NUREG/CR-4905

SAND85- 1263

R3

Printed June 1987

~- I

Detonability of H2-Air-Diluent Mixtures

Sheldon R. Tieszen, Martin P. Sherman

William B. Benedick, Marshall Berman

Prepared by

Sandia National Laboratories

Albuquerque, New Mexico 87185 and Livermore, Calitornia 94550

tor the United States Department ot Ehergy

under Contract DE-AC04-76DP00789

'J

eeae for'

U, s-iiUCLEAR

SF2900Q18-81 I
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 em- ployees, 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

third party would not infringe privately owned rights.

Available from

Superintendent of Documents

U.S. Government Printing Office

Post Office Box 37082

Washington, D.C. 20013-7082

and

National Technical Information Service

Springfield, VA 22161
NUREG/CR-4905

SAND85-1263

R- 3

DETONABILITY OF H2 -AIR-DILUENT MIXTURES

Sheldon R.

Martin P.

William B.

Marshall

Tieszen

Sherman

Benedick

Berman

June 1987

Sandia National Laboratories

Albuquerque, New Mexico 87185

operated by

Sandia Corporation

for the

U.S. Department of Energy

Prepared for

Division of Reactor System Safety

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555

Under memorandum of Understanding DOE 40-550-75

NRC FIN No. A-1246

ABSTRACT

This report describes the Heated Detonation Tube (HDT).

Detonation cell width and velocity results are presented for H2 - air mixtures, undiluted and diluted with C02 and H2 0 for a range

of H2 concentration, initial temperature and pressure. The

results show that the addition of either C02 or H2 0 significantly

increases the detonation cell width and hence reduces the

detonability of the mixture. The results also show that the

detonation cell width is reduced (detonability is increased) for

increased initial temperature and/or pressure.

iii /iv

TABLE OF CONTENTS

Page

ABSTRACT iii! iv

Preface xiii

ACKNOWLEDGMENTS xiv

EXECUTIVE SUMMARY 1

CHAPTER 1 - INTRODUCTION 1-i

1.1 PURPOSE OF THE FACILITY 1-1

1.2 LITERATURE 1-1

1.3 REFERENCES FOR CHAPTER 1 1-9

CHAPTER 2 - FACILITY DESCRIPTION 2-1

2.1 DESIGN CONSIDERATIONS 2-1

2.2 HDT DESCRIPTION 2-2

2.3 REFERENCES FOR CHAPTER 2" 2-10

CHAPTER 3 - PROCEDURE 3-1

CHAPTER 4 -RESULTS 4-1

4.1 DETONATION CELL WIDTH, X4-1

4.1.1 Modeling 4-9

4.1.2 H2 -Air;

P,T = Constant (Test Series #1) 4-10

4.1.3 H2 -Air-C02 ;

P,T = Constant (Test Series #2) 4-11

4.1.4 H2 -Air-Steam;

Pair,T = Constant (Test Series #3,4) 4-12

4.1.5 H2 -Air;

PainT = Constant(Test Series #5) 4-13

4.1.6 H2 -Air;

XH2,P = Constant (Test Series #6)

p = Constant (Test Series #7) 4-13

4.2 DETONATION VELOCITY MEASUREMENTS 4-14

4.3 REFERENCES FOR CHAPTER 4 4-19

CHAPTER 5 - DISCUSSION AND CONCLUSIONS 5-1

5.1 DISCUSSION 5-1

5.2 CONCLUSIONS 5-2

5.3 FUTURE WORK 5-4

5.4 REFERENCES FOR CHAPTER 5 5-5

v
Page

APPENDICES

APPENDIX A - DETAILS OF THE EXPERIMENTAL APPARATUS A-i

A.1 STRUCTURE A-i

A.1.1 The Main Tube A-i

A.1.2 The Secondary Piping A-6

A.1.3 The Structural Supports A-9

A.2 ELECTRICAL A-13

A.2.1 General Power A-13

A.2.2 Detonation Tube Heating System A-13

A.3 THERMAL ASPECTS A-25

A.3.1 Insulation A-26'

A.3.2 Temperature Monitoring Thermocouples A-26

A.3.3 Thermal Limits A-27

A.4 EXPLOSIVE INITIATOR CIRCUIT A-28

A. 5 INSTRUMENTATION A-30

A.5.1 Static Pressure Instrumentation A-30

A.5.2 Temperature Instrumentation A-31

A.5.3 Smoked Foil Instrumentation A-31

A.5.4 Dynamic Pressure Instrumentation A-39

A.5.5 Humidity Instrumentation A-40

A.6 REFERENCES FOR APPENDIX A A-48

APPENDIX B - DETAILS OF PROCEDURE B-i

B.1 TEST SERIES #1 B-2

B.2 TEST SERIES #2 B-3

B.3 TEST SERIES #3, 4 B-4

B.4 TEST SERIES #5 B-5

B.5 TEST SERIES #6 B-5

B.6 TEST SERIES #7 B-6

APPENDIX C - TABULATED DATA C-i

APPENDIX D - ESTIMATE OF UNCERTAINTY BOUNDS D-1

D.1 DETONATION CELL WIDTH D-1

D.1.l Comparison Between Test Apparatus D-2

D.1.2 Uncertainty Bounds for.Detonation

Cell Width Measurements D-6

D.i.2.1 Comparison Between Test

Apparatus D-7

D.1.2.2 Multiple observers D-7

D.1.3 Bounds on the HDT Test Series D-10

D.2 DETONATION PRESSURE D-11

D.3 DETONATION VELOCITY D-17

D.4 THERMODYNAMIC STATE D- 19

D.4.1 Variance Estimates for Measured

Variables D-23

D.4.1.i Temperature Standard Deviation

Estimate D- 24

vi
Page

D.4.1.2 Pressure Standard Deviation

Estimate D- 25

D.4.1.3 Uncertainty in the Uniformity

of the Gas Mixture D-26

D.4.1.4 Steady State Criteria D-27

D.4.2 Standard Deviation Estimates Of Pairi

0, XH0 and XCO2 D-28

D.4.3 Standard Deviation Estimates of

Detonation Cell Width and Velocity

Due Initial Thermodynamic State D-36

D.5 REFERENCES FOR APPENDIX D D- 37

APPENDIX E - THERMODYNAMICS AND CELL WIDTH E-1

E.1 THERMODYNAMIC RELATIONS E-1

E.2 GENERAL FUNCTIONAL RELATIONSHIP E-5

E.3 EFFECT OF TEMPERATURE E-6

APPENDIX F - ANALYSIS OF THE TEMPERATURE

DISTRIBUTION AND THERMAL TRANSIENT

RESPONSE OF THE HDT F-i

F.1 NOMENCLATURE F-1

F.2 DERIVATION OF THE MODEL F-3

F.3 SOLUTION TO PROBLEM #1 - HEATERS FULL ON F-5

F.4 SOLUTION TO PROBLEM #2 - HEATERS AT

CONSTANT TEMPERATURE, Tr F-9

F.5 COMPARISON BETWEEN THE MODEL AND THE HDT F-i5

APPENDIX G - DATA ACQUISITION SYSTEM DETAILS G-i

G.1 HARDWARE G- 1

G.1.1 Tektronix 7612D Transient Digitizers G-1

G.1.2 CANAC Transient Digitizers G-2

G.1.3 Storage/Processing Hardware G-2

G.2 SOFTWARE G-2

G.2.1 HDT Control Program G-2

G.2.2 Data Acquisition Programs G-3

G.2.3 Data Storage Formats G- 3

G.2.4 Data Processing Programs G-3

G.3 REFERENCES FOR APPENDIX G G-4

vii
LIST OF FIGURES

Figure Page

1-1 Percent Hydrogen Concentration vs. Percent

Metal-Water Reaction for Various Plants. 1-3

1-2 Early Prediction of the Detonability Limits

of H2 -Air-Steam Mixtures. 1-4

1-3 Cellular Pattern Left on Sooted Plate from

Passing Detonation Wave in Argon Diluted

Fuel/oxygen. 1-6

1-4 Effect of Geometry on Propagation of

Detonation Waves. 1-7

1-5 Detonation Cell Pattern on a Smoked Foil

for a H2 -Air Mixture. Note "irregular"

structure compared to Figure 1-3. 1-8

2-1 Heated Detonation Tube without Thermal

Insulation. 2-3

2-2 Heated Detonation Tube with Thermal

Insulation Layer 2-4

2-3 Schematic of the Secondary Piping 2-5

2-4 Schematic of the Heater Control Circuit. 2-7

4-1 Typical Smoked Foil from HDT 4-2

4-2 Detonation Cell Width vs. Equivalence Ratio

for Test Series #1. (H2 -Air at P=1 atm,

T=20-C) 4-3

4-3 Detonation Cell Width vs. Equivalence Ratio

for Test Series #2. (H2 -Air-C02 at P=1 atm,

T=20*C) 4-4

4-4 Detonation Cell Width vs. Equivalence Ratio

for Test Series #3, 4. (H2 -Air-H2 0 at

P~air=4 1 .6 moles/in 3 , T=100*C 4-5

4-5 Effect of Initial Conditions on Detonation

Cell Width of H2 -Air Mixtures 4-6

4-6 Detonation Cell Width vs. Temperature for

Test Series #6, 7. (H2 -Air at XH2=O-l7) 4-7

4-7 Uncertainty Ranges for the HDT Data in

Figure 4-5. 4-8

viii
Figure Page

4-8 Detonation Velocity vs. Equivalence Ratio

for Test Series #1, 2.' (H2 -Air-C02 at

P=1 -atm, T=20*) 4-15

4-9 Detonation Velocity vs. Equivalence Ratio

for Test Series #3, 4. (H2 -Air-H20 at

Pair=4 1 .6 moles/rn 3 , T=100*C) 4-16

4-10 Effect of Initial Conditions on Detonation

Velocity of H2 -Air Mixtures 4-17

4-11 Detonation Velocity vs. Temperature for Test

Series #6,7. (H2 -Air at XH2=O-l7) 4-18

5-1 Constant Detonation Cell Width on Mixture

Coordinates (for T = 100*C, Air

Density = 41.6 mole/rn3 ) 5-2

5-2 Effect of Geometry on Propagation

of Detonation Waves. 5-3

5-3 Detonation Cell Width vs. Equivalence

Ratio for Test Series #3,4. (H2 -Air-H2 0

at Pair=4 1 .6 moles/rn3 , T=100*C) 5-5

A-i Cross-Section of a Gas Recirculation

Penetration A- 2

A-2 Cross-Section of a Transducer Penetration A-3

A-3 Cross-Section of a Pipe Flange A-4

A-4 Schematic of the Secondary Piping A-7

A-S Detonation Tube Supports A- 10

A-6 Tube Support V-Block Positioning Device A-li

A-7 Heater Section Schematic - Long Pipe

Section, Sides and Bottom A-i5

A-8 Heater Section Schematic - Long Pipe

Section, Top A-17

A-ý Heater Section Schematic - Pipe to Pipe

Flanges A- 18

A-l0 Heater Section Schematic - Short Pipe A-19

A-11 Heater Section Schematic - Endplates,

Flanges A- 21

ix
Figure Page

A-12 Heater Control Circuit Schematic A-23

A-l3 High Explosive Initiator A-29

A-14 Transducer Fitting Cross-Section A-47

D-1 Detonation Cell Width Measurement (a) Use

of High Contrast Individual Cells (b), Use

of High Contrast Long Running Lines D-2

D-2 Detonation Cell Width Measurements for HDT

Test Series #3 (H2 -Air, Pair=4 1.6 moles/rn3 , T=l0O*C). D-4

D-3 Detonation Cell Width Measurements for HDT

Test Series #5 (H2 -Air, Pair=4 1.6 moles/in3 , T=20*C). D-5

D-4 Comparison of Detonation Cell Width Data

Between the HDT and McGill University.

(HDT Test Series #1, P=1 atm, T=25*C). D-8

D-5 Normalized Detonation Cell Width

(X Au~thor/X Knystautas) vs. HDT Test Number. D-9

D-6 Typical PCB Pressure Trace - Small Cell Width

(X =5 mm , Test HT-84). D-13

D-7 Typical Kistler Pressure Trace - Small Cell

Width (X = 5 mm , Test HT-84). D-14

D-8 Typical PCB Pressure Trace - Large Cell Width

(X = 400 mm , Test HT-96). D-15

D-9 Typical Kistler Pressure Trace - Large Cell

Width (X = 400 mm--, Test HT-.96). D-16

F-1 Control Volume for the l-D Unsteady Fin Model. F-4

F-2 Comparison of Temperature Distribution and

Transient Response of the HDT and 1-D Unsteady

Fin Model F- 16

x
LIST OF TABLES

Table Page

3-i - Test series 3-2

4-i - Equivalence Ratio as a Function of Steam

and H2 Concentrations in Total Mixture by

Volume 4-10

A-i - Temperature Limits of Detonation Tube

Components A- 27

A-2 - Axial Location of Instrumentation Ports

Relative to the Initiation Endplate

Inside Face A-30

A-3 - Type and Location of Initial Thermodynamic

State Measurements A- 32

A-4 - Temperature, Pressure and Humidity

Instrumentation A- 37

A-5 - Type, Number and Digitizing Frequency for

Dynamic Pressure Measurement A-41

A-6 - Dynamic Pressure Instrumentation A-46

B-i - Test Series B-2

C-i - Tests in Each Series c-2

C-2 - Detonation Cell Width Data C-3

C-3 - Detonation Velocity Data C-9

C-4 - Initial Thermodynamic State C-14

D-i - Effect of Initial Transient on Detonation

Velocity D-1i8

D-2 - Upper and Lower Bounds on the Detonation

Velocity D-20

D-3 - Variables Chosen to Specify the Initial

Thermodynamic State of the Mixture D-22

D-4 - Measured Variables D-22

xi
Table Page

D-5 - Standard Deviation Estimates of Measured

Variables. (Using Engineering Judgement) D-24

F-1 - Numerical Values of the Model Parameters F-15

xii
Preface

This document is intended to serve two purposes. First, it

provides a complete summary of the Heated Detonation Tube test

results for the general reader. Second, it completely documents,

for scientific accuracy and archival purposes, the apparatus,

procedures, and uncertainties associated with data from the

Heated Detonation Tube Program. The appendices contain a

detailed description of the apparatus, procedures and uncertainty

analysis of the data.

xiii
ACKNOWLEDGMENTS

The authors would like to recognize the considerable

contribution to the field of detonation research and its

application to reactor safety by Professors John H. Lee and

Romuald Knystautas of McGill University, Canada. They have

assisted us throughout this project from its conceptual design to

reviewing the results. The authors would also like to

acknowledge valuable technical discussions with J. Shepherd who

developed the model used to correlate the data in this report.

The authors would like to thank NRC Contract Managers J. Larkins

and P. Worthington. The authors also appreciate the technical

support of C. J. Daniel, D. Montgomery, M. Oliver, D. Beeker, J.

Lee and J. Barry in obtaining the data in this report.

xiv
EXECUTIVE SUMMARY

Hydrogen combustion as related to reactor safety has been

studied since the accident at Three Mile Island. The recent

accident at Chernobyl, during which a hydrogen detonation (or

accelerated deflagration) may have occurred, strengthens the

concern that hydrogen combustion can occur during a severe

accident. It is important to understand the various modes of

combustion which can occur, both in terms of the possibility and

consequences. One mode of combustion is detonation.

This report documents test results from gaseous detonation

studies in the Heated Detonation Tube (HDT) . Detonations have

peak pressures that are well above the quasi-static pressures

associated with ordinary deflagrations. Should a detonation

occur inside a reactor containment, both the containment and

safety-related equipment could be severely damaged.

Test results reported are the detonation cell width, X, and

detonation velocity. X is an intrinsic length scale that

characterizes detonations. Highly detonable mixtures have small

cell widths, while increasingly less detonable mixtures have

increasingly larger cell widths. Previous research has shown

that the limits of detonation propagation are related to the

ratio of X to a characteristic geometric length-scale. X has

been related to dynamic detonation parameters such as limits of

propagation in tubes, channels, and other ducts, the transmission

from a duct to an unconfined space, and initiation energy for a

high-explosive charge. Detonation cell width measurements have

been used to establish the relative detonability for a broad

range of fuel-oxidizer mixtures.

The HDT is a 43-cm (17-in) inside diameter, 13-in (43-ft)

long heated tube. It is designed to study H2 -air-steam mixtures.

To the authors' knowledge, no prior experimental detonation data

existed for this ternary mixture, which is the most likely

mixture to occur in a severe accident. Further, much of the

earlier detonation limit data for dry H2 -air mixtures are of

limited relevance because of the small scale in which the

experiments were done. Experimental results from the large

diameter HDT have shown that H2 will detonate for a broader range

of concentrations than previously believed; a mixture as lean as

13% H2 has detonated. Experiments show that the addition of

steam to a H2 -air mixture at 100*C, with an air density of 41.6

moles/in3 (standard density of air), significantly decreases the

sensitivity of the mixture to detonate. The energy required to

detonate a stoichiometric H2 -air mixture increases by factors of

220, 8000, and 2.2 x 105 for addition of 10%, 20%, and 30% steam,

respectively.

Tests have also shown that the detonation cell width, and

hence detonability, depends on the initial thermodynamic state of

the mixture as well as on the gas composition. Changing the
temperature and pressure (or density) of the mixture affects the

detonability of that mixture. Increasing the temperature or

pressure of the mixture sensitizes the mixture making it more

detonable.-

Experimental results reported here can be applied directly

to detonation safety analysis to answer the question, "Can a

detonation propagate in a given mixture in a given geometry?"

The results do not address related questions associated with the

generation, transport and mixing of hydrogen in containment.

Such additional information is necessary to better use the

results of this report in a safety analysis. Further, this

report does not address the question of how a detonation is

initiated, i.e., the deflagration-to-detonation transition

question, nor does it address possible damage from detonation

overpressures.

2
CHAPTER 1

INTRODUCTION

1.1 PURPOSE OF THE FACILITY

The main 'purpose of the Heated Detonation Tube (HDT) facility is to study the detonability of hydrogen-air-steam mixtures.

To the best of our knowledge, there have been no previous experimental studies of these ternary mixtures. Such mixtures can form

in a severe nuclear-reactor accident involving core damage.

Detonations cause peak loads in addition to the quasi-static

loads of, weak deflagrations. They pose a potential threat to the

containment structure and to saf ety-related equipment. Detonability is related to detonation cell width, the primary measurement obtained from the HDT experiments.

In addition to studying detonations in hydrogen- air- steam

mixtures, necessarily at elevated temperatures, the Heated Detonation Tube has been used to study dry hydrogen-air mixtures.

Hydrogen-air mixtures have been studied at ambient and elevated

temperatures, various densities, and at mixtures farther from

stoichiometric than had been detonated at any other facility.

Some studies with hydrogen-air-carbon dioxide were also made to

confirm and extend previous data for this ternary mixture.

1.2 LITERATURE

Serious study of H2 -air detonations began after the ThreeMile-Island (TMI-2) accident during which a hydrogen deflagration

occurred. The source of the burned hydrogen in containment was

the oxidation of the zirconium cladding in the degraded core.

The hydrogen mole fraction prior to combustion has been estimated

to be about 8%. [1] If the concentration of hydrogen, even

locally, were considerably higher, then there could exist the

danger of a detonation.

Prior to the TMI-2 accident, the reactor safety community

was concerned with design basis accidents where only a limited

degree of metal-water reaction was specified. The relatively

small amount of hydrogen produced from this type of accident,

coupled with early research which indicated that at least 18%

hydrogen was needed for a detonation, led many researchers to

minimize the threat of a hydrogen-air detonation.

Research since the TMI-2 accident has identified, and in

some cases quantified, several factors which play a role in

determining the threat'of detonation. Some of these factors are

the rates and amounts of hydrogen released, the rate of transport

and mixing of the hydrogen, the presence of diluents such as

steam, the source and timing of ignition, the local turbulent

environment where a deflagration might undergo a transition to a

1-1
detonation, the containment volume and design, and the location

of safety-related equipment.

Fig. 1-1, from Ref. [2] shows the hydrogen concentration as

a function of percent metal-water reaction for various nuclear

reactor containments. Multi-comparltment lumped-volume computer

models developed for deflagration studies have shown that locally

high concentrations of H2 are possible in certain containments in

certain accident scenarios, particularly in the upper plenum of

an ice condenser PWR [3]. Research has also shown that detonations can result from confinement and turbulent interaction with

a deflagration. Recent observations of Lee [4], Pfb5rtner [5] and

Sherman et al. [6] showed that turbu lence- induced transition to

detonation can occur even in off-stoichiometric H2 -air mixtures,

not only under confined, but also under partially and even

unconfined conditions.

The only prior work on hydrogen-air- steam mixtures appears

to be an estimate of detonation limits in the report of Shapiro

and Moffette [7], which was repeated in the WASH 1400 Reactor

Safety Study [8] and the Core-Meltdown Review [9]. The "detonation limit" is defined as the limiting mixture ratios of fuel to

oxidizer, at given pressure and temperature, that will propagate

a detonation. In these reports a triangular diagram appeared,

Fig. 1-2, in which "detonation limits" for hydrogen- air- steam

mixtures were shown. For no steam, the limits are the 18% and

59% values quoted in the older combustion literature, e.g., [10].

It appears that the values for the limits with steam may have

been estimated by drawing two lines nearly parallel to the axes

and rounding off the intersection at about 32% steam mole fraction. This is equivalent to predicting that for steam mole fractions below about 25%, steam has a negligible effect on the lean

and rich detonation limits for hydrogen.

Several experimental studies that have been completed in the

last decade in dry H2 -air mixtures have shown that the classical

18% and 59% detonation limits are not correct [11,12,13,14,15,

16]. The entire idea of a detonation "limit" has undergone considerable review. It is now known that detonation limits are not

fixed values of mixture composition, but depend on the ratio of

geometric .size to what is termed "detonation cell width (or

size).

