

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-21. Test CSI, gas temperature T101.

0

6

0

'-~0

0

C~0~

~-40

~4h()

S

0

0

0

c,,

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-22. Test CSI, gas temperature T102.
A-13

0

0

0

0

C~O~

~40

S

0

0

0

0

0.0 250.0 500.0 750.0 1000.0 1250.0 ,1500.0

time(s

Figure A-23.. Test CSI, gas temperature T1 18. 0

0

6

0

C,.,

00

0

0.0 250.0 500.0 750.0 .1000.0, 1250.0 1500.0

time (s)

Figure A-24. Test CS2, gas pressure P102.
A-14 A-14 A DATA PLOTS

0

cq

Q.)

U)

U) a.)

0

6Q

v-4

0

0

0.0 250.0 500.0 750.0 1000.0 1250.0

time (s)

Figure A-25. Test CS5, gas pressure P102.

1500.0

0

C')

"'0

4-4

A*4

0

6

0.0 250.0 500.0" 750.0O 1000.0 1250.0 1500.0

time (s)

Figure A-26. Test CS5~, total heat flux H503.
A-15

0

6o

0

6

0

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-27. Test CS5, gas temperature T118.

0

0

0S

0.0 250.0 500.0 750.0 1000.0, 1250.0 1500.0

time (s)

Figure A-28. Test CS5, wall temperatures T120, T121.
A-16 A-16 A DATA PLOTS

0

0

00N

CUo

9

0

0

0.0 250.0 500.0 750.0 1000.0 1250.0 1500.0

time (s)

Figure A-29. Test CS5, gas temperature T101.

0o

coC

0U

0

6

0

0.0 250.0 500.0 '.750.0 1000.0 1250.0 1500.0

time (s)

Figure A-30. Test CS5, gas temperature T102.
A-17

0

CS~i

0.0 1000.0 2000.0

time (s)

3000.0 4000.0

Figure A-31. Test CS6, gas pressure P102.

B-i

B MOL for Conduction Equation

This appendix describes the solution of the one-dimensional heat transfer problem

by the method of lines or MOL. The simple problem that we want to consider is the

solution of the' conduction equation in a planar geometry of finite extent, i.e., a slab

between x = 0 and x = 1. To illustrate the method, consider the transient conduction

process in a slab with an insulated back boundary and a specified time-dependent flux

q(t) at the front surface.

The temperature distribution inside the slab is determined by solving the conduction

equation

. ru- (B-i1)

at X

with boundary conditions

-k- aT q (B -2)

and

aT

-k-T = 0. (-3)

The partial differential equation for' the slab temperature is. reduced to 'a set of

ordinary differential equations by appr oximating the spatial derivative by ce ntered

second-order differences on a discrete uniform spatial mesh

aX2 (AX) 2

where Ax is the mesh spacing. If there are N mesh points then substituting Eq. (20)

into the conduction equation results in N ordinary differential equations for the mesh

point temperatures Tk.

dTk (kl-2k+Tj (B -5)

dt -(AX)

2 (k1-2'.+T~

At the end points, nonphysical mesh points k = 0 and k = N + 1 must be introduced

for closure and to implement the boundary conditions. The boundary conditions are

incorporated by using the fictitious point outside the domain at each end and evaluating

the flux by a centered-difference approximation.

ax 2Ax

Applying this approximation to the insulated end of the slab, x = t, the boundary

condition implies that
B-2 B MOL FOR CONDUCTION EQUATION

TN+1 = TNi.-

At the end of the slab with the specified flux, x =0, the boundary condition implies

that

2Ax

TO= kq(t) - T2

Substituting these conditions into the system of equations an d setting6 f .I /(AX) 2 ,

the final set of equations to be solved are

dTk = (Tk1 2 Tk+Tk) for 2< k< N-1 (B -7)

dt_

dTN

The reduction of the conduction equation to a set of N ordinary differential equations allows the use of existing subroutine packages to obtain the solution. For parabolic

systems such as the heat equation, an implicit predictor-corrector method is the best

choice for an algorithm. The time step is automatically determined by the error control

procedure within the package. An example of a package that has been successfully used

to solve these equations is the routine DEABM of the SLATEC mathematical library. 12
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Analysis of Diffusion Flame Tests 4. DATE REPORT COMPLETED

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12. SUPPLEMENTARY NOTES

13. ABSTRACT (200 words or less)

This report discusses the results and analysis of hydrogen diffusion flame tests

conducted at the Nevada Test Si~te by EPRI and the U. S. NRC. Those tests were

designed to simulate the effects of hydrogen combustion inside a nuclear power plant

containment following a degraded-core accident. Test initial conditions and sample

data plots are given for 16 tests. Mixing and ignition phenomena are discussed in

terms of the source parameters and igniter location. A simple model is developed for

simulating the heat transfer and computing convective heat transfer coefficients for

experimental pressure measurements. Convective heat transfer coefficients are reported

for four tests. The effect of stagnation-point heat transfer is estimated.

14. DOCUMENT ANALYSIS - a. KEYWORDS/DESCRIPTORS

data analysis, continuous injection combustion experiments, diffusion

flame, NTS hydrogen dewar

b. IDENTIFIERS/OPEN-ENDED TERMS

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STATEMENT

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16, SECURITY CLASSIFICATION

unclassified

(This report)

unclassified

17. NUMBER OF PAGES


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