1.2.1 Detonation Cell Width

Detonations are known not to be simple planar waves with a

leading, normal shock wave closely followed by a rapid chemical

reaction, as in the Zel'dovich-von Neumann-Doering (ZND) model

developed in the 19401s. Gaseous detonations are composed of a

complex pattern of transverse oblique shock waves with Mach

triple-point intersections followed by chemical reactions (defla.-

grations). The locus of Mach triple-point intersections can be

shown by the pattern a detonation makes passing over a smoked

surface.. A regular pattern of such diamond shapes is shown in

1-2
100 .

BWR-MARK I & 11 V =300.000 0t

90 BWR-MARK III V =1,500.000 ft 3

PWR-ICE CONDENSER

80 V -- 1,250,000 ft

80 ALSO PWR-SUBATMOSPHERIC

V =1,850,000 ft

z -

w 70 -PWR-DRY V 2,000.000 ft3

z

z

O 60

z

z

w

o 50

0

140

w

0 30

20

10

PWR-DRY V0,500,0ft

0 10 20 30 40 50 60 70 80 90 100

% METAL WATER REACTION

Figure 1-1. Percent Hydrogen Concentration vs.. Percent

Metal-Water Reaction for Various Plants.

1-3
100% AIR

10 .0% 80 60 40 20 100%

H2 PERCENT H2 STEAM

FLAMMABILITY LIMITS

750 F -0 psig (240 C - 101 kPa)

0- 30 F -0 psig (1490 C - 101 kPa

0-.- 3000 F -100 psig ( 1490 c - 792 kPa)

*Actual temperatures used in producing the data for

this curv~e are 680F - 187%' ( 200C - 860C)

Figure 1-2. Early Prediction of the Detonability Limits of

H2 -Air-Steam Mixtures. [From Reference 7]

1-4
Fig. 1-3 from studies in argon diluted fuel-oxygen mixtures [17].

The width of these diamond patterns is the detonation cell width, X.

The three-dimensional transverse wave structure which produces the diamond pattern is the direct consequence of the nonlinear coupling of the exothermic chemical reactions and the

shock-induced hydrodynamic flow field. Extensive evidence shows

that all self-sustaining gaseous detonation waves have this

structure. The cell width is believed to be proportional to the

chemical length scale of a given explosive mixture under detonating conditions and can be used to define the detonation sensitivity of that particular mixture. Moreover, in recent years the

broader significance of the detonation cell width has been demonstrated via the quantitative links that have been established

with the other "dynamic" detonation parameters [11,12] such as

the critical initiation energy and the critical tube diameter.

It also has direct relevance to establishing criteria for transmission of detonation [13], onset of transition [14], and definition -of detonability limits [ 15] Examples are shown in Fig.

1-4.

other measures of detonation sensitivity exist, such as the

critical tube diameter [18]. The critical tube diameter is the

minimum diameter of a rigid tube or orifice from which a detonation in a given mixture will continue to propagate as it diffracts into an unconfined volume. In fuel-air mixtures the

critical tube diameter can become quite large, on the order of

meters, making measurements inconvenient. Further, when the

desired initial conditions are other than ambient, measuring

critical tube diameter becomes even more difficult.

Detonation cellular structure is relatively easy to record;

however, there is a certain amount of irregularity that characterizes fuel-air mixtures, unlike the fuel-oxygen mixtures with

high argon dilution shown in Fig. 1-3. This randomness, or

irregularity, makes the interpretation of smoked foil records

uncertain. A typical smoked foil record is shown in Fig. 1-5.

It appears that a range of detonation cell widths exist. Typically, experimenters report only one detonation cell width for a

given mixture. The rationale used is that there is only one

intrinsic detonation cell width for a given mixture, and the

randomness is due to the response of the detonation wave to

external perturbations.

A few experimenters have assigned error estimates to their

detonation cell width data [19,20]. Recently, there have been

some questions raised concerning the validity of the rationale

that there is only one intrinsic detonation cell width for a

given mixture. It has been proposed that the irregularity of

some of the smoked foil records indicates that a detonation wave

in fuel-air mixtures has more than one detonation cell width or

mode [20,21]. The causes of irregularities are currently an

active area of research.

1-5
Figure 1-3 Cellular Pattern Left on Sooted

Plate from Passing Detonation

Wave in Argon-Diluted Fuel/Oxygen.

[From Reference 17]

1-6
() I-,-min=

PROPAGATION DOWN A CYLINDERt

PROPAGATION DOWN A TWO-DIMENSIONAL CHANNEL

- 131 ROUIND TUBE

D - Ill SQUARE TUBE

-i

min

WIDE CH1ANNEL

TRANSMISSION FROM A

"CRITICAL

TUBE INTO A LARGE OPEN SPACE

TUBE DIAMETER"m

a, Z77 7ý7 J.-Z 'r .- . 7-77-7

w.

-Imin

= 1. 5)

TRANSMISSION FROM A CHANNEL INTO A CLOUD

CONFINED ON ANY ONE SIDE

Figure 1-4. Effect of Geometry on Propagation

of Detonation Waves.

1-7
Figure 1-5. Detonation Cell Pattern on a Smoked Foil for a H2 -Air Mixture.

Note "irregular" structure compared to Figure 1-3.
older data on detonation limits, e.g., [10] were obtained in

small diameter tubes, usually 2.5 cm (1 inch) or less in diameter. We now know that the old values represented the limit of

propagation for that diameter tube. Larger tubes have produced

wider limits and the large length scales associated with reactor

containment buildings can be expected to have yet wider limits of

propagation. Atkinson et al., have predicted that the limits in

an infinite (unconfined) geometry would be 13% and 70% [22].

1.2.2 Modeling

The first successful attempt to model detonation waves was

developed around the turn of the century. The theory was based

on equilibrium thermodynamics and was proposed by Chapman and

Jouguet (C-J). Extensive data from decades of research since the

(C-J) theory was proposed have shown that detonations have pressures approximately 10 to 15% lower than the C-J predicted

pressure and velocities typically 1% higher than the C-J values

[23]. It has also been shown that the velocity is affected by

the size of the detonation tube [24]. Measured velocities from

small-diameter detonation tubes are lower than those in larg~er

diameter tubes.

The next significant advancement in detonation modeling

occurred in the 1940's with the proposals of Zel'dovich, von

Neumann and Doering (ZND). They independently proposed that

detonations are one-dimensional shock waves followed by deflagrations. This type of model is used to predict a characteristic

length scale associated with the chemical reaction distance

behind the shock waves. This model has been extended recently to

include detailed chemical kinetics '[25,26,27]. These models

determine the distance behind the initial shock wave for the

chemical reaction to reach an arbitrary degree of equilibrium.

These models are termed "induction-length models" but usually the

length scale defined by these models contains the reaction zone

as well as the chemical -induction zone. These models are onedimensional and, hence, do not predict detonation structure; it

is assumed *that they represent a spatial average of the actual

detonation structure. Empirical relations are used to relate the

induction-zone length to the detonation cell size.

Since the late 19701s, two-dimensional models have been

developed to investigate the detonation wave structure [28,29].

These models are computationally intensive and hence have used

simplified chemical kinetics. These models have shown the detonation cell pattern developing from a disturbed one-dimensional

detonation wave.

1.3 REFERENCES FOR CHAPTER 1

1. Henrie, J. 0. and Postma, A. K., Analysis of the Three Mile

Island (TMI-2) Hydrogen Burn, Thermal-Hydraulics of Nuclear

1-9
Reactors, Vol. II. Amer. Nuci. Soc., LaGrange, IL, U.S.

A.S.M.E., 1983, pp. 1157-1170.

2. Berman, M. and Cummings, J. C., "Hydrogen Behavior in LightWater Reactors," Nuclear Safety, Vol. 25, No. 1, pp. 53-74,

1984.

3. Camp, A. L., Behr, V. L., and Haskin, F. E., "MARCH-HECTR

Analysis of Selected Accidents in an Ice-Condenser Containment," NUREG/CR-3912, SAND83-0501, December 1984.

4. Lee, J. H., Knystautas, R., Chan, C. K., "Turbulent Flame

Propagation in Obstacle Filled Tubes," Proceedings of the

20th Symposium (International) on Combustion, Published by

the Combustion Institute, Pittsburgh, PA, pp. 1663-1672,

1984.

5. Pf~rtner, H., Schneider, H., Drenchen, W., Koch, C., "Flame

Acceleration and Pressure Buildup in Free and Partially

confined Hydrogen-Air Clouds," presented at the Ninth

International Colloquium on Dynamics of Explosions and Reactive Systems, Poiters, France, July, 1983.

6. Sherman, M. P.., Tieszen, S. R., Benedick, W. B., Fisk, J.

W., Carcassi, M., "The Effect of Transverse Venting on Flame

Acceleration and Transition to Detonation in a Large Channel," AIAA Progress in Astronautics and Aeronautics Series,

Vol. 106, pp. 66-89, 1986.

7. Shapiro, Z. M. and Moffette, T. R., Hydrogen Flammability

Data and Application to PWR Loss-of-Coolant Accident, WAPDSC-545, Bettis Plant, September 1957.

8. Reactor Safety Study, WASH-1400 (NUREG-75/014) U. S. Nuclear

Regulatory Commission (October, 1975).

9. Core-Meltdown Experimental Review, SAND77-0382, Sandia

National Laboratories, Albuquerque, March 1977.

10. Lewis, B., and Elbe, G. von, Combustion, Flames and Explosions of Gases, 2nd Ed., New York, Academic Press, 1961.

11. Lee, J. H. S.,"Dynamic Parameters of Gaseous Detonations,"

Annual Review of Fluid Mechanics, V. 16, pp. 311-336, 1984.

12. Knystautas, R., Guirao, C. M., Lee J. H., and Sulmistras A.,

"Measurements of Cell Size in Hydrocarbon-Air Mixtures and

Predictions of Critical Tube Diameter, Critical Initiation

Energy, and Detonability Limits," Progress in Astronautics &

Aeronautics, Vol. 94, pp. 23-37, 1984.

1-10
13. Liu, Y. K., Lee, J. H. S., Knystautas, R., "Effect of Geometry on Transmission of Detonation Through an orif ice,"m

Combustion and Flame V. 56, pp. 215-225, 1984.

14. Lee, J. H., Knystautas, R., Chan, C. K., "Turbulent Flame

Propagation in Obstacle Filled Tubes," Proceedings of the

20th Symposium (International) on Combustion, Ann Arbor, (In

Press).

15. Dupre, G., Knystautas, R., and Lee, J. H., "Near Limit

Propagation of Detonation in Tubes," AIAA Progress in

Astronautics and Aeronautics Series, Vol. 106, pp. 244-260,

1986.

16. Bull, D. C., "Concentration Limits to the Initiation of

Unconfined Detonation in Fuel/Air Mixtures," Trans IChemnE,

Vol. 57, pp. 219-227, 1979.

17. Strehlow, R. A., Combustion Fundamentals, McGraw-Hill Series

in Energy, Combustion & Environment, 1984.

18. Moen, I. 0., Murray, S. B., Bjerketvedt, D., Rinnan, A-.,

Knystautas, R., and Lee, J. H., "Diffraction of Detonation

From Tubes Into A Large Fuel-Air Explosive Cloud," 19th

Symp. (Int'l.) on Combustion, The Combustion Institute,

Pittsburgh, PA, 1982, pp. 635 - 645.

19. Bull, D. C., Elsworth, J. E., Shuff, P. J.,"Detonation Cell

Structures in Fuel/Air Mixtures," Combustion and Flame, V.

45, 1982, pp. 7-22.

20. Moen, I. 0., Funk, J. W., Ward, S. A.,Rude, G. M. and

Thibault, P. A., "Detonation Length Scales for Fuel-Air

Explosives," AIAA Progress in Astronautics and Aeronautics,

Vol. 94, 1984, pp. 55-79.

21. Moen, I. 0., Sulmistras, A., Thomas, G. 0., Bjerketvedt, D.,

and Thibault, P. A., "The Influence of Cellular Regularity

on the Behavior of Gaseous Detonations," AIAA Progress in

Astronautics and Aeronautics, Vol. 106, pp. 220-243, 1986.

22. Atkinson, R., Bull, D. C., Shuff, P. J., "Initiation of

Spherical Detonation In Hydrogen/Air," Combustion and Flame,

V. 39, 1980, pp. 287-300.

23. Fickett & Davis, Detonations, Univ. of California Press,

Berkeley, CA, 1979, Chapter 1A.

24. Manson, N., Brochet, C., Brossard, J. and Pujol, T., Ninth

Symposium (International) on Combustion, Academic Press, New

York, 1963, p. 461.

25. Westbrook, C. K., and Urtiew, P. A., "Chemical Kinetic

Prediction of Critical Parameters in Gaseous Detonation,"

1-11
19th Symp. (Int'l.) on Combustion, The Combustion Institute,

Pittsburgh, PA, 1982, pp. 615 - 623.

26. Shepherd, J. E., "Chemical Kinetics and Hydrogen-Air-Diluent

Detonations, " AIAA Progress in Astronautics and Aeronautics

Series, Vol. 106, pp. 263-293, 1986.

27. Tarver, C. M. , "Chemical Energy Release in One-Dimensional

Detonation Waves in Gaseous Explosives," Combustion and

Flame, Vol 46, pp, 111-133, 1982.

28. Oran, E. S. , et al. , "Numerical Simulations of Detonations

in Hydrogen-Air and Methane-Air Mixtures," Eighteenth Symposium (International) on combustion, pp. 1641-1647, 1981.

29. Hiramatsu, K. , Fujiwara, T. , and Taki, S. , "A Computational

Study of Transmission of Gaseous Detonations to Unconfined

Space," presented at the Twentieth Symposium (International)

on Combustion, Ann Arbor, Michigan, USA, August 12-17, 1984.

1-12
CHAPTER 2

HDT FACILITY DESCRIPTION

This section briefly describes the HDT facility and its

design. A detailed description of the facility appears in

Appendix A.

2.1 DESIGN CONSIDERATIONS

At the time (1982) that construction of the Heated Detonation Tube (HDT) was proposed, it was known that composition

limits for detonation propagation were not fixed quantities but

appeared to depend on the ratio of a characteristic geometric

size to detonation cell width. Because we were interested' in

obtaining information on the detonation of leaner mixtures than

previously tested and extrapolating the results to reactor containment scales, a decision was made to build a larger diameter

tube than had been used in previous studies. To minimize corrosion due to steam, stainless steel tubing was selected. To

initiate the detonation, a thin sheet of high-explosive was

selected. We chose a 43-cm (17-in)-inner-diameter tube with a

length-to-diameter ratio of about 30 to provide adequate distance

for the initiation transient to decay prior to recording the

detonation cell width. The selection of a large diameter tube

for the HDT has proved to have advantages beyond those originally

considered. Results from small diameter detonation tubes are

affected by boundary layer effects. Small values of velocity

deficit obtained in our facility indicate that boundary layer

effects are minimal for our large-diameter tube.

A major design decision was the selection of the method for

heating the tube and its contents. Our goal was to obtain a

uniform elevated temperature. Three methods were considered:

electric resistance heating using heater tapes, direct electric

resistance heating of the tube, and steam heating using a jacketed tube. The steam heating idea was dropped due to potential

cost and complexity. In particular, passing transducers through

a coaxial jacket posed a problem. Direct heating of the tube

would require enormous currents at very low voltages, and was

deemed impractical. Use of electric resistance tapes was the

simplest method. A major concern was the uniformity of temperature that could be achieved. A heat transfer analysis indicated

that the temperature variations in the tube due to the finite

spacing of the tapes and heat loss through the insulation would

be small (see Appendix F).

Originally, it was decided to support the tube from chains

hung on a steel framework and support the insulation in wooden

boxes. The design became too complex and costly. In the end,

simple V block wooden-faced supports mounted on concrete-filled

barrels were inexpensively made and have proven to be effective.

These supports are similar to those used for shock tubes. It was

2-1
expected that there would be some motion of the tube back and

forth in the guides, but no such motion has been evident. Apparently frictional forces are sufficient to prevent the large, but

fast alternating axial forces from moving the tube. Fiberglass

insulation was wrapped around the tube and was covered with

plastic sheet to shield it from rain.

Construction of the Heated Detonation Tube (HDT) was concurrent with another project, the FLAME combustion channel (1]. The

HDT was designed to use the same computer-controlled data acquisition system designed for FLAME. The needs of the two facilities for data acquisition are somewhat different but considerable

use was made of the FLAME data acquisition system. High-speed

digital data acquisition equipment used for DOE programs were

available and also used.

2.2 HDT DESCRIPTION

The HDT is shown in Fig. 2-1 and Fig. 2-2, before and after

the installation of the insulation. The HDT is composed of the

main detonation tube, gas injection/recirculation secondary piping, computer-controlled heaters, explosive initiator circuit,

instrumentation, and data acquisition system.

The detonation tube is composed of three pipe sections

attached end-to-end. All are made of type 304 stainless steel

and have a 45.7-cm (18-in) outer diameter. Two sections are

6.1 m (20 ft) long and have a 1.27-cm (0.5-in) thick wall and the

third is 0.91 m (3 ft) long with a 2.54-cm (1-in) thick wall.

The short, heavy-walled section serves as the initiation end.

Transient initiation pressures due to the high explosive are much

greater than the gaseous detonation pressure. Flat endplates

cover each end of the detonation tube and are made of 3.18-cm

(1.25-in) thick, type 304 stainless steel.

A schematic of the secondary piping is shown in Fig. 2-3.

The piping provides for evacuation, injection and circulation of

the gaseous mixture. The secondary piping consists of an inline

filter, circulation pump, and appropriate tubing, fittings and

valves. The gas flow is from the outlet port on the terminal end

of the main tube, through a shutoff valve, the filter, the pump,

past the high-point vent and the gas and steam injection ports,

along the main tube to the shutoff valve on the inlet port at the

initiation end of the main tube.

Gases, with the exception of steam, are introduced into the

secondary piping from standard gas cylinders. steam is introduced from a specially designed steam generator. The steam generator is a 1-liter stainless steel sample cylinder that has a

500-W flexible rod heater wrapped around the bottom of the

vessel. The heater and cylinder were immersed in a molten lead

bath contained in a larger cylinder to provide a thermal mass. A

premeasured amount of water is introduced into the vessel prior

2-2
tQ A t

P4

142

Figure 2-1. Heated Detonation Tube Without Thermal Insulation
Figure 2-2. Heated Detonation Tube With Thermal

Insulation Layer

2-4
POP OFI

FLEXIBLE LINE

VACUUM

PUMP

PORT

(J1

AIR, H2 &

CO 2

INJECTION

PORT .fl

HEATERS

Figure 2-3. Figre Schematic -3. of the Secondary Piping.
to a test and is completely boiled out into the circulation line

leading to the detonation tube.

The detonation tube heating system is composed of 15 individually controlled sections of resistance heaters on the surface

of the main tube, one section on the steam heating bottle, and

one section on the secondary piping. The heaters on the detonation tube and secondary piping are resistance-type, siliconerubber strip heaters. These heaters are held against the surface

of the detonation tube with fiberglass cord or RTV adhesive. All

heater sections except on the secondary piping are under computer

control. Each section contains several heaters of various sizes,

wired in series and parallel, to achieve the desired power level.

Each section also has three Chromel-Alumel, type-K thermocouples to measure the anticipated hottest, coldest and an intermediate temperature in each section. The anticipated hottest

temperature is underneath a heater tape, the coldest temperature

is midway between heater tapes, and the intermediate temperature

is midway between the hot and cold thermocouples. The hot

thermocouple is used to control the heating process, while the

other two measure the nonuniformity in temperature.

The heating system is controlled by on-off, set-point-logic

controlled relays which supply power to the heater strips. Control feedback is maintained by monitoring the temperature of the

thermocouple underneath a heater strip in each section and comparing it to the desired set-point temperature. The thermal

inertia of the system is high enough that on-off control is

sufficiently stable to maintain the detonation tube temperature.

A schematic of the control circuit is shown in Fig. 2-4. The

control decisions are made by a BASIC program running in the

Digital LSI-11/23 computer. To ensure that the heaters are

turned off in case of a computer failure, a Standard Engineering

Corp. "Watch Dog Timer" is used to monitor the computer system.

The insulation used to cover the detonation tube and secondary piping is Certainteed Snap Wrap foil-backed fiberglass which

has a thermal conductivity of 0.048 W/mOK (R - value of 3 (hr ft2

*F)/(Btu in)). The detonation tube is covered with 8.9 cm (3.5

in) of this insulation. A plastic sheet is used to protect the

insulation from moisture. Pre-formed 2.5-cm (1-in) thick cylindrical sections of insulation are used on the secondary piping.

The endplates are covered by large insulating endc~aps. The endcaps are made to slip over the f langes and are intended to be

easily removable because they must be removed after each test.

The endcaps are fabricated from a 20-gage galvanized sheet metal

outer shell in the form of a cup. The diameter of the shell is

94 cm (37 in) and the sides are 45.7 cm (18 in) deep. The inside

is lined with 15.2 cm (6 in) of insulation in the base and sides.

The most convenient method of initiating a gaseous detonation in the HDT is to use high explosive. This eliminates the

2-6
Figure 2-4. Schematic of the Heater Control Circuit.
need f or long run-up distances required f or DDT devices such as

Shchelkin spirals. The disadvantage of using high explosives is

that the gaseous detonation will be .overdriven for a certain

distance. This is due to the very high pressures initially generated by detonating the high explosive. To minimize overdriving,

we used a thin (1-mm thick) sheet of DuPont Detasheet high explosive cut into a 25.4-cm (10-in) diameter spoked-wheel shape to

both minimize the amount of high explosive and to effect almost

planar initiation. The explosive is initiated by an exploding

bridgewire detonator.

The instrumentation used on the HDT includes pressure gages,

thermocouples, and gas bottles- to determine the initial gas composition. To measure detonation properties, we use pressure

transducers mounted flush in the tube wall at various axial locations and at one azimuthal position, and a thin smoked aluminum

cylindrical section (foil) placed around the inner circumference

of the tube at the end farthest from the driver. The pressure

gage used to determine gas pressure is either a Wallace & Tiernan

0 to 800 mm Hg gage for one total atmosphere (101 kPa) tests, or

a Wallace & Tiernan 0 to 50 psia gage for superatmospheric ( >101

kPa) tests. The gas temperature measurement was made with a Ktype thermocouple probe mounted through the wall of the detonation tube.

To measure detonation pressure, fast response quartz piezoelectric transducers are used. Normally, from 6 to 10 pressure

transducers have been used in each test. The main value of their

data has been to provide detonation time of arrival. Data from

the transducer couplers travels about 100*m (300 ft) over coaxial

cable to the instrumentation building. The pressure signals are

recorded simultaneously on two high-impedance data acquisition

systems. The FLAME data acquisition system is based on the use of

two BiRa 5906 transient digitizer modules mounted in CAMAC (Computer Automated Measurement and Control) crates. The system is

controlled by a Digital LSI 11/23 computer which communicates to

the CAMAC crates with a GPIB (General Purpose Interface Bus)

interface.

Each BiRa transient digitizer is run with four active channels, giving a maximum sampling rate of 40 kilosample/second

(25 yss period) and a memory of 8K (8196 points) per channel. For

detonations travelling at 1600 m/s, typical of a leaner hydrogen

mixture, the time between recorded samples corresponds to a

travel of 40 mm. The pressure transducers are capable of faster

response, and a faster sampling rate would produce superior

results.

In addition to the CAMAC digitizers, the HDT uses 3

Tektronix 7612D transient digitizers, each with two data channels. These units are capable of sampling speeds up to 200

megasample/second (5 ns), with preprogrammed changes in sampling

speed. Typically, we use these units with sampling rates up to 2

MHz (0.5 #is). For detonations travelling at 1600 m/s, the time

2-8
between samples of 0.5 jus corresponds to a travel of 0.8 mrm. A

limitation of these units is the limited memory, 2K (2048 points)

per channel. To extend the data sampling "window" while

maintaining the same sampling speed during the detonation, slower

sampling speeds are used both before and after the period in

which the detonation arrival at the gage is expected. The

7612D's are also on the GPIB network and are partially controlled

by the LSI 11/23 computer. The 7612D's use two 7A16A amplifiers.

Several settings such as amplifier gains must be set by hand on

these units. Further details and a description of the

controlling software are given in Appendix G.

To measure detonation cell width, a smoked aluminum sheet

(foil) is used. The sheet is 1.2 m (4 ft) wide by 3.7 m (12 ft)

long and approximately 0.5 mm (0.020 in) thick. For tests without steam, the sheet is smoked with a MAPP (stabilized methylacetylene-propadiene) torch using no oxygen to produce black

soot. For tests with steam, the best results were obtained using

furnace oil in a wicked flame holder to produce soot on a foil

with a surface preparation coating which consisted of a mixture

of one-third Dow Corning Sylgard 186 and two-thirds Xylene. This

surface preparation prevents spotting of the soot which occurred

without the preparation. The sheet is rolled into a long cylinder around stiffening rings attached at each end and placed

around the inside circumference of the HDT at the end opposite

the explosive initiator.

2-9
2.3 REFERENCES FOR CHAPTER 2

1. Sherman, M. P. , Tieszen, S. R. , Benedick, W. B. , Fisk, J.

W., Carcassi, M., "The Effect of Transverse Venting on Flame

Acceleration and Transition to Detonation in a Large Channel," AIAA Progress in Astronautics and Aeronautics Series,

Vol. 106, pp. 66-89, 1986.

2-10
CHAPTER 3

PROCEDURE

The test procedures used for the Heated Detonation Tube

experiments were developed and improved upon as the test program

developed. The data have been categorized into 7 test series

listed in Table 3-1. The general procedures for each test series

are discussed in this chapter. Specific procedures for each

series, including variations in procedure for each series are

discussed in Appendix B.

All experiments in the HDT began by preparing a smoked foil

and by assembling the explosive initiator. After a foil has been

smoked, it is attached to stiffening rings at each end and inserted into the HDT. The endplate is then bolted in place. At

the other end of the tube, the assembled explosive initiator is

inserted into a protective coaxial tube and installed into the

HDT. The detonator is connected to an electrical feed-through in

the endplate, and the plate is bolted in place.

After the smoked foil and explosive initiator are installed

in the detonation tube and the endplates secured and insulated,

gases are then introduced. For each test series, air is the

first gas introduced into the detonation tube followed by hydrogen, except for series #2. In test series #2, CO2 is introduced

before the hydrogen. In tests prior to HT49, ordinary ambient

air, whose relative humidity had been measured, was used. From

test 49 on, bottled dry air is used. Steam is added after heating the detonation tube.

To ensure a homogeneous mixture, the circulation bellows

pump runs continuously from the introduction of the first gas

until just before the detonation initiation sequence to ensure

homogeneous mixture. At least one detonation tube volume of gas

is allowed to circulate during the addition of each gas to the

recirculation line and at least one additional tube volume of gas

is allowed to circulate prior to recording the temperature and

pressure of the gas mixture. one tube volume of gas takes

approximately 15 minutes to circulate. Temperature and pressure

measurements are used to determine gas composition. For mixtures

without steam, perfect gas is assumed for calculating compositions; for mixtures with steam, a virial equation of state is

used.

For test series #1, #2, and #6, the partial pressure of each

gas was adjusted so that the total initial pressure prior to

detonation was 101 kPa (1 atm). For test series #3, #4, and #5,

the air pressure was adjusted so that the air density was 41.6

moles/in3 . This density corresponds to air at 101 kPa (1 atm) and

3-1
Table 3-1

Test Series

Series #/ Description # of Tests in Series

1 H2-Air @ P=1 atm, T=20 0G 16

2 H2-Air-G02 @ P=.1 atm, T=200G 10

3 H2-Air @ Pair=41 .

6 moles/rn3 , T=1000G 16

4 H2-Air-H20 @ Pair=4 1.6 moles/rn3, T=1000G 18

5 H2-Air @ Pair=4 1 .

6 moles/rn3, T=200C 6

6 H2-Air @ XH2=O.17, P=1 atm 4

7 H2-Air @ XH2=O-l 7, p=42 moles/rn3 3

200 C. For test series #7, the partial pressure of each gas was

adjusted so that the total initial gas density was 42 moles/rn 3 .

For test series #1, #2, and #5, the detonation tube was not

heated but maintained at ambient temperature while the composition was varied. For test series #3, the temperature was held at

100 0C and the composition was varied. For test series #6 and #7,

the temperature was varied while the composition was held fixed.

Typically, heating took approximately 5 hours to reach 100 0C.

IThe detonation initiation sequence is the same for all

tests. After the temperature and pressure are measured for the

last gas injected into the tube and it has reached its equilibrium temperature, the *secondary piping is isolated from the

detonation tube to protect the pump. The manifold to the static

pressure gage is closed, the power supplies to the dynamic pressure transducers are turned on, and the detonator lines are connected. All personnel are then required to leave the vicinity of

the detonation tube and enter the control room in Bldg. 9920.

For elevated temperature tests, the heaters are turned off. The

computer is then configured to control the data acquisition

equipment. The area is cleared and the high voltage capacitor in

the firing circuit is charged. A trigger pulse discharges the

high voltage capacitor into the exploding bridgewire detonator

that initiates the detonation and simultaneously starts the data

acquisition equipment. The time between secondary piping

isolation and the initiation of the detonation is typically 12

minutes. The time between turning off the heaters and the initiation of the detonation is typically 8 minutes.

3-2
CHAPTER 4

RE SULTS

Detonation cell width, velocity and pressure are measured in

the HDT. The detonation cell width and velocity results will be

discussed in the following sections. Tabular results are presented in Appendix C. The detonation pressure is not reported

because of uncertainty associated with the data (see Appendix D).

4.1 DETONATION CELL SIZE, X

Results of the tests performed in the detonation tube are

shown in Figs. 4-1 through 4-7. Smoked foil records from H2 -air

detonations show a somewhat irregular cell structure as in Fig.

4-1. As noted in the literature review, most experimenters quote

a single detonation cell width for a given mixture. A current

area of active research is to test the validity of the assumption

that a given mixture has a given unique detonation cell width, as

opposed to a range of detonation cell widths. Testing completed

for this report was not intended to address this question. For

this report, a single detonation cell width has been selected for

a given mixture using established methods of selecting detonation

cell width.

Two methods of selecting a single detonation cell width are

described by Moen, et al. [1], the single cell method and the

dominant mode method. Both methods depend on observer interpretation of the detonation cell tracks on the the smoked foil

record, and are subject to observer bias. In the single cell

method the observer measures a large sample of individual cells

(diamond shapes) . Subjectivity enters into deciding what constitutes a detonation cell. The dominant cell method is really

an extension of the single cell method. In the dominant cell

method, the criteria for what constitutes a cell is defined by

the number of cells between parallel bands, usually in one

direction. These methods are discussed in Appendix D. Subjectivity enters into deciding what are parallel lines. Most 'lines

are wavy and vary in contrast along the length of the line. In

this method a few parallel bands are measured using the longest

running parallel lines with the highest contrast.

In this report, the dominant mode method is used to determine the detonation cell width. The "UI-shaped curve of detonation cell width versus equivalence ratio is assumed to be smooth

to assist in the selection of the detonation cell width. It must

be noted that the process of selecting detonation cell width is

subjective. Details and uncertainty estimates are given in

Appendix D.

4-1
Figure 4-1. Typical Smoked Foil front HDT.
0

C

0

0.11 10

Equivalence Ratio- cO

Figure 4-2. Detonation Cell Width vs. Equivalence

Ratio for Test Series #1. (H2 -Air at

P=1 atm, T=20*C)

4-3
4-0

0

0.11 10

Equivalence Ratio

Figure 4-3. Detonation Cell Width vs. Equivalence

Ratio for Test Series #2. (H2 -Air-C02

at P=1 atm, T=20*C)

4-4
10

0

0

0.1 1 10

Equivalence Ratio

Figure 4-4. Detonation Cell Width vs. Equivalence

Ratio for Test Series #3 4. (H2 -AirH2 0 at Pair=4 1 .

6 moies/mi, T=100*C)

4-5
K

Q)

E

0

0

1000:

100-

10-

4 4

02

0

- 00

0

0

0

* 0~

01)

0

0

0 0

G

INITIAL CONDITIONS

0- To -298 K Po - I atm (Sandia HDT)

-To -298 K Po 1 atm (McGill U.)

-To - 293 K Pair - 41.6 mole/rn 3 (HDT)

0 -To - 373 K Pair - 41.6 mole/rn3 (HDT)

1- 7 t i t I i I i t I

0.3 I

Equivalence Ratio-1b

Figure 4-5. Effect of Initial Conditions on Detonation

Cell Width of H2 -Air mixtures.

4-6
450-

400-

o Po = 1 atm HDT DATA

o Po = 42 moI/m5

* Po = 1 atm SHEPHERD

0 Po = 42 mourn5

' MODEL

-c

-0

0

350-

300±

250-

0

200+

0

1504+

R 0

100± 0

:1

50+

0 I I I I

260 280 300 320 340 3

Initial Temperature (K)

60 380

Figure 4-6. Detonation Cell Width vs.

Ratio for Test Series #6,

at XH2=O-l7)

Temperature

7. (H2 -Air

4-7
1000. ±

~-100-

0

a 10-

0

INITIAL CONDITIONS

o-To - 298 K Po - I atm (Sandia HDT)

-To - 293 K Pair - 41.6 mole/rn 3 (HDT)

0 To - 373 K Pair - 41.6 mole/rn 3 (HDT)

0.31

Equivalence RatioFigure 4-7. Uncertainty Ranges for the HDT Data in

Figure 4-5.

4-8
A relative uncertainty bound can be estimated to be +/-25%

for measured detonation cell width when a comparison is to be

made among data in the report. An "absolute" uncertainty bound

can be estimated~to be a factor of 2 for comparison with data

from other reports. Since subjectivity is involved in measuring

detonation cell width, subjectivity is also involved in the estimation of uncertainty bounds. For the purpose of a conservative

detonability hazard analysis, it is strongly recommended that the

detonation cell width in this report be divided by 2.

For clarity in identifying the functional relationship between detonation cell width and equivalence ratio, diluent mole

fraction, and initial thermodynamic state, the uncertainty bars

have been deleted from Figs. 4-2 through 4-6. Fig. 4-7 shows the

relative uncertainty bars for the data in Fig. 4-5. A complete

listing of the data and relative uncertainty estimates is given

in Appendix C. The details used to establish the values in

Appendix C are discussed in Appendix D. A short discussion of

uncertainty in irregular H2 -air detonation cell measurement is

also given in Ref. [2].

For Figs. 4-2 through 4-5, the detonation cell width is

plotted versus the equivalence ratio, q5. The equivalence ratio

is def ined as the fuel (H2 ) to air molar ratio divided by the

same ratio at stoichiometry. This ratio is invariant with

respect to the type and amount of added diluent. Some values of

equivalence ratio are listed in Table 4-1. Various thermodynamic

relationships including the relation between 0 and the mole fraction of H2 are developed in Appendix E.

4.1.1 Modeling

The detonation cell width data presented in Figs. 4-2

through 4-4 and 4-6 have been compared by Shepherd [3] with a

characteristic reaction zone length computed from a Zel'dovichvon Neumann-Dbring (ZND)-type model. The model integrates a set

of hydrogen oxidation reactions (reaction rates given in [4]))

along the Rayleigh line. As first suggested by Shchelkin and

Troshin (5], the characteristic reaction zone length, L, is

believed to be approximately proportional to the cell size, X,

X =A L

The validity of this relation has been discussed by Lee, et

al., [6] and by Westbrook and Urtiew [7]. For the model used in

thi~s report, the length of the reaction zone, L, is defined as

the distance behind the shock wave where the flow Mach number M =

0.75. The constant A is determined by requiring the predictions

to match the data at the stoichiometric point for H2 -air detonations in test series #1. A value of A = 22 was determined in

this manner. Alternative definitions of L and a complete discussion of the model and its validity is found in Ref. [3].

4-9
Table 4-1

in Total Mixture by Volume

I % H20 in mixture by volume

%H2

in mixture 0 10 20 30

by volume

10 0.27 0.30 0.34 0.40

15 0.42 0.48 0.55 0.65

'20 0.60 0.68 0.80 0.95

25 0.80 0.92 1.08 1.33

30 1.03 1.19 1.43 1.79

40 1.59 1.91 2.39 3.18

50 2.39 2.98 3.98 5.91

60 3.58 4.77 7.16 14.32

70 5.57 8.35 16.71 0

The calculations shown in Figs. 4-2 through 4-5 were made

for a limited number of points corresponding to the detonation

cell width measurements. spline interpolation was used to generate continuous curves. Unless otherwise noted, nominal values

(see Table 3-1) were used for initial conditions. Calculations

were also made for the exact initial conditions for each test.

These results are listed in Appendix C.

4.1.2 Hj-Air; P,T = Constant (Test Series #1)

Detonation cell width (X) measurements for the H2 -air

system, at one atmosphere total pressure and 200C, derived from

laboratory- scale experiments at McGill University and from the

HDT measurements at Sandia, are displayed in Fig. 4-2. These

experimental results for the hydrogen-air system represent the

widest known compositional range for the detonation cell width in

any fuel-air mixtures. The leanest and the richest compositions

(i.e., 13.5% H2 -air and 70% H2 -air) have detonation cell patterns

that have one set of dominant tracks indicating that the mixtures

are close to mixtures that correspond to the onset of a singlehead spin in the 43 cm diameter HDT. These limits are much wider

than the previously believed 18-59% discussed by Lewis and Von

Elbe f 8], which were influenced-by the small size of the experimental tube rather than any intrinsic limit of the H2 -air system.

4-10
Note that the results of the HDT (43-cm dia. ) are close to

those obtained in the largest tube (30-cm dia.) at McGill

University. Since subjectivity is involved in estimating X,

R. Knystautas of McGill University measured the detonation cell

width from the smoked foils for this test series and at McGill

University. By determining the detonation cell width for both

sets of experiments, differences in the application of the

criteria for determining detonation cell width between different

observers were reduced. During this test series, Knystautas

instructed the authors in the methods of measuring detonation

cell width from smoked foils. These data compare to within

+/-25% as discussed in Appendix D.

The detonation cell measurements are correlated with both

the Westbrook [7] and Shepherd [3] kinetic models. The correlation requires the establishment of an empirical link between the

calculated reaction zone length, as calculated by Westbrook or by

Sh~epherd, and the detonation cell width. This is done via the

single-point matching at the stoichiometric composition. It is

clear that the kinetic models recover the qualitative trend and,

to some extent, the quantitative trend of the cell width measurements. However, using single-point matching for both the

Westbrook and the Shepherd models, there is significant discrepancy between calculation and experiment on the rich side of the

compositional range, and for the very lean and very rich compositions.

4.1.3 H2 -Air-C02 ; P,T = Constant (Test Series #2)

As a prelude to H2 -air-steam detonation measurements, and to

assess the inhibiting effect of an inert diluent on the detonability of H2 -air miixtures, a series of detonation experiments

using H2 -air-C02 mixtures was carried out using smaller diameter

tubes at McGill University and the HDT. Fig. 4-3 shows the

effect of C02 dilution on the detonability of H2 -air mixtures as

represented by the detonation cell width X. The immediate effect

that can be observed is the severe desensitization of the mixtures with even modest additions Of C02 . For example, the addition of 5, 10 and 15% CO2 to a stoichiometric H2 -air mixture

increases the detonation cell width by approximately a factor of

1.5, 2.8, and 12.8, respectively. Because detonation sensitivity, according to the Zel'dovich criterion, is inversely proportional to the cube of the chemical length scale and hence X, C02

decreases the detonability by the corresponding iactors of 3.4,

22, and 2100.

The experimental measurements for the detonation cell width

have been correlated with the numerical calculations of reaction

zone length by Shepherd [3] for the H2 -air--C0 2 system. The correlation is based on the single-point matching at stoichiometry

described previously for the H2 -air system. It is remarkable to

observe that in spite of the fact that the single-point matching

was done for a stoichiometric mixture of H2 -air, the quantitative

calculations from this model and cell width measurements for the

4-11
H2 -air-C02 mixtures are within 100-200%. This degree of correlation is acceptable considering the crudeness of the model and the

uncertainty involved in detonation cell width measurements. More

elaborate correlation using the existing H2 -air results gives

better agreement for the H2 -air-C02 mixtures [3].

4.1.4 H2 -Air-Steam; Pair,T = Constant (Test Series #3,#4)

An extensive series of tests was carried out to measure the

detonation sensitivity of H2 -air-steam. mixtures. All experiments

were carried out at elevated initial temperature, nominally at T = 100*C in the HDT. To simulate the nuclear reactor environment

in the event of hydrogen release, the initial air partial density

of the mixture was fixed for air conditions at NTP (i.e., an

initial air density of 41.6 moles/in3 ). The hydrogen and steam

were then added, resulting in an initial mixture pressure which

was superatmospheric, ranging from 1.5 to 3 atm depending on the

amounts of H2 and steam added. A range of H2 -air mixtures, to

which 10, 20 and 30% steam had been added, were studied in the

HDT. Results for these tests are displayed in Fig.4-4, where the

detonation cell width, X, is plotted as a function of equivalence

ratio and steam mole fraction. It can be observed that the role

of steam is to desensitize the mixture by a substantial factor.

As an example, for stoichiometric compositions of H2-air, the

addition of 10, 20 and 30% of steam leads to an increase in the

detonation cell width, X, by the corresponding factors of 6, 20

and 60. According to the Zel'dovich criteria of dependence of

the mixture sensitivity on the inverse cube of the chemical

length scale, this corresponds to a reduction in detonability by

factors of 220, 8000 and 2.2 x 105, respectively. As discussed

in Chapter 1, a prediction made by Shapiro and Moffette [9]

indicated that steam concentration had a negligible effect on

detonability below about 25% steam. The data do not support this

prediction.

Detonations were recorded with 30% steam for equivalence

ratios of 0.9 and 1.0. Predictions by Shapiro and Moffette were

that 32% steam would completely inert a detonation. For the

stoichiometric mixture at 100*C, saturation corresponds to a

steam mole fraction of 35.6%. In the present tests with a

stoichiometric H2 -air mixture and 30% steam dilution, the measured detonation cell width is well below the detonation limit of

the tube. Consequently, we believe that a stoichiometric steamsaturated mixture could be. detonated in our facility. The

detonation cell width data measured in the HDT for the H2 -airsteam mixtures have been correlated with the ZND model results of

Shepherd [3] in the manner described for the H2 -air-C02 mixtures.

The agreement is remarkably good in spite of the preliminary

nature of this type of empirical correlation. The chemical

kinetics model again appears to recover the essential qualitative

features of the experimental results.

4-12
4.1.5 H2 -Air; PairT = Constant (Test Series #5)

Note that the effectiveness of steam addition to H2 -air

mixtures in reducing detonation sensitivity is affected by the

initial temperature and pressure. The addition of steam in

significant quantities to a fixed volume of H2 -air requires

(a) elevated temperatures and (b) elevated pressures. Evidence

indicates that both of these conditions, the increased initial

temperature and pressure above STP, tend to sensitize the detonable mixture. A comparison of the three sets of experimental

points, and corresponding theoretical curves using the ZND model,

are shown in Fig. 4-5. For the lower two sets of points and

curves, the difference in detonation cell width at a given equivalenice ratio is due to the temperature difference at constant

mixture density. For the upper two sets of points and curves, .the

difference in detonation cell width at a given equivalence ratio

is due to the difference in mixture density at constant temperature.

4.1.6 H2 -Air; XH2,P = Constant (Test Series #6)

p = Constant (Test Series #7)

Test series #6 and #7 examine the effect of temperature at

constant pressure and constant density, respectively, for one

composition, XH2=O-l66. The detonation cell width results are

shown in Fig. 4-6 along with the ZND model of Shepherd predictionis [3] using the exact test initial conditions. There is a

large uncertainty associated with the detonation cell width

measurements in this series due to the small number of tests.

Because of the uncertainty, care must be taken in drawing conclusions from this small sample. However, the general trend is a

decrease in detonation cell width with temperature for both

constant density and constant pressure.

The constant density results are in agreement with the

results of test series #5 and both constant density and constant

pressure results are in qualitative agreement with the Shepherd

model for this of f-stoichiometric composition. However, previous

predictions by both Westbrook and Urtiew [7] and Shepherd [3]

show that detonation cell width increases slightly with increasing temperature when the pressure is held constant for a

stoichiometric H2 -air mixture. They note that the increase in

detonation cell width is due to two effects. The primary effect

is that the post-shock reactant density decreases with increasing

temperature when the pressure is held fixed. The second effect

is that the post-shock temperature decreases slightly with

increased initial temperature.

If the effect predicted by Westbrook and Urtiew [7] can be

substantiated, then the temperature effect is compositionally

dependent. For near stoichiometric mixtures, an increase in

temperature at constant pressure will produce an increase in

detonation cell size. For of f-stoichiometric (or at least lean)

4-13
mixtures, an increase in temperature at constant pressure produces a decrease in detonation cell size. A mechanism exists for

such a composition-dependent initial - temperature effect; the

controlling chemical kinetic mechanism changes for H2 -air mixtures between stoichiometric and lean limit compositions [3].

4.2 DETONATION VELOCITY MEASUREMENTS

Detonation velocity measurements have also been made in the

HDT for H2 -air-diluent mixtures. The results are displayed in

Figs. 4-8 through 4-11, together with the Chapman-Jouguet (C-J)

velocity calculated from the Gordon-McBride code [10]. The

calculations are made for a limited number of data points corresponding to the actual test conditions. Spline interpolation

was used to generate continuous curves (except for Figure 4-11).

The calculations used the exact initial conditions, not nominial

values., For Figs. 4-8 through 4-11, the detonation velocity is

plotted versus the equivalence ratio, 0. This ratio is invariant

with respect to the type and amount of added diluent. Various

thermodynamic relationships, including the relation between 0 and

the mole fraction of H2 , are developed in Appendix E.

All the results indicate that the measured detonation ve-locities, even in marginal H2 -air-steam mixtures, is within a few

percent of the calculated C-J values. No velocity deficit can be

observed in any of the present tests. This is in agreement with

the observations of Dupre, et al. [11] described in a recent

paper where detonation propagation has been studied in a range of

detonation tube diameters. It was observed that the velocity

deficit does not exist for tube diameters in excess of 5 cm and

atmospheric initial pressures. It has been postulated that the

velocity deficit is related to the wall boundary layer effect in

small diameter tubes and/or low initial pressures, where the

Reynolds number is such that the boundary layer effect is significant. At the larger tube diameters and at high initial pressures, the Reynolds number is large and the relative effect of

the boundary layer growth in the detonation propagation begins to

vanish. This is most certainly indicated in the present measurements.

4-14
2.4

2.3-

2.2-

E

2-

0 1.

Ca

C0

0 1.7- 0

C1 0 0% 002 HDT DAT

1.60,f 5% C02

0 10% C02

AS A 15% C02

x 0% C02 0-J VEL.

1.5 5% 002

O 0 10% C02

x 15% C02

1.4- 01 i

0.31

Equivalence Ratio -

Figure 4-8. Detonation Velocity vs. Equivalence

Ratio for Test Series #1, 2.

(H2 -Air-C02 at P=1 atm, T=200C)

4-15
2-3

2.2-

a ag & A . A d

o0 0% 1120 Sandie HDT

o 10% H120

A~ 20% H120

0 30%01120

X 0% 1120 C-J VELOCITY

0

EC

0

.0-

0

2.1-

2

1.9-

* 10%.H120

*( 20% 1120

EB 30% 1120

1.8+

1.7-

1.6-

0

i ~ ~ i 

0.3

Equivalence. Ratio

Figure 4-9. Detonation Velocity vs. Equivalence

Ratio for Test Series #3 14. H-2--Air--

H120 at Pair=4 1 .

6 mole /m , T=1OO0C)

4-16
2.4-

2.3-

I I . . . I I

0

0

Co

0

.60

a)

2.1-

2-

1.7-

E

A

1.6-

1.5-

1.4-

0

0

0i A

ci

x

INITIAL CONDITIONS

To = 298 K, Po = 1 atm HDT DATA

To = 293 K,.Pair - 41.6 mourn 3

To - 373 K.PaIr - 41.8 moD/m-5

To - 298 K, Po - 1 atm C-J VELOCITY

To =293 K-PaIr = 41.8 mol/m3

To - 373 K-PaIr - 41.6 moI/rn3

. I V0.3 1

I I I

Equivalence Ratio- (

Figure 4-10. Effect of Initial Conditions on Detonation

Velocity of H2 -Air mixtures.

4-17
2

1.9-

1.8-

E

4-.

0

0

C

0

1.7-

1.6-

1.5-

1.4-

1.3-

U LD~ '~1

1.2-

1.1 -

* Po 1 atm HDT DATA

* 0o 42 mourn

* Po 1 atm.C-J VEL.

* o 42 molrn

I-II I I I

260 280 300 320 340 3'

Initial Temperature (K)

60 380

Figure 4-11. Detonation Velocity vs. Temperature

for Test Series #6, 7. (H2-Air at

XH2=O.17)

4-18
4.3 REFERENCES FOR CHAPTER 4

1. Moen, 1. 0. , Murray, S. B. , Bjerketvedt, D. , Rinnan, A. ,

Knystautas, R., Lee, J. H., "Diffraction of Detonation From

Tubes Into A Large Fuel-Air Explosive Cloud, " 19th Symp.

(Int'l.) on Combustion, The Combustion Institute,

Pittsburgh, PA, 1982, pp 635 - 645.

2. Bull, D. C., Elsworth, J. E., Shuff, P. J., "Detonation

Cell Structures in Fuel/Air Mixtures," Combustion and

Flame, V. 45, 1982, pp 7-22.

3. Shepherd, J. E., "Chemical Kinetics and Hydrogen-AirDiluent Detonations," AIAA Progress in Astronautics and

Aeronautics Series, Vol. 106, pp. 263-293, 1986.

4. Miller, J. A., Mitchell, R. E., Smooke, M. D., and Kee,

R. J., "Towards a Comprehensive Kinetic mechanism for

Oxidation of Acetylene," 1 9 th Symposium (International) on

Combustion, The Combustion Institute, Pittsburgh, Pa.,

1983, pp 181-196.

5. Shchelken, K. I. and Troshin, Ya. K., Gasdynamics of

Combustion, Mono Book Corp., Baltimore, Md., 1965.

6. Lee, J. H., Knystautas, R.*, Guirao, C., Benedick, W. B.,

Shepherd, J. E., "Hydrogen-Air Detonations," Proceedings of

the Second International Conference on the Impact of

Hydrogen on Water Reactor Safety, NUREG/CP-0038, EPRI RP

1932-35, SAND82-2456, October 1982, pp 1007-1026.

7. Westbrook, C. K., and Urtiew, P. A., "Chemical Kinetic

Prediction of Critical Parameters in Gaseous Detonation,"

19th Symp. (Int'l.) on Combustion, The Combustion

Institute, Pittsburgh, PA, 1982, pp 615 - 623.

8.. Lewis, B., and Elbe, G. von, Combustion, Flames and

Explosions of Gases, 2nd Ed., New York, Academic Press,

1961.

9. Shapiro, Z. M. and Moffette, T. R., Hydrogen Flammability

Data and Application to PWR Loss-of-Coolant Accident, WAPDSC-545, Bettis Plant, September 1957.

10. Gordon, S., and McBride, B. J., "Computer Program for Calculation of Complex Chemical Equilibrium Compositions,

Rocket Performance, Incident and Reflected Shocks, and

Chapman-Jouguet Detonations," NASA SP-273, 1971.

11. Dupre, G., Knystautas, R., and Lee, J. H., "Near Limit

Propagation of Detonation in Tubes," AIAA Progress in

Astronautics and Aeronautics series, Vol. 106, pp. 244-260,

1986.

4-19

CHAPTER 5

DISCUSSION AND CONCLUSIONS

5.1 DISCUSSION

The data from the HDT tests can be used to analyze the

possibility of detonation propagation in reactor containment

buildings. In the past this type of analysis has often made use

of the predicted hydrogen-air-steam detonability limit by Shapiro

and Moffette~l]. Shapiro and Moffette plotted their detonability

limits'on ternary mixture coordinates. This is common for deflagration analysis since deflagration limits are strong functions of mixture concentration and only weak functions of other

variables, such as temperature and pressure, in the range of

interest. These other variables are often shown parametrically

on the ternary diagrams.

Chapter 1 reviewed detonation studies completed since

Shapiro and Moffette which conclusively show that detonation

limits are a strong function of geometric scale and pressure in

addition to mixture concentration. The hydrogen-air- steam data

from the HDT tests also show that the detonation limits are a

function of mixture temperature. The detonation limit prediction

by Shapiro and Moffette is invalid since it does not address

these additional variables. A single ternary mixture diagram is

not sufficient to plot all the variables. However, for a given

mixture temperature and pressure (or density), contours of

constant detonation cell width can be plotted on ternary mixture

coordinates.

Figure 5-1 shows these contours for a mixture temperature of

100*C and an air molar density of 41.6 moles/in 3 . For comparison,

the theoretical prediction by Shapiro and Moffette is also shown.

The lines of constant cell width correspond to lines of constant

detonation sensitivity. As the detonation cell width increases,

the smallest room dimension which will allow detonation propagation increases. A large room will allow a broader range of mixtures to propagate a detonation compared to a smaller room.

To evaluate which mixtures will propagate a detonation in a

given geometry, the detonation cell width is compared to geometric propagation correlations discussed in Chapter 1. For convenience, the detonation propagation correlations c4iven in Figure

1-4 have been copied again as Figure 5-2. As an example, take a

long'.duct of square cross-section, 1 m by 1 m. From Figure 5-2,

the proper detonation propagation correlation is that between

parallel plates. Therefore the detonation cell width that will

just marginally propagate in the duct is 1 m, the same dimension

as the duct. This means that the area to the lef t of the 1 m

contour in Figure 5-1 is detonable for the given temperature and

air density. If the duct were only 0.5 in on a side, then the

area to the left of the 0.5 in contour would be the detonable

region, etc.

5-1
80 220

60 40

'p

A

.9

40 60

20 880

80 60 40 20

% HYDROGEN

Figure 5-1. Constant Detonation Cell Width on

Mixture Coordinates. (For T =

100*C, Air Density = 41.6 mole/rn3 )

5-2
-A

PROPAGATION DOWN A CYLINDER

') Dmi /

7m

PROPAGATION DOW(N A TWO-DINENSIOtIAL CHANNEL

D

=131 ROUJND TUBE

II1I SQUARE TUBE

-IWmi 3

WIDE CHANNEL

TRANSMISSION FROM A TUBE INTO A LARGE OPEN SPACE

"CRITICAL TUBE DIAMETER"

£~Lrw1z:

-r-r F 4' ý e

w.

-Imin

= 1. 51

TRANSMISSION FROM A CHANNEL INTO A CLOUJD

CONFINED ON ANY ONE SIDE

Figure 5-2. Effect of Geometry on Propagation

of Detonation Waves.

5-3
It is not necessary to use the ternary mixture diagram to

evaluate detonability. For a given mixture, the plot of

detonation cell width as a function of equivalence ratio can be

used, e.g. Figure 4-4. For convenience, Figure 4-4 has been

copied to Figure 5-3. For example if a mixture is formed at

100*C with an initial air density of 41.6 moles/in 3 with 30% H2 0

and 29.5% 112, Fig. 5-3 shows that the dominant mode detonation

cell width is 300 mm. From Fig. 5-2 the minimum channel width

for propagation of a detonation is 300 num. Any channel narrower

than this will not continue to propagate a detonation in this

mixture. Similarly, the smallest tube diameter for propagation

is 100 mm. The smallest tube diameter that will allow a detonation to propagate from the tube into free space is 3.9 m, etc.

For accident conditions that have not been directly tested in the

HDT, the test data can be interpolated. For example, a mixture

of 21% H2 (0 = 0.63) and 15% H20 at 100 0C can be anticipated to

have a dominant mode detonation cell width of approximately

400 mm.

Two qualifications need to be considered when using the

data. First, great care should be taken in trying to extrapolate

trends in the data. A state-of-the-art chemical kinetics model

[2] is used in this report to extrapolate the data to obtain the

one and two meter detonation contours in Fig. 5-1. The model is

discussed briefly in Chapter 4, but it is beyond the scope of

this report to evaluate the predictive capability and uncertainty

associated with this class of models. However., the chemical

kinetics model shows that changes in initial conditions,

equivalence ratio, and diluent concentration can change the ratecontrolling reactions. Therefore, an attempt to extrapolate

trends from the data could lead to very large errors.

Secondly, there are large. uncertainties in the measurement

of detonation cell width and in the detonation propagation

correlations based on detonation cell width. The analyst using

the detonation cell width data in this report is urged 'to read

Appendix D. A range of detonation cell widths appears on a

smoked foil record. The characterization of this range is an

area of current research and may have a significant impact on

safety analysis. Mixtures with broad distributions (irregular)

may have different propagation criteria than those with narrow

(regular) distributions. For this reason, the authors strongly

recommend that safety analysts divide the dominant mode

detonation cell widths in this report by a factor. of two for use

in safety calculations. For example, the one meter detonation

cell width contour in Fig. 5-1 should be considered as a 0.5 m

contour in safety calculations. In some cases dividing by a

factor of two may be conservative and in other cases it may not

be. The factor of two is recommended because there is almost

always structure that could be interpreted as a detonation cell

width that is a factor of two smaller than the dominant mode

measured on smoked foil records. other researchers have termed

this smaller cell width "substructure" and have noted its

existence for many fuel-air mixtures (3,4].

5-4
-7-

C 0

0

.0-0

C 10-

0

o 0% H20 Sandia HDT

o 10% H20

A 20% H20

c 30% H20

Shepherd Model

0.1 110

Equivalence Ratio

Figure 5-3. Detonation Cell Width vs. Equivalence

Ratio for Test Series #3,4. (H2-AirH2 0 at Pair=4 1 .

6 mole/rn3 , T=100*C).

5-5
The nonlinear nature of the chemical processes complicates a

direct comparison of the effectiveness Of CO2 and H2 0 directly

from the data taken in this report. The H2 0 data are at higher

initial temperature and pressure than the CO2 data. It was

expected that the effect of CO2 and H20 dilution on detonation

cell width would be similar because of similar heat capacities.

However, the chemical kinetics model used in this report indi-.

cates that CO2 and steam affect the hydrogen -oxidation reactions

chemically as well as thermally, and it predicted that steam

should be less effective than C02 as a diluent.

5.2 CONCLUSIONS

1. For H2 -air mixtures at 200C and a total pressure of 101 kPa,

detonations have been achieved between 13.5% and 70% H2 mole

fraction. This compositional range is wider than the detonability limits previously reported for smaller tubes.

2. The addition of CO2 to H2 -air mixtures greatly reduces the

detonability of the mixture.

3. For given initial temperature, air density and equivalence

ratio, the addition of steam to an H2 -air mixture greatly

decreases the detonability of the mixture.

4. At 100*C and an air density of 41.6 moles/meter 3 , detonation

of H2 -air mixtures with up to 30% steam have been recorded.

5. For H2 -air mixtures, the detonability increases with increasing initial temperature at constant density. Consequently,

the diluent effect of the addition of steam to a fixed volume

of a H2 -air mixture in reducing detonability is partially

offset if there is a concomitant temperature increase.

6. At 100*C and an air density of 41.6 moles/meter 3 , a 13.0%

H2 -air mixture has been detonated.

7. Within the measurement uncertainty, the detonation velocities

in the HDT agree with the velocities predicted by the

Chapman-Jouguet theory.

5.3 FUTURE WORK

The purpose of this work has been-to determine the detonability of H2 -air-diluent mixtures, particularly H2 -air-steam

mixtures for conditions of interest in nuclear reactor safety.

We have developed a data base that covers some of the range of

temperatures and pressures of interest. The current research has

focused on the need to validate theoretical models by identifying

specific effects such as temperature, density, H2 concentration

and diluent concentration. The tests have been conducted at

5-6
constant molar air density which is a valid condition assuming

globally uniform mixing. To evaluate the threat of localized

detonations due to transient mixing, tests will have to be

conducted at constant pressure. Hydrogen rich conditions will

exist locally around the source. Much of the testing to dat 'e has

been done for lean to stoichiometric conditions. Further work

will need to be conducted on the hydrogen rich side.

Isolating individual effects has contributed substantially

to code validation. Chemical kinetics modeling has shown promise

as a tool to interpolate and potentially extrapolate experimental

results. Given the broad range of possible initial thermodynamic

states and compositions that may develop as a result of an accident, particularly early in an accident prior to complete mixing,

this type of research should continue. Some testing is planned

to compare H2 0 and CO2 diluents directly.

The experimental technique to obtain detonation cell width

information has not improved significantly for more than a

decade. Measurement of detonation cell width still requires

experimental judgement in interpreting the pattern on the smoked

foil. Work is beginning that uses modern digital image processing to lessen human judgement in the measurement process.

The largest uncertainty in predicting whether a detonation

will occur is the deflagration-to-detonation transition (DDT)

problem. Detonation cell width has been related to the minimum

spherical charge (energy) required to detonate a mixture but has

not yet been solidly linked to turbulence parameters. Detonation

tube experiments such as those in the HDT can be used to identify

the detonation cell width but will not yield DDT criteria

directly.

5.4 REFERENCES FOR CHAPTER 5

1. Shapiro, Z. M. and Moffette, T. R., Hydrogen Flammability

Data and Application to PWR Loss-of-Coolant Accident, WAPDSC-545, Bettis Plant, September 1957.

2. Shepherd, J. E., "Chemical: Kinetics and Hydrogen-AirDiluent Detonations," AIAA Progress in Astronautics and

Aeronautics Series, Vol. 106, pp. 263-293, 1986.

3. Moen, 1. 0. , Murray, S. B. , Bjerketvedt, D. , Rinnan, -A. ,

Knystautas, R., Lee, J. H., "Diffraction of Detonation From

Tubes Into A Large Fuel-Air Explosive Cloud, " 19th Symp.

(Int'l.) on Combustion, The Combustion Institute,

Pittsburgh, PA, 1982, pp 635 - 645.

4. Bull, D. C., Elsworth, J. E., Shuff, P. J., "Detonation

Cell Structures in Fuel/Air Mixtures," Combustion and

Flame, V. 45, 1982, pp 7-22.

5-7

APPENDIX A

DETAILS OF THE EXPERIMENTAL APPARATUS

This appendix describes in detail the structural, electrical, and thermal aspects of the Heated Detonation Tube (HDT), the

explosive initiator circuit, and instrumentation.

A.1 STRUCTURE

The HDT can be divided into three structural segments, the

main tube, the s~econdary piping, and the tube and piping supports. Each will be described and the appropriate structural

limits identified.

A.1.1 The Main Tube

The main tube is composed of three pipes, one short thickwalled section used for initiation of the detonation followed by

two long sections for propagation. All are made of 304 stainless

steel and have a 45.7-cm (18-in) outer diameter. The short

initiator section is 0.91 m (3 ft) long with a 2.54-cm (1-in)

thick wall. The two long sections are 6.1 m (20 ft) long and

have a 1.27-cm (0.5-in) thick wall. The short thick initiator

section has one penetration for gas recirculation. The two long

sections each have 7 penetrations for transducers. The second

long section also has one penetration for gas recirculation.

Figure A-1 shows a cross-section of a gas recirculation penetration. Figure A-2 shows a cross-section of a transducer penetration. The gas recirculation penetrations are 90* clockwise from

the vertical and the transducer penetrations are 640 counterclockwise from the vertical as viewed from the initiation end.

The pipes are bolted together, and endplates are bolted to

the ends of the connected pipes, through flanges that have been

welded on the ends of each pipe. A cross-section of the flange

is shown in Figure A-3. The O.D. of the flange is 63.5 cm (25

in) and is 4.45 cm (1.75 in) thick. Sixteen 3.18 cm (1.25 in)

unthreaded bolt holes are on a 57.79 cm (22.75 in) bolt hole

circle. The bolts used are 2.86 cm (1.125 in) diameter, ASTM 325

hardened, UNC-7 thread, 12.7 cm (5 in) long with matching nuts

and 0.36 cm (9/64 in) thick by 5.08 cm (2 in) O.D.' washers.

.A gas seal between the pipes and pipe/endplate is provided

by an 0-ring. 0-ring grooves are cut into the face of the

flanges on the initiator section and the second long section.

The mating flanges and endplate faces have no grooves. The

0-ring grooves are 8.69 mm (0.342 in) wide at the base by 5.21 mm

(0.205 in) deep and 50.902 cm (20.04 in) in diameter. The 0-ring

material is high temperature grade ethylene-propylene, Parker #2-

468E692-75 rated at 260*C.

A-i
1.?S0NPT

FigureI Peetaion __.CosSct

eiclto

A- 2
2. >LD>

ý)x>c::<=, IP-'

I ~ ~ ± >-C

I.OOO

!0.010I

Figure A-2. Cross-Section of a Transducer Penetration.

A-3
or-. So4

~CDoDo.

11L)

~M~.AEiaieoi ~.T*~JL

Figure A-3. Cross-Section of a Pipe Flange.

A-4
The endplates are 3.18 cm (1.25 in) thick 304 stainless

steel disks 63.5 cm (25 in) diameter having the same bolt hole

pattern as the pipe flanges. The plate on the initiation end, has

a hole for a 2.54 cm (1 in) pipe thread for a detonation initiator cable feed-through. The plates have a 3.8 cm (1.5 in)

diameter, 1.27 cm (0.5 in) thick eyelets welded on the upper edge

for lifting purposes.

The long pipes have a theoretical yield pressure under

static loading of 11.5 MPa (1667 psi) and a burst pressure of

28.7 MPa (4167 psi). The initiation section has a yield pressure

of 23 MPa (3333 psi) and a burst pressure of 57.5 MPa (8333

psi). The yield and burst values for dynamic loading can conservatively be taken as 1/2 the static values. The endplates are

more limited in strength. Reference A-1 gives the following

formula for statically loaded flat heads under uniform pressure

rigidly bolted to the flange:

h =d C Ps (Eq. A-i)

FSd

where: h = plate thickness (in)

d = bolt hole circle (in)

C = 0.162

Ps= static pressure (psi)

Sd= Allowable stress with safety

factor.

Rearranging,

Ps= Sd [{h2 (Eq. A-2)

C _

The dynamic pressure can be considered to be twice the static

pressure, or

= Sd [ h ]2 (Eq. A-3)

2C Ld

where Pd is the dynamic pressure

The diameter, d, in equation A-3 is to the bolt hole circle.

However, for small deflections, the pressure does not extend to

the bolt hole circle but stops at the 0-ring groove. The

allowable stress can be taken as the static yield stress which is

A-5
290 MPa (42000 psi). The dynamic yield stress is approximately

1.4 times this value. Using the static value of 290 MPa gives a

safety factor of 1.4.

Pd(= 4200 1.5 506 psi = 3.4 MPa = 34 atm

H2 -Air detonations have pressure ratios between 10 and 15

times the initial pressure depending on the mixture. Therefore,

the maximum initial pressure is between 2.3 atm and 3.4 atm

absolute.

A.1.2 The Secondary Piping

A schematic of the secondary piping is shown in Figure A-4.

The piping provides for evacuation, injection and circulation of

the gaseous mixture. The secondary piping consists of a circulation pump, inline filter, and the appropriate tubing, fittings

and valves. The gas flow is from the outlet penetration on the

terminal (foil) end of the main tube, through a shutoff valve,,a

filter, a pump, past a high point vent and gas and steam injection ports, along the main tube to a shutoff valve on the inlet

penetration at the initiation end of the main tube. The main

shutoff valves are use to isolate the secondary piping prior to

initiating a detonation to protect the secondary side from the

detonation pressures. The valves are Swagelock SS-65F12 ball

valves.

The pump and gas injection/evacuation port and vents are

mounted on a wooden platform suspended from a main tube support.

Flexible tubing is used to connect these components to the rest

of the secondary piping which is attached to the main tube. The

flexible lines allow for motion between the secondary piping

attached to the main tube and the components attached to the

fixed main tube support.

The secondary tubing attached to the main tube 'is mounted

against the main tube wall and held in place with large diameter

steel hose clamps. It is mounted between heating tapes and the

main tube wall so that it is maintained at the main tube temperature. At the flanges on the main tube, flexible lines are used

instead of rigid piping to circumvent the flange in order to

minimize the number of sharp bends that create pressure losses.

All rigid piping throughout the secondary except the pump

manifold is 1.91 cm (0.75 in) diameter, 1.25 mm (0.049 in) wall

thickness, 304 stainless steel tubing. The flexible lines are

braided stainless steel with a teflon core. The pump has two

pumping chambers which are piped in parallel by inlet and exit

manifolds. The manifolds are made of 1.27 cm (0.5 in) diameter,

304 stainless steel, 0.89 mmn (0.035 in) wall thickness tubing.

A- 6
VACUUM

PUMP

POTWATER v

INLET AIR, H 2 &

CO 2

INJECTION

STEAM PORT

BOTTLE

; HEATERS

Figure A-4. Schematic of the Secondary Piping.
Swagelock tube fittings are used throughout except the first

reducing bushing at the main tube penetrations.

The pump is a Metal Bellows Corp. sealed bellows pump Model

MB-602-XP. It is rated at 2.83 std. L/s (6 scfm) with no back

pressure. The inline filter protects the pump from particle

debris resulting from the explosive initiator products. The

filter is a Balston type 62A-3/4 case with a type 150-19-CQ

filter cartridge made of borosilicate and removes 8 psm particles.

This material does not absorb moisture. The filter is positioned

immediately downstream of the main shutoff valve on the outlet

gas recirculation port of the tube.

Downstream of the filter and pump is the high point vent

tee. Venting can occur through two paths. One is through a

manual valve used to release gases after a test which has a

temperature rating of 2050C (400*F). The other path has a pop-off

type relief valve set at 345 kPa (50 psig). Both pipes are 1.27

cm (0.5 in) diameter tubing and vent approximately 3 m (10 ft)

above the ground. Downstream of the tee leading to the high

point vents are the gas injection port tee and steam injection!

evacuation tee respectively.

The gas injection port has a ball valve for flow control and

0.64 cm (0.25 in) Swagelock double shutoff quick disconnect stem

to accommodate the transfer line from the gas supply bottles.

The gas transfer line is a 0.64 cm (0.25 in) flexible hose with a

teflon inner liner. The gas supply bottles are standard, nominal

5.67 m3 (200 ft3 ), pressurized cylinders with appropriate two

stage regulators with secondary side pressures of 690-1380 kPa

(100-200 psi). The regulator outlets are connected to a needle

valve for flow regulation and a Swagelock 0.64 cm (0.25 in) quick

disconnect body to accommodate the transfer line.

The steam bottle is a 1-liter gas sample cylinder that has a

500 W flexible rod heater wrapped around the bottom of the

vessel. The heater and cylinder were immersed in a molten lead

bath that was allowed to harden in a larger cylinder. The 1

liter vessel sets under a 1.91 cm (0.75 in) diameter vertical

pipe with two tees. The vertical pipe has a pipe plug which is

removed to introduce a premeasured amount of water into the steam

vessel. One tee leads to a BS & B 2.54 cm (1 in) diameter UA-2

burst disk holder with a 2.4 MPa (350 psi) vacuum supported burst

disk. For early tests, 345 kPa (50 psi) disks were used. The

other tee connects the steam bottle with the secondary piping

through a ball type shut off valve. (Note: this type of valve

does not provide enough flow control and will be replaced in

future testing.)

The evacuation line tees into the line running from the

steam bottle to the secondary piping. The evacuation line also

contains a ball-type shutoff valve and a special 0-ring type

fitting to connect the vacuum pump line. The vacuum pump is a

A-8
Leybold-Heraeus model E-150. It is designed to handle some

condensed liquids but is being used beyond its liquid handling

capacity to handle the water generated from the H2 -Air detonations. The oil is changed frequently to maintain the vacuum

pump.

The primary pressure restriction on the secondary system is

the circulation pump. The pump has a design pressure of 276 kPa

(40 psig). The remainder of the system can take detonation level

overpressures with the possible exception of the filter casing.

The filter casing has a working pressure of 1.7 MPa (250 psi).

The 1.91 cm (0.75 in) secondary tubing has a static yield of 27

MPa (3900 psi), the flexible lines have a static yield of 6.7 MPa

(975 psi), the 1.27 cm (0.5 in) tubes on the pump manifold have a

static yield of 29 MPa (4200 psi). The fittings used, both brass

and stainless, have similar or higher yield pressures than the

tubing. It was found that the pump would not restart once it had

stopped if the pressure in the system was above 136 kPa (20

psia).

The popoff relief valve on the high point vent was installed

to protect the pump from accidental overpressure. In the case of

an accidental detonation, the pump bellows will be destroyed

before the pressure can be vented to a safe level. To protect

personnel from shrapnel, a 6.3 mmn (0.25 in) thick box was placed

over the pump bellows.

A.1.3 The Structural Supports

The detonation tube is held in place by W"V block type

supports mounted on 55 gallon drums that have a concrete base as

shown in Figure A-5. The V blocks are made of 10. 2 cm (4 in)

structural steel channel with a 10.2 cm (4 in) square crosssectional wood block setting in the channel. The wood provides

an insulating surface for the heated detonation tube to set on.

The channels that form the V are hinged and can be adjusted by a

hinged 3.79 cm (1.25 in) diameter threaded rod assembly shown in

Figure A-6. Adjusting the length of the threaded rod provides

alignment for adjustment of the detonation tube. The threaded

rod assembly and V blocks are hinged to a horizontal 15.3 cm (6

in) structural steel channel. The hinges are made by 1.27 cm

(0.5 in) diameter steel dowels inserted through holes in the

mating pieces and held in place by cotter pin restrained washers.

The V-block assembly is mounted on the top of the 55 gallon

drums which are filled with concrete and are bolted to two 3.79

cm (1.25 in) diameter threaded rods that are embedded deep into

the concrete. The base of the 55 gallon drums are set in a

1.22 m (4 ft) square by 15.3 cm (6 in) deep concrete pad. Four

holes were cut in the sides of the 55 gallon drums approximately

7.6 cm from the bottom at 9Q* angles and two 3.79 cm (1.25 in)

threaded rod was inserted through the barrel. The threaded rod

and "Chicken wire" served as rebar for the concrete pad and to

A-9
Detonation Tube

Wood

Insuiati

4 "Channel

on6 "Channel

55 Gal. Barrel

b* Lifting Bar

IA

.A A

Figure A-5. Detonation Tube Supports.

A-10
I 4" STRUCTURAL

;;ý CHANNEL

MAIN TUBE

11/4" THREADED ROD

6" STRUCTURAL

CHANNEL

55 GALLON DRUM

FILLED WITH

CONCRETE

Figure A-6. Tube Support V-Block Positioning Devi~ce.

A-11
hold the pad to the 55 gallon drums. The square pads are oriented so the maximum force required to tip the supports is

parallel and perpendicular to the axis of the detonation tube.

Five supports are used to hold the detonation tube, two each

per long section of pipe and one on the short section. Since

there are five supports, the load distribution is statically

indeterminate. Assuming that the load is spread evenly to the

supports, the weight of the tube on each support is 500 kg (1100

lb). Static analysis shows that it requires a 5.69 kN (1280 lb)

force at a height corresponding to the elevation of the detonation tube (1.4 m - 56 in) to tip the 500 kg (1100 lb) weight of

the tube per support and 545 kg (1200 lb) weight of the support,

either parallel or perpendicular to the axis of the tube.

The largest tipping moment parallel to the detonation tube

axis is provided by the detonation of gases in the tube. The

coefficient of friction between the wood and detonation tube can

conservatively be estimated as 0.6. For the 500 kg (1100 lb)

tube weight per support, the tipping force is 2.94 kN (660 lb)

giving a safety factor of 1.9 for tipping parallel to the tube.

Perpendicular to the axis of the tube, the maximum tipping

moment will come from wind or blast loading. A maximum wind

speed can be estimated to be no more than 129 km/hr (80 mph)

which yields a force of 1.1 kN (250 lb). Blast loading can occur

due to the other experiments conducted at the 9920 Firing Site.

In particular, the detonation tube is located parallel to the

FLAME facility. Blast loading has high pressures but the total

impulse is low because of the short duration. The detonation

tube has suffered no noticeable effects from several detonations

in the FLAME facility.

Structurally the weakest member of the tube support is the

1.27 cm (0.5 in) diameter pin hinge between the 3.18 cm (1.25 in)

threaded rod and the 10.2 cm (4 in) V structural channel. The

safety factor due to the tube weight alone is 5. The pin hinge

between the base of the threaded rod and the 15.3 cm (6 in) horizontal channel was sleeved to reduce the bending moment and has a

higher safety factor. Sleeving the other pin hinge will improve

its safety factor as well.

The pump and gas injection/evacuation manifold is supported

from a platform from the 55 gallon drum nearest the foil end of

the detonation tube. The platform is a 1.9 cm (0.75 in) thick

plywood platform 0.76 m (2.5 ft) by 1.5 m (5 ft) mounted 'on a

wooden 5 cm by 10 cm (2 by 4 in) frame supported by a welded

metal frame attached to the 55 gallon drum. The steam bottle is

separately supported by insulating bricks stacked on the ground.

The gas bottles are on a pallet tied to a rack in which the

static pressure gage and gas temperature reference are mounted.

A- 12
The pallet is weighted by sand bags to prevent it from tipping

over.

A.2 ELECTRICAL

The electrical system can be divided into two parts. The

first is general power to supply the pumps, manually controlled

heaters and instrumentation. The second is the computer controlled heating system.

A.2.1 General Power

Power to supply the heated detonation tube originates from a

2.5 kV, 400 kW, 3 phase trunk line passing through the 9920

Firing Site. A transformer on the east side of building 9920

reduces the voltage to 220 V before the line passes through a

fuse box with 100 amp fuses on each phase. A 100 amp, 220 V, 3

phase line is buried underground along the south side of 9920 to

the termination building at the detonation tube. The line terminates in a breaker box and is split into one 220 V line to

interior and exterior outlets, and into several 110 V single

phase lines. The 110 V power supplies an exterior double duplex

box and two interior double duplex boxes in the termination

building. All three phases also go to the power relay box

described in the next section to heat the detonation tube, and to

three additional relay controlled exterior double duplex outlets.

Power is supplied to the circulation pump, a Digitec temperature reference and a variac controlling a secondary line

heater by an extension cord from an external outlet on the termination building. The pump is rated at 372 W (1/2 HP) . The

secondary line heater is rated at 400 W. The temperature reference draws little power.

A.2.2 Detonation Tube Heating System

The detonation tube heating system is composed of 17 indivi-_

dually controlled sections of resistance heaters and control/

measurement thermocouples mounted on the surface of the detonation tube, secondary piping and steam bottle. With the exception

of the heater on the steam bottle, all heaters are resistance

wires embedded in a silicon rubber strip and have a power density

of 0.775 W/cm2 (5 W/in2 ) made by Watlow. Sixteen of these sections are under computer control. Each section contains several

heaters of various sizes wired in both series and parallel to

achieve the desired power level. The heaters are mounted by

either 1.6 mm (1/16 in) diameter fiberglass cord or Dow Corning

736 RTV silicone rubber adhesive.

Each section also has three Chromel-Alumel, K-type, thermocouples to measure the anticipated hottest, coldest and an intermediate temperature in each section. The anticipated hottest

A- 13
temperature is underneath a heater tape, the coldest temperature

is midway between heater tapes, and the intermediate temperature

is measured midway between the hot and cold thermocouples. The

hot thermocouple is used to control the heating process, 'while

the other two measure the nonuniformity in temperature.

The thermocouples are made from 0.25 mm (10 mil) kapton

coated wire. The beads have been pressed to form a disk for

better contact with the pipe. The thermocouples are mounted by

using kapton tape. one layer is placed against the pipe to

provide an electrical isolation barrier. The flattened bead is

pressed against this layer of tape by a second layer of tape

placed over the bead. The wires are held in place by Dow Corning

736 RTV (silicone adhesive) to prevent the bead from being accidentally pulled loose.

The sixteen individual computer-controlled heater sections

can be divided int 'o five different configurations. Each of these

configurations, a manually controlled heater section, and the

computer control system are described below.

Long pipe sections, sides and bottom - of the sixteen

individually controlled sections, eight are configured to heat

the sides and bottom of the two long sections of pipe. Figure

A-7 shows the electrical schematic of this configuration. Each

section is 1.49 m (58.75 in) long, 1/4 of the length of one long

section of pipe, and covers an arc of 255* around the underside

of the pipe. The heaters are 5.1 cm wide by 1 m long (2 in by 40

in) and are wrapped circumferentially around the underside of the

pipe with the 1 m (40 in) length covering the 255*. Axially, the

heaters are spaced 24.9 cm (9.8 in) center to center or 19.8 cm

(7.8 in) between tapes. The heater tapes are laced tightly to

the pipe by fiberglass cord tied to eyelets in the silicone

rubber at each end of the heater. Each heater is rated at 400 W

@ 110 V and the overall power for the six heater tapes in each

section is 600 W.

Three thermocouples are mounted in each section. One

thermocouple is mounted underneath a heater tape. The second is

mounted axially midway between the heaters, 9.9 cm (3.9 in) from

the edge of a heater. The third is axially midway between the

second thermocouple and the heater edge.

Long pipe section, top - Two individually controlled heater

sections are used to heat the top of the two long sections of

pipe, one heater section for each pipe section. The individual

heater tapes are 15.2 cm wide by 1 m long (6 by 40 in) and six

are laid end to end to form a 15.2 cm (6 in) wide row covering

the top of each section of pipe. They are held in place by the

fiberglass cords used to tie the ends of bottom and side heaters

together. Each section is intended to heat the top 105* of

circumference (41.9 cm or 16.5 in) not heated by the tapes which

cover the underside of the pipes. Each heater tape is rated at

A- 14
M-0 R40 - 2 2 R0 R4 0 -2 =40" LONG

BY

2" WIDE,

400 WATT HEATER

10-2 1R 4 0 -2 R4-

Figure A-7. Heater section Schematic - Long

Pipe Section, Sides and Bottom.

A- 15
1200 W @ 110 V. Figure A-8 shows the wiring schematic. The

overall power of the six heater tapes in each section is 800 W.

Three thermocouples are mounted in each section. one is

mounted underneath the row of 15.2 cm (6 in) wide heater tapes

covering the top of the pipes. The second is mounted half way

between this row of heaters and a heater strip mounted circumferentially around the pipe to heat the sides and bottom of the

long pipes (See previous section). The third thermocouple is

spaced equidistant from the top row of heaters and two of the

circumferentially spaced heaters, nominally 10 cm (4 in) from

each.

Pipe to pipe flanges - Two individually controlled heater

sections are used to heat the pipe to pipe flanges, one for each

flange. The heaters used are 5.1 cm by 1 m (1 in by 40 in) and

two are laid end to end and wrapped completely around the 2 m

flange circumference for each 4.5 cm wide flange. They are held

in place with RTV adhesive. Figure A-9 shows the wiring

schematic. The four individual heaters are 400 W @ 110 V and the

total power is 400 W per section.

Three thermocouples are mounted in each section. one is

mounted underneath the row of heaters on the edge of the flange.

The second thermocouple is mounted halfway down the side of the

4.5 cm wide section of the flange approximately 3.8 cm (1.5 in)

from the heaters. It is mounted circumferentially at a nominal

17 cm (6.7 in) from the edge of the top heaters. The third

thermocouple is mounted on the thick circumferential weld used to

mount the flange. It is approximately 7.6 cm (3 in) from the

f lange heaters. For the f lange between the long pipes, it is

nominally 7.6 cm (3 in) from the top heaters. For the f lange

between the long and short pipe, it is nominally 13 cm (5 in)

from the top heaters.

Short pipe section - one individually controlled heater

section is used to heat the short initiator section of piping.

Four 15.2 cm wide by 1 m long (6 in by 40 in) heater strips are

mounted spirally along the 0.91 m length of the short section of

pipe. The heaters are held in place with fiberglass cord and the

maximum spacing between the heaters is 0. 3 m (12 in) at the top

center. Figure A-10 shows the wiring schematic. The heaters are

1200 W @ 110 V and the total power for the section is 1200 W.

Three thermocouples are mounted in the section. The thermocouples are mounted axially in a place where there is nominally

20 cm (8 in) between heaters. One thermocouple is mounted under

a heater, the second is mounted 10. 2 cm (4 in) f rom the heater

edge, and the third is midway 5. 1 cm (2 in) between the heater

edge and the second thermocouple.

Endplates, flanges - Two individually controlled heater

sections are used to heat the endplates and flanges, one for each

A-16
R40- R-4-6 R0-6= 40"1 LONG

BY

6" WIDE,

1.2 kw HEATER

Figure A-8. Heater section Schematic - Long

Pipe Section, Top.

A- 17
R02= 40" LONG

BY

2" WIDE,

400 WATT HEATER

FigureA-9. Heater Section.Schematic - Pipe

to Pipe Flanges.

A-18
R40-6R40-6R40-6= 40'" LONG

BY

6" WIDE,

1.2kw HEATER

R40-6 

R4 0-6I

Figure A-10. Heater section Schematic - Short Pipe.

A-19
end of the detonation tube. The initiation end plate has a

single 5.1 cm wide by 1 m long (2 in by 40 in) heater mounted in

the f orm of a V with RTV adhesive. The other endplate has two

shorter heaters placed vertically 20.3 cm between centers. The

heaters are 5.1 cm wide by 0.5 m long (2 in by 20 in). The

flanges on each end are covered by four 2.54 cm wide by 1 m long

(1 in by 40 in) heaters. The arrangement is the same as the pipe

to pipe flanges, i.e., two heaters each laid end to end around

the circumference of the pipe flange and endplate. All heaters

are held in place with RTV adhesive. Figure A-11 shows the

wiring schematic. The 1 m long heaters are 400 W @ 110 V and the

0.5 m heaters are 200 W @ 110 V. The total power f or each

section is 600 W.

Three thermocouples are mounted in each section. For the

ignition endplate, the first thermocouple is mounted on the face

of the endplate under the V heater. The second thermocouple is

mounted on the face of the endplate near the base of the V shaped

heater, 1.27 cm (0.5 in) from the bottom rim of the endplate The

third thermocouple is mounted on the face of the endplate at the

top of the V heater, 11.4 cm (4.5 in) equidistant from each leg

of the V and the top rim of the endplate. For the other end.-

plate, the first thermocouple is mounted on the face of the

endplate in the middle of one of the short vertically mounted

heaters. The second thermocouple is mounted on the face of the

endplate 7.6 cm (3 in) from either heater strip and 1.9 cm (0.75

in) from the bottom rim of the end plate. The third thermocouple

is mounted on the face of the endplate between one heater and the

plate rim, 9.5 cm (3.25 in) from the rim and 8.3 cm (3.75 in)

from the heater.

Steam Bottle - One individually controlled heater section is

used to control the temperature of the steam bottle. One 500 W

rod type heater embedded in lead and spirally wound around the

bottom of the steam bottle is used to heat the vessel. The

windings are tight leaving no space between them. The heater

covers the base and approximately 2.5 cm (1 in) of the side of

the vessel. The heater and vessel are completely immersed in

approximately 23 kg (50 lb) of lead.

Three thermocouples are mounted in this section. Two

thermocouples are in 3.2 mm (0.125 in) stainless steel sheaths

with 0.5 mm (20 mil) ungrounded tips. The first is embedded in

the lead so that the tip is touching the lead side surface of the

edge of the heater coil. The second thermocouple is mounted

through the plug on the top of the pipe leading to the steam

bottle. The tip of the thermocouple is suspended in the piping

approximately 2.5 cm (1 in) from the top of the vessel to measure

gas temperature. The third thermocouple is made from 0.25 mm (10

mil) kapton coated wire and is mounted just below the upper surface of the lead bath surrounding the steam bottle approximately

2.5 cm (1 in) from the surface of the steam bottle.

A- 20
R4 0 - 2 =40" LONG BY 2" WIDE R20 -.2 = 20" LONG BY 2" WIDE

400 WATT HEATER 200 WATT HEATER

R4 0 -1=40" LONG BY 1" WIDE

200 WATT HEATER

INITIATION END TERMINATION END

Figure A-11. Heater Section Schematic -

Endplates, Flanges

A-2 1
Secondary piping - one heater is used to heat the secondary

piping between the steam bottle and the vertical flexible line

leading f rom the manif olding on the pump table to the piping

along the surface of the tube (see structural discussion). This

heater is not computer controlled and was added to prevent

condensation from occurring in the secondary piping. The heater

is a 5.1 cm wide by 1 m long (2 in by 40 in) 400 W @ 110 V strip

heater that is wrapped around the 1.9 cm diameter secondary

piping. The heater is controlled by a variac mounted on the pump

table.

one thermocouple is used in this section. It is a K-type,

0.5 mm (20 mil) ungrounded tip in a 3.2 mm (0.125 in) stainless

steel sheath. It is mounted in a plug in a tee with the tip

centered in the lowest elevation of the 1.9 cm diameter secondary

piping.

Heating System Control - The heating system is controlled by

on-off set-point-logic relays which supply power to the heater

strips.. Control feedback is maintained by monitoring the temperature of the thermocouple -underneath a heater strip in each

section and comparing it to the desired set-point temperature.

The thermal inertia of the system is high enough that on-off

control is sufficiently stable to maintain the detonation tube

temperature.

A schematic of the control circuit is shown in Figure A-12.

The control decisions are made by a BASIC program running in the

Digital LSI-11/23 computer. The program is designed to run in two

modes, continuous operation and delayed start. In the continuous

mode, the program acquires temperature data from a temperature

monitor and compares these values to user assigned set-point

temperatures. If the measured temperature is below the set

point, the computer sends a signal for a relay to close. If the

measured temperature is above the set point, then the computer

sends a signal for the relay to open.

The relay unit is a Kinetic Systems Model 3074-AlA, 24 bit

isolated output register with reed relays and is a module in a

CAMAC crate. The communications interface between the module and

the computer is a LeCroy 8901 GPIB Crate Controller communicating

with a Tektronix CP4100/IEEE 488 board on the back-plane of the

LSI-11/23. The 10 volt-amp reed relays are not sufficient to

switch the power needed to heat the detonation tube. They are

used to switch 28 Vdc power to close solid-state power relays

which are used to switch power to the detonation tube heaters.

The 28 Vdc power supply is a Harrison Labs Model 6266A located in

the control building, 9920.

The relays which control the power to the detonation tube

heaters are Teledyne Model 615-5 solid state, optically isolated,

relays rated at 40 amps @ 110 V. The relays are normally open

and can be closed with 3 to 32 Vdc input. These relays are

A-22
Figure A-12. Heater Control Circuit Schematic.
controlled by the 28 Vdc signal coming from the Kinetics relay

module and are located in the termination building near the

heated detonation tube. The cable between the Kinetics relays

and the power relays is a 9-pair cable and is located in the

south trench (see reference A-2 for layout of instrumentation

cabling trenches).

Sixteen relays are used to control the sixteen individual

sections of the detonation tube described in the last section.

The source of the 110 V power to heat the detonation tube was

described in the general power subsection. Sixteen cables run

from the power relays in the termination building in an underground cable trench which surfaces at the base of the foil end

tube support. The cables are #12 So three wire cables with

standard neoprene insulation. These cables are run along the the

length of the detonation tube and are tied to a horizontal

unistrut that runs the length of the tube to provide mechanical

isolation to prevent a cable from being pulled loose. The ground

wires on all sixteen leads are tied to the horizontal unistrut

which is in turn electrically connected to the detonation, tube to

provide a grounding path in case of an electrical short against

the tube wall.

The insulation of these cables is not sufficient to take the

temperature of the detonation tube. These cables are spliced to

#16 teflon-coated wire just outside of the insulation on the

tube. This teflon-coated wire is spliced to the pig tail leads

on the heater strips. The splices used are a plastic-coated

crimp-type splice with a temperature rating of 105*C. These

splices have been coated with Dow Corning 736 RTV for mechanical

isolation and increased temperature resistance.

The feedback mechanism to control the heaters is the comparison of the heater temperature as measured by the thermocouple

under a heater strip in a given section to the user supplied setpoint temperature in the computer program. The thermocouples -and

mounting were described in the heating system section. The

thermocouple wiring runs along the base of the detonation tube

between the tube wall and the surrounding insulation. The

insulation of the thermocouple wire is rated at 2300C. The

wiring terminates at a Nema 4 type enclosure mounted midway down

the length of the detonation tube on vertical unistruts.

Two twenty-four pair K-type thermocouple extension cables

connect to the 16 control and 32 measurement thermocouple wires.

These 24 pair cables terminate in a patch panel in the termination building. From the termination building two 24 pair K-type

run underground to the control room in building 9920 (See Reference A-2 for details). one of the two 24 pair cables carrying

the 16 control temperatures is split off and terminated in a

temperature monitored Kinetics Model 1991 isothermal panel.

Copper-copper wire is used to connect this reference junction to

a Kinetics Systems 16 Channel Temperature Monitor Model 3525-AIK

A- 24
mounted in a CAMAC crate. This module converts the voltage data

from the thermocouples to temperature.

The LSI-11 computer interrogates this module to compare the

measured temperature and the set point temperature f or each

section. Based on the comparison, the computer commands the

Kinetics relay module to open or close the power relays which

control the power to the detonation tube heaters. This cycle

occurs approximately once every 20 seconds. For convenience, the

program displays the measured and set-point temperatures and the

time each cycle. The time is obtained from a Borer Model 1413

Clock which is mounted in the CAMAC crate.

The second mode in which the computer program operates is

the delayed start mode. In this mode the user enters a time at

which the heating process is to begin. The computer compares the

time f rom -the Borer clock to the set point. When the set-point

time is reached the program switches to back to the first mode.

To provide a fail safe condition, a Standard Engineering

Corp. WDT 1000 "Watch Dog Timer" is used to monitor the heating

system. The watch dog timer controls the 28 V dc line betw~en

the power supply and the Kinetics reed relay module and is

mounted in a CAMAC crate. The watch dog timer is a timercontrolled relay device which is normally open, preventing power

to be switched by the Kinetics module to the control lines

leading to the power relays. The watch dog relay will close only

if it is communicated with by the computer every 64 seconds.

In normal operation the computer communicates with the watch

dog timer every cycle and the relay remains closed allowing the

detonation tube to heat. If a power failure occurs, the computer

program will not restart and the watch dog timer will open the

circuit to the power relays in 64 seconds. The thermal inertia

in the detonation tube will prevent failure due to uncontrolled

heating for this short period of time. The watch dog timer is

connected to two alarm buzzers which are activated if the watch

dog timer relay becomes open. The buzzers are located in buildings 9920 and 9926.

A.3 THERMAL ASPECTS

Several options were considered in the design of the heating

system for the detonation tube. one design was a shell within a

shell using hot water under pressure in the annulus between the

coaxial tubes. This design was rejected because of the difficulty in instrumenting the tube with pressure transducers through

the coaxial tube. Another design was to heat the tube by induction. This design was rejected because the impedance of the

thick wall detonation tube is to low. The internal impedance of

the generator would have to have been very low requiring massive

coils.

A- 25
The heating system chosen is based on using strip heaters

under insulation. Analysis indicated that the temperature nonuniformity present in this type of heating would be acceptable if

the insulation was sufficient. The heating system was described

in the last section. A description of the insulation, temperature monitoring thermocouples, and thermal limits are discussed

in this section. The analysis which led to the design is contained in Appendix F.

A.3.1 Insulation

The insulation used to cover the detonation tube and secondary piping is Certainteed Snap-Wrap which has a thermal conductivity of 0.048 W/m 0 K (R - value of 3 (hr ft2 *F)/(BTU in)). The

insulation was purchased in two thicknesses, 5.1 cm and 3.8 cm (2

in and 1.5 in) in 91.4 cm (36 in) wide rolls for use on the

detonation tube. Pre-formed 2.5 cm (1 in) thick cylindrical

sections of insulation are used on the secondary piping.

Two layers of insulation is used to wrap around the detonation tube pipes, one layer of 5.1 cm (2 in) and one layer of 3.8

cm (1.5 in) thick insulation. The layers are offset axially so

that the seams do not overlap on the long pipes where 6 sections

are used which cover 5.5 m of the 6.1 m length. With the two

layers of insulation, the outer diameter of the insulation is the

same as the pipe flanges. Two layers of insulation are placed

over the flanges between the pipes so that the flange insulation

overlaps the insulation over the pipe body.

The endplates are covered by large endcaps. The endcaps are

made to slip over the flanges and are intended to be easily

removable, as they must be removed after each test. The endcaps

are fabricated out of a 20 gage galvanized shell, 94 cm (37 in)

in outer diameter by 45.7 cm (18 in) deep lined with 15.2 cm (6

in) of insulation in the base and sides. It was found with use

that the endcaps are heavy enough to "sag" and the gas seal

gained by having the endcap-slide over the insulation on the pipe

body is compromised. Ambient, cold air could circulate around

the gap in insulation and cool the endplate. This effect was

enhanced by the need to cut a hole in the insulation in the

endcap to slide over the lifting lug on the endplate.

Several attempts were made to eliminate this leakage problem; none were entirely satisfactory. Better results were

obtained by replacing the endcaps with loose fiberglass

insulation placed over the endplates and tightly sealed with

plastic. Future tests will have a different endcap design.

A.3.2 Temperature Monitoring Thermocouples

Three thermocouples are located in each temperature controlled heating section of the HDT. One thermocouple is used to

control the heaters and the other two measure the nonuniformity

A-26
in temperature. The thermocouples, mounting and cabling to the

control room in building 9920 are described in the Electrical

section, A.2.2.

The reference junction for the 32 measurement thermocouples

is a Sandia Laboratory design constant temperature block. The

temperature of the block is measured and the voltage measurements

are compensated for the reference junction temperature. The

temperatures are recorded on fan folded paper tape from a Vidar

AutoData Eight datalogger.

A.3.3 Thermal Limits

Table A-1 lists the temperature limits of various components

of the heated detonation tube.

Table A-1

Temperature Limits of Detonation

Tube Components

Component

304 Stainless Steel

0-rilngs (#2-468E-692-70)

Dow Corning Compound 4 0-ring grease

ASTM 325 hardened bolts

Swagelock Swack pipe joint compound

Gordon Thermocouple Feed-Thru's (TFE Gland)

Dow Corning 736 RTV (RED)

Delrin transducer fittings

Nylon transducer fittings

Transducer 0-rings (#2-019E692-75)

Pressure Transducer (electronics)

High purity Goop 0-ring grease

Silicone Rubber Heaters

Fiberglass Heater Cord

Teflon Heater Wire Insulation

E L506 Explosive (DTA)

RP-2 Initiator

Brass Secondary pipe fittings

Circulation Pump

Insulation

Burst Disk

Valves (Teflon packing)

Temperature

650*

260

204

400*

180

230

260

82**

82 -93 ** *

260

135

204

260

250

230

93

121

>200 *

<230*

230

230

* 15% loss of strength

** Melting point is 175*C

Melting point is 250*C ~ TFE seal temperature - motor will probably overheat

before this temperature ~ Continuous loss of strength with temperature

A-27
A.4 EXPLOSIVE INITIATOR CIRCUIT

The most convenient method of initiating a gaseous detonation is to use high explosive. The disadvantage of this method

is that the gaseous detonation will be overdriven for some

distance due to the very high pressures associated with high

explosives. To overcome this disadvantage, we used a thin (1 mm

thick) sheet of DuPont Detasheet high explosive cut into a 25.4

cm (10 in) diameter spoked-wheel shape to both minimize the

amount of high explosive and to effect an almost planar initiation. The explosive is initiated by a detonator at the hub of

the spoked wheel as shown in Figure A-13, where the detonation

proceeds radially outward at about 7.2mm/,ssec. The gaseous

detonation proceeds at about 2mm/psec so the high explosive

initiation is quasi-planar.

To mount the explosive perpendicular to the detonation tube

axis, the sheet explosive is attached to a thin mylar sheet which

is suspended from lugs at four points using nylon braid. The

lugs are welded inside a 35.6 cm (14 in) diameter stainless steel

pipe which is 40.6 cm (16 in) long. This inner pipe has four

spacers which provide coaxial placement of the pipe within the

detonation tube. The purpose of this inner pipe is to prevent

detonator shrapnel from impinging on the inner wall of the

detonation tube and to prevent very high pressure loading of the

detonation tube. The explosive charge is located approximately

30 cm (12 in) forward of the endplate to minimize shock loading

on the endplate.

The nominal explosive weight is 40 grams for all gaseous

mixtures except the very insensitive mixtures. The less sensitive mixtures require a high explosive charge which more fully

covers the 25.4 cm (10 in) diameter. The explosive charge weight

is nominally 80 grams for these mixtures.

The detonator used to initiate the high explosive is a

Reynolds Industries exploding bridgewire (EBW) type RP-2.

Transition to the DuPont EL506C1 Detasheet explosive is by means

of a few grams of plastic explosive type Composition C-4. This

transition charge is held in place with a fabric tape which is

stapled to the sheet explosive using a specially modified paper

stapler. Electric wires to the detonator are teflon insulated

twisted pair. These wires are crimp connected to wires passing

through an insulated feed-thru in the endplate. 'The connection

is covered with teflon tubing.

High voltage, low impedance type 'C" coaxial cable is connected to the feed-thru connector outside the insulated endplate.

To initiate the high explosive detonation, the EBW is subject to

the discharge of a 3 ytfd capacitor charged to 4-5 kilovolts which

is located in the control room in Bldg. 9920.

A-28
Figure A-13. High Explosive Initiator.
A. 5 INSTRUMENTATION

Four types of instrumentation are used on the detonation

tube. The initial thermodynamic state is established by static

pressure and temperature measurements. Detonation properties are

obtained by smoke foil measurement of detonation cell width.

Pressure measurements are used to obtain time-of-arrival to

establish the detonation velocity. There are 14 access ports in

the detonation tube for instrumentation. Table A-2 lists the

axial location of these ports with respect to the initiation

endplate. Circumferentially, the ports are all located 640 from

the top of the detonation tube.

Table A-2

Axial Location of Instrumentation Ports

Relative to the Initiation Endplate

Inside Face

Port # Distance (in) Port # Distance (mn)

1 1.039 8 7.201

2 1.689 9 7.810

3 2.603 10 8.725

4 3.823 11 9.944

5 4.737 12 10.853

6 5.956 13 12.078

7 6.871 14 12.992

A.5.1 Static Pressure Instrumentation

The static pressure measurement is taken from port 12. A

high pressure 15.2 MPa (2200 psi) black rubber hose with a plug

valve connects this port to a pressure gage or manifold on an

instrumentation rack. Tables A-3, 4 list the static pressure

gages for each test. For tests H-T-1l to 30 a Wallace & Tiernan,

Model 61A-10-0800, Serial #SS-14109, 0 - 800 mm Hg, absolute

pressure gage was used to measure the pressure. This gage has a

1 mm Hg resolution and an accuracy of 0.8 rmm Hg. For tests 31,32

and 33, this gage was used to establish ambient pressure and a 0-

100 psig, Heise pressure gage, Serial #47971, was used for gage

pressure. The Heise gage has a 0.1 psig resolution and an accuracy of 0.1 psig. From test 34 - 96, a Wallace & Tiernan, Model

61A-1A-0050, Serial #TT11757, 0 - 50 psia, absolute pressure gage

was used to measure the pressure. This gage has a resolution of

0.05 psia and an accuracy of 0.1 psia for measurements above 4

psia. Prior to initiation of the detonation, port 12 is isolated

from the pressure gage by the plug valve to prevent over-ranging

of the gages.

A-30
A.5.2 Temperature Instrumentation

For tests HT-11 to 19 and 73, the gas temperature was taken

to be the average of the tube temperature as measured by the

thermocouples described in the previous section. Tables A-3, 4

list the type and location of the gas temperature measurement for

each test. From test 20 to 96 (excluding 73), the temperature

was measured by a thermocouple inserted in port 6. The thermocouple is a Chromel-Alumel, K-type, in a 3.2 mm (0.125 in) stainless steel sheath made with 0.51 mm (20 mul) wire. The thermocouple is inserted through a Gorden Th-2571-T-125 feedthrough

that is mounted in a "blank" transducer fitting (see dynamic

pressure instrumentation for fitting description).

For tests 20 to 72 the thermocouple tip was inserted approximately 3.2 mm (0.125 in) into the gas mixture. For tests 74 to

96, the thermocouple tip was inserted approximately 2.5 cm (1 in)

into the gas mixture. When the thermocouple was removed after

test 96 it was noted that the detonations had bent the thermocouple to a 450 angle.

For test 20 to 81 excluding 79, the temperature reference

junction was a hand held Fluke DMM Model 8024B, Serial #3275848,

with a temperature readout for K-type thermocouples. The resolution of the unit is 1*C with an accuracy of 3*C. For tests 79,

81 to 96, the reference junction was a Digitec Model 2831, Serial

#53930983, self-calibrating thermocouple reference junction with

digital temperature readout. The resolution of the Digitec is

0.10 C with an accuracy of 0.30C.

A.5.3 Smoked Foil Instrumentation

During the first ten shakedown tests of the HDT (HT-l to

10), the smoke foil size and shape were determined. Early foils

were 1.2 m (4 ft) wide and 1.2 m (4 ft) long made of ~-1 mm aluminum sheet. The sheet was machine rolled into a 43.2 cm (17 in)

diameter cylinder for insertion into the HDT. With this thickness of sheet, the post-test foils were permanently set by the

detonation into the cylindrical shape and were hard to handle.

For tests HT-1l through HT-96, the smoked foils were made of

aluminum sheets 1.2 m (4 ft) wide by 3.7 m (12 ft) long and

ranged between 0.4 mm (0.016 in) and 0.64 mm (0.025 in) in. thickness. The longer length was found to give a better record and

the thinner material could be flattened out after a test for

storage. In addition, the thinner material did not have to be

machine rolled into a cylindrical shape. However, the sheets had

to be reinforced with stiffening rings at each end of the sheet

to hold it against the HDT wall to keep it from crumpling. The

best overall thickness of aluminum sheet was found to be 0.51 mm

(0.02 in).

A- 31
TABLE A-3

TYPE AND LOCATION OF

INITIAL THERMODYNAMIC STATE MEASUREMENTS

TEMPERATURE

Point or Depth Ice Point Static

Average Position Reference Pressure

Test

cJJ

11*

12

13

14

15

16

17

18.

19

20

21

22

23

24

25

Series

1,6

1

2

2

2

2

2

2

A**

A

A

A

A

A

A

A

A

P

P

P

P

P

P

1

1

1

1

1

1

1

1

1

1

1

1

~1

1

1

Humidity

Measurement

1

1

1

1

1

1

1

1

1

1

1

1

* Tests 1-10 are

**Refer to TABLE

system development.

A-4 for instrumentation.
TABLE A-3 (Cont'd)

TYPE AND LOCATION OF

INITIAL THERMODYNAMIC STATE MEASUREMENTS

Test Series

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

Point or

Ave rage

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

TEMPERATURE

Depth

Position

Ice Point

Reference

Static

Pressure

Humidity

Measurement

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1 1

1&2

1&2

1&2

3

3

3

3

3

3

3

3

3

1 1
TABLE A-3 (Cont'd)

TYPE AND LOCATION OF

INITIAL THERMODYNAMIC STATE MEASUREMENTS

Test

w

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Series

U

6

6

5

5

5

5

3

3

3

3

3

3

3

3

3

3

3

Point or

Average

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

TEMPERATURE

Depth

Position

1

1

1

1

Ice Point

Reference

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

Static

Pressure

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

Humidity

Measurement
TABLE A-3 (Cont'd)

TYPE AND LOCATION OF

INITIAL THERMODYNAMIC STATE MEASUREMENTS

Test

wl

U,

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

Series

3

3

1

1

1

1

1

Point or

Average

P

P

P

P

P

P

P

P

P

P

P

P

A

P

P

P

P

TEMPERATURE

Depth

Position

1

1

1

1

1

1

1

1

1

1

1

1

Ice Point

Reference

Static

Pressure

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

Humidity

Measurement

2

2

2

2
TABLE A-3 (Cont'd)

TYPE AND LOCATION OF

INITIAL THERMODYNAMIC STATE MEASUREMENTS

Test

w

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

Series

3

3

3

3

3

3

3

3

3

3

3

3

3

4

4

4

4

4

4

Point or

Average

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

TEMPERATURE

Depth

Position

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

Ice Point

Reference

Static

Pressure

H umidi 'ty

Measurement
Table A-4

Temperature, Pressure and Humidity Instrumentation

Temperature:

Average: Instruments: Thermocouples, Type K, used to control heater tapes

overall uncertainty estimate

30C.

Thermocouple, Type K, 1/8" diameter ss sheath,

magnesium oxide insulated, ungrounded tip.

Point: Instrument:

Location: Port 6

Depth: Position 1 - tip is 1/8" from

the wall :k 1/16"

Position 2 -tip is 1' from

the wall * 1/4"

Reference/Recorder: 1 Fluke Multimeter 8024B

Serial #3275848

Accuracy: 3*C)mfg. calibration

Resolution: 1*C)"

2 Digitec Model 2831

Accuracy: O.30 C)mfg. calibration

Resolution: O.1*C)" 1

Pressure-Static:

Instrument: 1 Absolute Pressure Gage, 0-800 mm Hg

Wallace & Tiernan, Model 61A-1D-0800

Serial #SS-14109

Resolution: 1 mm Hg division

Accuracy: 0.8mm Hg

Sandia cal 7/13/83

exp 1/31/85

Pressure Gage, 0-100 psig

Heise, Serial #47971

Resolution: 0. 1 psig

Accuracy: 0.1 psig

Sandia field cal 2/18/82

2

A-37
Table A-4 (cont'd.)

Pressure-Static: (cont'd.)

Instrument:

Location:

3 Absolute Pressure Gage, 0-50 psia

Wallace & Tiernan, Model 61A-1A--0050

Serial #TT11757

Resolution: 0.05 psia divisions

Accuracy: 0.1 limited range

(0.4 full range)

Sandia cal 6/21/84

exp 7/30/85

Port 12

Humidity

1.

2.

Ambient Air: Humidity measured with

Environmental Systems, Inc., Model. 22012

Uncertainty 3%

Dry Air: Dew Point -75 F

No humidity measurement taken

A- 38
Several types of stiffening rings were used. Early rings

were made of 3.2 mm (1/8 in) carbon steel and were approximately

2.5 cm (1 in) wide. Later rings were made of two layers of 0.25

mm (0.01 in) spring steel welded together. The ring at the

initiation end of the foil widened to approximately 15 cm (6 in).

The aluminum sheet was attached to the ring by rolling the sheet

over the ring and riveting the foil to the ring with low-prof ilehead rivets.,

Because the smoked foil is only 121.9 cm wide and the

circumference of the EDT is 135.7 cm wide, the foil does not form

a complete cylinder. A 13.8 cm slot is formed along the length

of the cylinder. When the smoked foil is inserted into the EDT,

the slot is placed along the axis of the pressure transducers so

there is no interference. However, a 3.81 cm (1.5 in) hole is

cut in the sheet 16.5 cm (6.5 in), from the end of the foil in

contact with the endplate to allow gas to enter the recirculation

line. The hole' is cut 39.4 cm (15.5 in) from the edge of the

foil to have the proper orientation with the recirculation line

and have the slot over the pressure transducer ports.

During the test program, the method of smoking the foils has

been modified and improved. Initially, the foils were rolled

into a cylinder and were stood on end where a MAPP (stabilized

Methylacetylene-Propadiene) gas torch was used to smoke them.

Attempts to improve the smoking technique led to the use of

furnace oil. The furnace oil was placed in an approximately

1/3 m long by 2 cm wide and deep trough which held a ceramic

wick. The foil was laid flat and supported on a wooden rack in a

semi-enclosed area. For the heated tests (Test Series #3,4,6,

and 7), particularly with steam, it was found that the furnace

oil alone would leave. "spots" on the foil as if the oil had

evaporated and left a residue. This problem was eliminated by

first coating the surface of the foil with a mixture of 1/3 Dow

Corning Sylgard 186 and 2/3 Xylene and then buffing the surface

dry. A side effect of this procedure was a reduction of the

contrast of the detonation tracks on the smoked foil. Therefore,

for steam dilution tests (Test Series #4), the furnace oil with

coating was used. In all other tests, the foil was smoked with a

MAPP gas torch.

It was found in both cases that the semi-enclosed area did

not provide enough protection from the winds in Albuquerque and a

permanent enclosure was built, the "smoke house.ý' In the smoke

house, the foil is clamped flat to an aluminum frame and suspended form the ceiling. In this position, either furnace oil or

MAPP can be used to smoke the foil.

A.5.4 Dynamic Pressure Instrumentation

Dynamic pressure is measured by transducers from two manufacturers, Kistler and PCB. Both gages are piezoelectric fast

A-39
response gages wit identical mounting requirements. Tables A-5,

6 list the type, number and digitizing frequency for the gages

used in each test. Five to six Kistler gages were used in each

test from HT-11 to 96. One to three PCB transducers were used

from test 31 through 34 and 42 through 96.

The Kistler transducers are Model 211B3 with a pressure

range of 0 - 3.4 MPa (0 - 500 psi). The rise time is 2 #s with a

resonant frequency of 250 kHz. The transducers have electronic

charge converters in the back of the transducer. The transducers

are powered by battery operated Kistler Model 5112, 2 mA power

supply couplers. The power supply has a decoupling capacitor so

the D.C. signal is not transmitted to the data recording

equipment.

Two types of PCB transducers are used. One type of PCB

transducer is Model 113A24 with a pressure range of 0 - 6.8 MPa

(0 - 1000 psi). The second type is Model 113A26 with a 5.1 cm (2

in) extender between the transducer and the electronic charge

converter. This distance places the temperature limited electronics outside of the insulation. The Model 113A26 has a range

of 0 - 3.4 MPa (0 - 500 psi). The rise time for both transducers

is 1/As with a resonant frequency of 450 kHz. The transducers are

powered by PCB Model 480B power supply couplers which are similar

to the Kistler coupler and have been interchanged.

The transducers are mounted in specially designed fittings.

Figure A-2 shows a cross-section of a pressure transducer penetration in the detonation tube piping. Figure A-14 shows the

fitting designed to mount pressure transducers in the transducer

penetration. Originally, brass fittings were made but the vibration of the transducer mount caused excessive noise on the

pressure data. Deirin and nylon fittings were used to isolate

the transducer from the detonation tube vibration. Nylon has a

higher temperature softening point but the surface subjected to

detonation temperatures. tended to char. The nylon is also

stronger than delrin. The delrin mounts tended to fail at the

neck of the mount near the 0-ring groove. The 0-rings are Parker

#2-019E692-75 ethylene-propylene.

To plug the instrumentation ports not being used, brass

"blanks" were made. These blanks are the same as the fittings in

Figure A-14 except they are not drilled and tapped for the

pressure transducers. These fittings are used to accommodate

other instrumentation such as the thermocouple to measure gas

temperature.

A.5.5 Humidity

For test HT-1l through HT-48, ambient Albuquerque air was

used. An Environmental Systems Inc. Series #22010 Psychrometer

was used to measure the humidity.

A- 40
TABLE A-5

TYPE, NUMBER AND DIGITIZING FREQUENCY

FOR DYNAMIC PRESSURE MEASUREMENT

Test

I-.

11 *

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

series

1,6

1

1

1

1

2

2

2

2

2

2

2

2

2

2

U

Type of

Gage

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

# of

Gages per

Type

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25

RECORDS

7612

Resolution

#__ (ASs) _

CAMAC

Resolution

(14s)

6

* Tests 1-10 are

**Refer to TABLE

system development.

A3 for Instrumentation.
TABLE A-5 (Cont'd)

TYPE, NUMBER AND DIGITIZING FREQUENCY

FOR DYNAMIC PRESSURE MEASUREMENT

RECORDS

Test Series

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

Type of

Gage

1,

1,

1,

1,

1,

12

12

1,

1

1

1

1,

1,2

1,2

# of

Gages per

Type

6

6

6

6

5,1

5,1

5,1

5,1

6

6

6

6

6

6

6

5,1

5,1

5,1

7612

Resolut'ion

#_ (ils)

CAMAC

Resolution

___I (AS )

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25
TABLE A-5 (Cont'd)

TYPE, NUMBER AND DIGITIZING FREQUENCY

FOR DYNAMIC PRESSURE MEASUREMENT

RECORDS

7612

Test

w

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

Series

6

5

5

5

5

3

3

3

3

3

3

3

3

3

3

3

3

3

1

Type of

Gage

1,2

1,2

1,2

1,2

1,2

1,2

1,2

1,2

1,2

-1,2

1,2

1,2

.1,2

1,2

1,2

1,2

1,2

1,2

1,2

# of

Gages per

Type

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

Resolution

10

10

10

10

10

10

1

1

1

1

1

1

1

1

1

1

1

1

1

25,

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25

CAMAC

Resoludtion

(14s)
TABLE A-5 (Cont'd)

TYPE, NUMBER AND DIGITIZING FREQUENCY

FOR DYNAMIC PRESSURE MEASUREMENT

RECORDS

Test Series

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

Type of

Gage

1,2

1,2

1,2

1,2

1,2

1,2

1,2

1,2

1,2

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

# of

Gages per

Type

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

5,1

6,1,2

6,1,2

6,1,2

6,1,2

6,1,2

6,1,2

6,1,2

6,1,2

6,1,2

6,1,2

7612

Resolution

____ (14s)

CAMAC

Resolution

(Ass)

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25

25
TABLE A-5 (Cont'd)

TYPE, NUMBER AND DIGITIZING FREQUENCY

FOR DYNAMIC PRESSURE MEASUREMENT

RECORDS

7612

Test

(11

83

84

85

86

87

88

89

90

91

92

93

94

95

96

Series

3

3

3

3

3

3

3

.3

4

4

4

4

4

4

Type of

Gage

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

1,2,3

# of

Gages per

Type

6,1,2

6,1,2

6,1,2

6,1,2

6,1,2,

6,1,2

6,1,2

6,1,2

6-,1,2

6,1,2

6,1,2

6,1,2

6,1,2

6,1,2

Resolution

25

25

25

25

25

25

25

25

25

25

25

25

25

25

CAMAC

Rýe s olut ion

(JUS)
Table A-6

Dynamic Pressure Instrumentation

Pressure - Dynamic

Instrument:

1. Pressure: Kistler Piezotron Pressure Transducer

Model 211B3

Rise time (10-90%) =2 uSs

Linearity = 1% FS

Resonant frequency -250' kHz

Pressure range: 0-500. psi

Coupler: Kistler Model 5112, 2mA power supply

2. Pressure: PCB Pressure Transducer

Model 113A24 with 401A charge

Rise time = 1 1ss

Linearity = 1% FS

Resonant frequency - 450 kHz

Pressure range: 0-1000 psi

converter

3.

Coupler: Used with either 1 or 3

Pressure: PCB Pressure Transducer

Model 113A26 with 074A247

2" extender & 401A charge converter

Rise time = 1 /.Ss

Linearity = 1% FS

Resonant frequency - 450 kHz

Pressure range: 0-500 psi

Coupler: PCB

Model 480B (Frequency response is

essentially that of the transducer)

A- 46
,,MACHINE FLATS

FOR 1.25" WRENCH

ON TWO FACES

OTHERWISE 1.5" DIAMETER 300 z -1 U- n-0941I 40.5 DlI

-9-I-

/0

0-RING

GROOVE

(see detail)

)IA W

0.500±0.0 1

0.125

/16- 24UNF

4

0.3

P/1 1.00

3 21-

±0.01

4

0.2 15

I OUNF

0.215i 0A1 I

0.221 DIA

+0.001

-0.000

-6 I

U- CHAMFER 450

-0-0.250 DIA

+0.001 0.085 ±tC

-0.000

,0.015"

ALL DIMENSIONS ARE IN INCHES

UNLESS OTHERWISE NOTED

ALL TOLERANCES ARE + .005

:t 0.002

Figure A-14. Transducer Fitting Cross-Section.

A- 47
A.6 REFERENCES FOR APPENDIX A

A-1. Maleev, V. L. , Hartman, J. B. , _Machine Design, Third Edition, International Tex., pp 334 - 335.

A-2. Sherman, M. P., et al., "The FLAME Facility - The Effect of

Transverse Venting on Flame Acceleration and Transition to

Detonation," SAND REPORT 85-1264, (to be published).

A-48
FIGURES

Figure

Figure

Figure

Figure

Figure

Figure

Figure

A-i.

A-2.

A- 3.

A-4.

A-5.

A- 6.

A- 7.

Figure A-8.

Figure A-9.

Figure A-10.

Figure A-l1.

cross-section of a Gas Recirculation Penetration.

cross-section of a Transducer Penetration.

Cross-section of a Pipe Flange

Schematic of the Secondary Piping

Detonation Tube Supports

Tube Support V-Block Positioning Device

Heater Section Schematic -

Long Pipe Section, sides and bottom

Heater Section Schematic -

Long Pipe Section, top

Heater Section Schematic -

Pipe to Pipe Flanges

Heater Section Schematic -

Short Pipe

Heater Section Schematic -

Endplates, Flanges

Heater Control Circuit Schematic

High Explosive Initiator

Transducer Fitting Cross-section

Figure

Figure

Figure

A-i2.

A- 13.

A- 14.

A- 49

APPENDIX B

DETAILS OF PROCEDURE

The test procedures used in the Heated Detonation Tube were

developed and improved as the test program developed. The data

have been categorized into 7 test series listed in Table B-i.

The specific procedures will be discussed for each series,

including variations in procedure for each series. The hardware

is described in Appendix A, and the effect of the change in

procedure/hardware on the data uncertainty is discussed in

Appendix D.

All tests begin with smoking a foil. The technique of"

smoking a foil is discussed in Appendix A. After the foil 'is

s'moked, it is rolled around steel stiffening rings and riveted to

the rings. A slot is formed along one side of the cylinder

because the foil is not as wide as the circumference of the HDT.

When the smoked foil is inserted into the HDT, the slot is placed

along the axis of the pressure transducers so there is no interference. The endplate is then bolted in place.

Next, the explosive initiator is assembled. An RP-2 detonator is attached to the precut detasheet charge in the explosives

assembly igloo. The complete initiator is mounted into the

coaxial pipe and inserted into the HDT. The initiator is connected with the feed-through connector on the endplate and the

endplate is bolted in place. The explosive initiator is not

connected to the firing 'circuit until after the gases have been

entered and the test is ready for detonation initiation.

After the smoked foil and explosive initiator are installed

into the detonation tube and the endplates bolted in place, gases

are then introduced into the recirculation line. The circulation

pump runs continuously from the introduction of the first gas to

the detonation initiation sequence to ensure a homogeneous mixture. Temperature and pressure are measured after the introduction of each gas to determine the composition. The specif ic

details for each test series are discussed following th e next

paragraph.

After the temperature and pressure are measured for the last

gas injected into the tube, the secondary piping is isolated from

the detonation tube to protect the pump. The manifold to the

pressure gage is closed, the power supplies to the dynamic

pressure transducers are turned on, and the detonator lines are

connected. All personnel are then required to leave the detonation tube and enter the control room in Bldg. 9920. For elevated

temperature tests, the heaters are turned off. The computer is

then configured to control the data acquisition equipment. The

area is cleared and the firing circuit is charged. The discharge

B-1
Table B-i

Test Series

Series # Description # of tests in series

1 H2 -Air @ P=1 atm, T=20*C 16

2 H2 -Air-C02 @ P=1 atm, T=200C 10

3 H2 -Air @ Pair=4 1 .6 moles/rn3 , T=1000 G 16

4 H2 -Air-H2 0 @ Pair=4 1 .

6 moles/rn3 , T=.100 0G 18

5 H2-Air @ Pair=4 1 .

6 moles/rn3 , T=20*C 6

6 H2-Air @ XH2=O.17, P=1 atm 4

7 H2 -Air @ XH2=O.17, p=42 moles/rn3 3

from the firing circuit simultaneously initiates the detonation

and triggers the data acquisition equipment. The time between

secondary piping isolation from the detonation tube and initiation of the detonation is typically 12 minutes. The time between

turning off the heaters and the initiation of the detonation is

typically 8 minutes.

B.1 TEST SERIES #1: H2 -Air @ P=1 atm, T=20 0C

The first test series is composed of tests HT11 through 15

and 62 through 72. After the explosive initiator and smoked foil

were placed in the detonation tube, air was introduced. In tests

11 through 15, the humid ambient air in the tube at the time the

endplates were put on was used. The air was typically at 84 kPa

(12.2 psia) . Wet and dry bulb measurements were recorded to

determine the humidity. The air was then partially evacuated to

a level at which the addition of H2 would bring the total pressure to one atmosphere. For tests 62 through 72, the tube was

evacuated to less than 3.4 kPa (0.5 psia) prior to injecting

compressed dry bottled air. The air pressure was 'set to a level

at which the addition of H2 would bring the total pressure to one

atmosphere.

The air was allowed to stabilize for at least 15 minutes

(typically 30 minutes) from the time the 'air pressure first

reached its pre-determined pressure. The air pressure was

adjusted while the gas achieved thermal equilibrium with the

detonation tube. At least 5 minutes (typically 15 minutes) were

B-2
allowed where no changes were made in the pressure. The temperature and pressure were then recorded.

Hydrogen was then introduced to bring the total pressure up

to one atmosphere. Hydrogen was introduced into the recirculation line at a rate slow enough that one equivalent tube volume

of mixture had circulated through the secondary piping, approximately 15 minutes. The pressure was adjusted while the gas

mixture achieved thermal equilibrium with the detonation tube.

The mixture was allowed at least 15 minutes to stabilize prior to

recording the temperature and pressure.

The temperature of the detonation tube was not controlled

but was in equilibrium with the ambient air. The standard detonation initiation sequence was then begun.

B.2 TEST SERIES #2: H2 -Air-C02 @ P=1 atm, T=20*C

The second test series is composed of tests HT16 through 25.

The air used in these tests was the ambient air in the tube after

the explosive initiator and smoked foil installed. The air was

typically at 84 kPa (12.2 psia). Wet and dry bulb measurements

were recorded to determine the humidity. The air was then partially evacuated to a level at which the addition Of C02 and H2

would bring the total pressure to one atmosphere. The air was

allowed to stabilize for at least 15 minutes (typically 30

minutes) from the time the air pressure first reached its predetermined pressure. The air pressure was adjusted while the gas

achieved thermal equilibrium with the detonation tube. At least

5 minutes (typically 15 minutes) were allowed where no changes

were made in the pressure. The temperature and pressure were

then recorded.

Carbon dioxide was then introduced into the recirculation

line at a rate slow enough that one equivalent tube volume of

mixture had circulated through the secondary piping, approximately 15 minutes. The pressure was adjusted while the gas

mixture achieved thermal equilibrium with the detonation tube.

The mixture was allowed at least 15 minutes to stabilize prior to

recording the temperature and pressure.

Hydrogen was then introduced into the recirculation line to

bring the total pressure up to one atmosphere. Hydrogen was

introduced at a rate slow enough that one equivalent tube volume

of mixture had circulated through the secondary piping, approximately 15 minutes. The pressure was adjusted while the gas

mixture achieved thermal equilibrium with the detonation tube.

The mixture was allowed at least 15 minutes to stabilize prior to

recording the temperature and pressure.'

B-3
The temperature of the detonation tube was not controlled

but was in equilibrium with the ambient air. The standard detonation initiation sequence was then begun.

B.3 TEST SERIES #3 and #4: .H 2 -Air-H2 0 @ Pair=4 1 .6 moles/rn3 , T=100*C

The third arnd fourth test series are composed of tests HT39,

41, 42, 50 through 61, and 73 through 90. For all tests except

39, 41, and 42, the explosive initiator and smoked foil were

placed in the detonation tube, and then the tube was evacuated to

less than 3.4 kPa (0.5 psia). Dry bottled air was injected. The

air pressure was set so that the air molar density, Pair, was

41. 6 moles/in 3 . The actual pressure depended on the detonation

tube temperature at the time of air injection, being superatmospheric for any temperature over 20*C. For the third test

series, the steam bottle was isolated from the secondary recirculation line and for the fourth test series, a premeasured

volume of water was then poured into the steam bottle.

The detonation tube and steam bottle were then heated to

1000C. From test 74 to 90 the detonation tube was allowed to

heat unattended overnight using the "watchdog" timer device.

Normal heating times were 5 hours. Typical temperature profiles

are shown in Appendix F. For tests prior to 74, the circulation

pump was run continuously during the heating process; for overnight heating the pump was turned on in the morning. After the

tube reached 970C or 98*C, and the circulation pump had run for

at least 30 minutes, any final adjustments were made to the air

pressure to achieve the desired air density. At least 5 minutes

(typically 15 minutes) were allowed where no changes were made in

the pressure. The temperature and pressure were then recorded.

Hydrogen was then introduced into the recirculation line at

a rate slow enough that one equivalent tube volume of mixture had

circulated through the secondary piping, approximately 15 minutes. The pressure was adjusted while the gas mixture achieved

thermal equilibrium with the detonation tube. The mixture was

allowed at least 15 minutes to stabilize prior to recording the

temperature and pressure. For tests 39, 41, and 42, the air and

hydrogen were added and then the tube was heated. For test

series #3, the standard firing sequence was begun, for test

series #4, steam was introduced into the HDT.

To produce steam in the superatmo spheric conditions in the

detonation tube, the temperature of the steam bottle was raised,

typically between 150 0C and 200*C. The steam bottle was then

opened to the secondary piping and allowed to flow in. Condensation in the secondary line was a problem on most tests because of

the poor metering characteristics of the ball valve between the

steam bottle and secondary piping. The condensate would reevaporate as detected by a thermocouple at the low point in the

B-4
secondary line and a concurrent increase in pressure. Future

tests will use a metering valve for better injection control.

The water in the steam bottle was determined to have completely evaporated when there was no change in the detonation

tube pressure and the temperature controller indicated that the

heater on the steam bottle was no longer cycling around the set

point temperature but was off for long periods, -p3 minutes. The

mixture was allowed at least 15 minutes to stabilize prior to

recording the temperature and pressure. The standard detonation

initiation sequence was then begun.

B.4 TEST SERIES #5: H2 -Air @ Pair=4 1 .6 moles/in3 , T=100*C

The fifth test series is composed of tests HT91 through 96.

After the explosive initiator and smoked foil were placed in the

detonation tube, the tube was evacuated to less than 3.4 kPa (0.5

psia). Dry bottled air was injected and the air pressure was set

so that the air molar density, Pair, was 41.6 moles/in3 . The

actual pressure depended on the detonation tube temperature at

the time of air injection. The air pressure was adjusted whi-le

the gas achieved thermal- equilibrium with the detonation tube.

At least 5 minutes (typically 15 minutes) were allowed where no

changes were made in the pressure. The temperature and pressure

were then recorded.

These tests were done in the fall of the year and the

ambient air temperature was below 20*C during the night and was

approximately that temperature during the day. The detonation

tube does not have' refrigeration coils. Two tests were run each

day for three days. The heaters were programmed to turn on early

in the morning with a set point of 180C. This allowed two

degrees of heating which occurred as during gas injection and

circulation. For the second test of the day the heaters were

turned off and the tube obtained the ambient temperature of the

day. The test temperatures varied between 19.2*C and 22.7 0 C.

Hydrogen was then introduced into the recirculation line at

a rate slow enough that one equivalent tube volume of mixture had

circulated through the secondary piping, approximately 15 minutes. The pressure was adjusted while the gas mixture achieved

thermal equilibrium with the detonation tube. The mixture was

allowed at least 15 minutes to stabilize prior to recording the

temperature and pressure. The standard detonation initiation

sequence was then begun.

B.5 TEST SERIES #6: H2 -Air @ XH2=O-l7, P=1 atm

The sixth test series is composed of tests HT46 through 49.

After the explosive initiator and smoked foil were placed in the

detonation tube, the endplates were put on. The humid air in the

B-5
tube at the time the endplates were placed on the detonation tube

was used as the air in the test. The air was typically at 84 kPa

(12.2 psia) . Wet and dry bulb measurements were recorded to

determine the humidity. The air was then partially evacuated to

a level at which the addition of H2 would bring the total pressure to one atmosphere and the H2 mole fraction to 0.17.

The air was allowed to stabilize for at least 15 minutes

(typically 30 minutes) from the time the air pressure first

reached its pre-determined pressure. The air pressure was

.adjusted while the gas achieved thermal equilibrium with the

detonation tube. At least 5 minutes (typically 15 minutes) were

allowed where no changes were made in the pressure. The temperature and pressure were then recorded.

Hydrogen was then introduced into the recirculation line to

bring the total pressure up to one atmosphere. Hydrogen was

introduced at a rate slow enough that one equivalent tube volume

of mixture had circulated through the secondary piping, approximately 15 minutes. The pressure was adjusted while the gas

mixture achieved thermal equilibrium with the detonation tube.

The mixture was allowed at least 15 minutes to stabilize prior to

recording the temperature and* pressure. For test---HT46, the

standard detonation initiation sequence was then begun.

For tests 47, 48 and 49, detonation tube was then heated.

For test 47 the tube was heated to 500 C, and for 48 and 49 the

tube was heated to 100 0C. The temperature was allowed to come to

equilibrium around the set point temperature typically with no

detectable change in temperature in 15 minutes. The standard

detonation initiation sequence was then begun.

B.6 TEST SERIES #7: H2 -Air @ XH2=O.17, p=42 moles/in 3

The seventh test series is composed of tests HT11, 44 and

45. Test HT11 is described in test series #1. The procedure for

tests 45 and 46 are described here. After the explosive initiator and smoked foil were placed in the detonation tube, the

endplates were put on. The humid air in the tube at the time the

endplates were placed on .the detonation tube was used as the air

for the test. The air was typically at 84 kPa (12.2 psia). Wet

and dry bulb measurements were recorded to determine the humidity. Additional air was introduced from a compre.ssed air source

at the 9920 site to bring the air density to a level at which the

addition of H2 would bring the total mixture density to 42

moles/in3 and the H2 mole fraction to 0.17.

The air was allowed to stabilize for at least 15 minutes

(typically 30 minutes) from the time the air pressure first

reached its pre-determined pressure. The air pressure was

adjusted while the gas achieved thermal equilibrium with the

detonation tube. At least 5 minutes (typically 15 minutes) were

B-6
allowed where no changes were made in the pressure. The temperature and pressure were then recorded.

Hydrogen was then introduced into the recirculation line to

bring the total pressure up to one atmosphere. Hydrogen was

introduced at a rate slow enough that one equivalent tube volume

of mixture had circulated through the secondary piping, approximately 15 minutes. The pressure was adjusted while the gas

mixture achieved thermal equilibrium with the detonation tube.

The mixture was allowed at least 15 minutes to stabilize prior to

recording the temperature and pressure.

The detonation tube was then heated. For test 45 the tube

was heated to 50*C, and for 44 the tube was heated to 100*C. The

temperature was allowed to come to equilibrium around the set

point temperature typically with no detectable change in temperature in 15 minutes. The standard detonation initiation sequence

was then begun.

B-7

APPENDIX C

TABULATED DATA

The data are tabulated by test series. Uncertainty estimates are included in the tables. For each variable listed,

three columns are defined, LB which is the lower bound, MP which

is the most probable, and UB which is the upper bound (see Appendix D). Table C-1 lists the test series. Table C-2 lists the

detonation cell width for each series. Within each series, the

data are listed in increasing equivalence ratio and increasing

diluent mole fraction.. Table C-2 also lists the results of the

model calculations (See Chapter 4). The Z.75 column is the

length required to reach Mach 0.75. The DCW/Z.75 column is the

most probable detonation cell width divided by this length scale.

The final column is 22 times the Z.75 column which is the predicted detonation cell width using a single point fit for the

constant A in the model. Table C-3 lists the detonation velocity

for each series. Within each series, the data are listed in

increasing equivalence ratio and increasing diluent mole fraction. Table C-3 also lists the data acquisition equipment used,

number of gages recording data, and the Chapman-jouguet theory

predicted velocity. Table C-4 lists the full initial thermodynamic state for each test series. Within each test series, the

data are listed in increasing test number.

C- 1
Table C-i

Test Series

Series # Description # of Tests in Series

1 H2-Air 0 P=1 atm, T=20*C 16

2 H2-Air-C02 a P=1 atm, T=20 0C 10

3 H2-Air 8 Pair=4 1 .8 moles/rn 3, T=100 0 C 16

4 H2-Air-H20 0 Pair=4 1 6 moles/rn 3, T=100*C 18

5 H2-Air 0 Pair=4 1 6 moles/rn 3

, T=200 C 6

6 H2-Air 0 XH2-0.17, P=1 atm 4

7 H2-Air a XH2=0.l7, P=42 moles/rn3 3

C-2
Table C-2

Detonation Cell Width Data

TEST SERIES #1

The 2S limits for T,P for the entire series are:

275. < T (K) < 306.

99.1 < P (kPa) < 101.7

n

w

TEST EQUIVALENCE RATIO DETONATION CELL WIDTH

(MM) Z.76

LB MP UB LB MP UB (MM)

15 0.3465 0.3743 0.4021 915. 1220. 1525. 179.

14 0.3529 0.3812 0.4094 900. 1200. 1500. 159.

67 0.3583 0.3868 0.4152 480. 640. 800. 95.0

68 0.3788 0.4071 0.4353 315. 420. 525. 53.3

66 0.3965 0.4248 0.4531 229. 305. 381. 34.5

12 0.4046 0.4334 0.4622 233. 310. 388. 48.7

69 0.4048 0.4335 0.4621 199. 265. 331. 30.0

65 0.4334 0.4623 0.4912 188. 250. 313. 16.1

11 0.4498 0.4792 0.5085 143. 190. 238. 19.2

64 0.4575 0.4867 0.5158 113. 150. 188. 9.52

63 0.4737 0.5037 0.5336 75. 100. 125. 7.77

70 3.5773 3.6647 8.7521 139. 185. 231. 4.99

71 4.3527 4.4655 4.5783 356. 475. 594. 15.6

72 5.5574 5.7129 5.8684 1013. 1350. 1688. 73.5

MODEL

DCW/Z.75 22*Z.75

(MM)

6.82 3938.

7.67 3498.

6.74 2090.

9.85 1173.

8.84 759.

6.37 1071.

8.83 660.

15.5 354.

9.90 422.

15.8 209.

12.9 171.

37.1 110.

30.4 343.

18.4 1617.
Table C-2 (cont'd.)

TEST SERIES #2

The 2S limit~s for T,P for the entire series are:

275. < T (K) < 299.

106.5 < P (kPa) < 106.9

TEST EQUJIVALENCE RATIO CO2 MOLE FRACTION DETONATION CELL WIDTH MODEL

(MM) Z.76 DCW/Z.75 22*Z.75

LB MP UB LB MP UB LB MP UB (MM) (MM)

16 0.4589 0.4877 0.5165 0.0406 0.0500 0.0594 368. 490. 613. 62.0 7.90 1364.

22 0.5369 0.5852 0.5936 0.0408 0.0498 0.0588 225. 300. 375. 15.2 19.7 334.

17 0.5672 0.5977 0.6282 0.0409 0.0505 0.0601 150. 200. 250. 13.4 14.9 295..

25 0.6430 0.6723 0.7017 0.0396 0.0486 0.0577 86. 95. 198. 3.95 24.1 88.9

21 0.6883 0.7182 0.7502 0.0914 0.0999 0.1085 125. 240. 260. 12.3 19.5 271.

18 0.7227 0.7558 0.7889 0.0912 0.1000 0.1088 180. 240. 300. 9.96 24.1 219.

24 0.8048 0.8379 0.8709 0.0916 0.1001 0.1086 100. 100. 200. 5.20 19.2 114.

23 0.7208 0.7559 0.7909 0.1419 0.1500 0.1581 340. 500. 520 35.9 13.9 790.

20 0.7983 0.8342 0.8700 0.1425 0.1505 0.1585 293. 390. 488. 20.3 19.2 447.

19 0.9953 1.0338 1.0723 0.1428 0.1509 0.1590 180. 180. 290. 9.99 18.0 220.
Table C-2 (cont'd.)

TEST SERIES #3

The 2S limits for T, air density for the entire series are:

388. < T (K) < 375.

40.4 < Air Density (moles/rn3) < 42.1

TEST EQUJIVALENCE RATIO

LB MP UB

74 0.3355 0.3575 0.3794

73 0.3526 0.3747 0.3967

77 0.386M 0.3827 0.4048

62 0.3990 0.4213 0.4437

76 0.4751 0.4981 0.5212

60 0.5820 0.6059 0.6297

78 0.5848 0.6088 0.6327

42 0.6253 0.6501 0.6750

80 0.6738 0.6985 0.7232

56 0.7830 0.8085 0.8339

82 0.8701 0.8964 0.9226

84 0.9687 0.9957 1.0228

53 0.9826 1.0098 1.0369

88 1.4887 1.5000 1.5313

50 1.9818 1.9974 2.0329

88 2.9832 3.0077 3.0522

STEAM MOLE FRACTION DETONATION CELL WIDTH

(MM)

LB MP UB LB MP UB

0.0000 0.0000 0.0000 315. 420. 525.

0.0000 0.0000 0.0000 247. 330. 413.

0.0000 0.0000 0.0000 221. 295. 389.

0.0000 0.0000 0.0000 131. 175. 219.

0.0000 0.0000 0.0000 49. 85. 81.

0.0000 0.0000 0.0000 19. 25. 31. 0

0.0000 0.0000 0.0000 18. 24. 30. 0

0.0038 0.0038 0.0038 14. 19. 24. 0

0.0000 0.0000 0.0000 11. 14. 18. 0

0.0000 0.0000 0.0000 7. 9. 11. 0

0.0000 0.0000 0.0000 5. 6. 8. 0

0.0000 0.0000 0.0000 4. 5. 6. 0

0.0000 0.0000 0.0000 4. 5. 6. 0

0.0000 0.0000 0.0000 5. 6. 10. 0

0.0000 0.0000 0.0000 7. 12. 24. 0

0.0000 0.0000 0.0000 22. 22. 35.

(MM)

33.3

12.E

.779

.774

.623

.537

.442

.399

.368

.387

.309

.37E

1.09

MODEL

65 DCW/Z.75 22*Z.75

(MM)

8.1 1142.

19.9 733.

10.5 620.

14.6 264.

123.8 60.1

32.1 17.1

31.0 17.0

I30.5 13.7

26.1 11.8

20.4 9.7

P15.0 8.8

I13.6 8.1

13.7 8.0

P19.5 6.8

32.0 8.3

P20.2 24.0

0

uI
Table C-2 (cont'd.)

TEST SERIES #4

The 2S limits for T, Air Density for the entire series are:

367. < T (K) < 376.

40.9 < Air Density (moles/m^3) < 42.0

TEST EQUIVALENCE RATIO STEAM MOLE FRACTION DETONATION CELL WIDTH MODEL

n

75

79

41

61

58

54

51

81

85

90

59

55

52

39

83

89

87

57

LB

0. 4713

0. 5779

0. 5829

0. 5955

0.7857

0. 9765

1. 9369

0.6687

0. 9753

0.6724

0. 7930

0.9812

1. 9350

0.7862

0. 8742

0. 8767

0. 9751

0. 9781

MP UB LB

0.4943 0.5173 0.0903

0.6018 0.6256 0.0898

0.6102 0.6374 0.0955

0.6195 0.6435 0.0919

0.8111 0.8366 0.0904

1.0036 1.0306 0.0901

1.9724 2.0078 0.0956

0.6932 0.7178 0.1446

1.0024 1.0295 0.1495

0.6969 0.7214 0.1792

0.8185 0.8440 0.1901

1.0082 1.0353 0.1896

1.9704 2.0057 0.1956

0.8167 0.8472 0.2415

0.9003 0.9265 0.2566

0.9028 0.9290 0.2903

1.0021 1.0291 0.2892

1.0051 1.0322 0.2821

0.0972

0.1026

0. 1514

0. 1662

0. 1856

0. 1965

0.1960

0.2018

0 .2483

0. 2624

0. 2959

0. 2948

0. 2877

0.1043

0. 1095

0. 1581

0. 1628

0.19k1

0.2028

0.2023

0.2080

0 .2560

0. 2683

0. 3015

0.3004

0. 2934

MP UB

0.0975 0.1046

0.0970 0.1041

0.1033 0.1110

0.0990 0.1062

0.0975 0.1046

LB

413.

173.

158.

150.

41.

22.

31.

153.

49.

265.

169.

60.

98.

210.

221.

350.

280.

170.

(MM)

MP

550.

230.

210.

200.

55.

29.

41.

207.

74.

310.

225.

95.

131.

280.

295.

365.

290.

325.

UB

688.

288.

263.

250.

69.

36.

51.

260.

99.

500.

281.

180.

164.

350.

369.

1070.

700.

330.

Z. 75

(MM)

37.7

10.6

11.3

9.29

2.09

1.05

2.20

12.0

26.1

19.7

10.3

4.54

10.1

22.5

16.6

25.8

16.7

15.3

DCW/Z.75 22*Z.75

(MM)

14.6 829.

21.7 233.

18.6 249.

21.5 204.

26.3 46.0

27.6 23.1

18.6 48.4

17.3 264.

28.4 57.4

15.7 433.

21.8 227.

20.9 99.9

13.0 222.

12.4 495.

17.8 365.

14.1 568.

17.4 367.

21.2 337.
Table C-2 (cont'd.)

TEST SERIES #5

The 2S limits on T, Air density for the entire Series are:

290. < T (K) < 298.

41.0 < Air Density (moles/rn3) < 42.0

TEST EQUIVALENCE RATIO DETONATION CELL WIDTH MODEL

LB

96 0.3709

95 0.4719

94 0.5733

93 0.7714

92 0.9771

91 1.9329

MP UB

0.3989 0.4270

0.5011 0.5.303

0.6036 0.6340

0.8038 0.8361

1.0116 1.0461

1.9776 2.0223

LB

300.

86.

29.

10.

7.

14.

(MM)

MP

400.

115.

38.

13.

10.

15.

UB

500.

144.

48.

16.

13.

29.

Z.75 DCW/Z.75 22*Z.75

(MM) (MM)

70.0 5.7 1540.

9.36 12.3 206.

2.07 18.4 45.5

0.550 23.6 12.1

0.417 24.0 9.1

0.567 26.5 12.5

TEST SERIES #6

2S limits for EQR and P for the entire series are:

0.446 < EQR < 0.511

100.1 < P (kPa) < 101.7

TEST TEMPERATAURE DETONATION CELL

(K) (MM)

LB MP UB LB MP

46 285.6 287.6 289.6 158. 210.

47 321.1 323.1 325.1 130. 135.

48 371.1 373.1 375.1 81. 106.

49 370.1 372.1 374.1 60. 65.

WIDTH MODEL

Z.75 DCW/Z.75 22*Z.75

UB (MM) (MM)

263. 16.1 13.0 354.

230. 8.35 16.2 184.

140. 2.61 40.6 57.

120. 1.97 33.0 43.
Table C-2 (cont'd.)

TEST SERIES #7

2S limits for EQR and AIR DENSITY for the entire series are:

0.448 < E(QR < 0.510

34.0 < AIR DENSITY> CMOLES/M 3) < 34.8

TEST TEMPERATAURE DETONATION CELL WIDTH MODEL

CK) (MM) Z.75 DCW/Z.76 22*Z.75

LB MP UB LB MP UB (MM) (MM) 11 274.9 276.9 278.9 143. 190. 238. 19.2 9.90 422.

45 321.6 323.6 325.6 90. 140. 150. 11.1 12.6 244.

44 368.1 370.1 372.1 82. 130. 137. 3.59 36.2 79.

C-8
Table C-3

Detonation Velocity Data

(Note: Velocity Sources - 1 = 7612D's ,2 = CAMAC)

TEST SERIES #1

2S limits for T,P for the entire series are:

275. < T (K) < 306.

99.1 (*P (kPa) < 101.7

TEST EQUIVALENCE RATIO

0

.0I

LB

15 0.34865

14 0.3529

67 0.3583

88 0.3788

868 0.39865

12 0.4046

69 0.4048

865 0.4334

11 0.4498

64 0.4575

63 0.4737

70 3.577 3

71 4.3527

72 5.5574

MIP

0.3743

0.3812

0.3868

0.4071

0.4248

0.4334

0.4335

0.4623

0.4792

0.4887

0.5037

3 .6847

4.4655

5.7129

UB

0.4021

0.4094

0 .4152

0 .4353

0 .4531

0.4622

0.4621

0.4912

0.5085

0.5158

0.5336

3.7521

4.5783

5.8884

OS.

4

4

4

S

5

6

DETONATION VELOCITY

(KM/S)

LB MIP UB

1.3984 1.4103 1.4245

1.3707 1.4523 1.5443

1.4516 1.4758 1.5009

1.5040 1.5086 1.5131

1.5007 1.5447 1.5914

1.5073 1.5287 1.5507

1.5307 1.5496 1.5690

1.5707 1.5749 1.5791

1.5314 1.5879 1.6488-

1.5896 1.8099 1.6307

1.6487 1.6539 1.6591

2.2435 2.2610 2.2788

2.2091 2.2757 2.3464

2.2281 2.2782 2.3305

CHAPLIAN-JOUWUET VELOCITY

(KM/S)

SOURCE

1 1.4520

1 1.4611

1 1.4718

1 1. 4986'

1 1.5211

1 1.5279

1 1.5313

1 1.5655

1 1.5819

1 1.5934

1 1.6115

1 -2.2511

1 2.2799

1 2.3109
Table C-3 (cont'd.)

TEST SERIES #2

'The 2S limits for T,P for the entire series are:

275. ( T (K) < 299.

1086. < P (kPa) < 106.9

TEST EQUIVALENCE RATIO C02 MOLE FRACTION

LB MP UB LB MP UB 01

16 0.4589 0.4877 0.5165 0.0406 0.0500 0.0694

22 0.5369 0.5652 0.5938 0.0408 0.0498 0.0588

17 0.56872 0.5977 0.6282 0.0409 0.0505 0.0601

25 0.6430 0.6723 0.7017 0.0396 0.0488 0.0577

21 0.6863 0.7182-0.7502 0.0914 0.0999 0.1085

18 0.7227 0.7558 0.7889 0.0912 0.1000 0.1088

24 0.8048 0.8379 0.8709 0.0918 0.1001'0.1086

23 0.7208 0.7559 0.7909 0.1419 0.1500 0.1581

20 0.7983 0.8342 0.8700 0.1425 0.1505 0.1585

19 0.9953 1.0338 1.0723 0.1428 0.150W 0.1590

BS.

5

6

5

5

5

5

DETONATION VELOCITY

(KM/S)

LB MP U8

1.4633 1.4766 1.5007

1.5299 1.5682 1.6098

1.6040 1.6321 1.6612

1.6859 1.6969 1.7290

1.6085 1.6156 1.6228

1.6057 1.6437 1.6836

1.6980 1.7115 1.7252

1.5219 1.5567 1.5931

1.5571 1.5949 1.6347

1.6708 1.6845 1.6985

CHAPMAN-JOAJQJET VELOCITY

(KM/S)

SOURCE

1 1.5100

1 1.5874

1 1.6154

1 1.8790

1 1.6239

1 1.8488

1 1.6959

1 1.5855

1 1.6091

1 1.6857

I-A

0

TEST SERIES #3

The 2S limits for T, air density for the entire series are:

366. < T (K) < 375.

40.4 < Air Density (moles/rn3) < 42.1

TEST EQUIVALENCE RATIO STEAM~ MOLE FRACTION DETONA

LB MP UB LB MP LB OBS. LB

74 0.3355 0.3575 0.3794 0.0000 0.0000 0.0000 7 1.3939

73 0.3526 0.3747 0.3967 0.0000 0.0000 0.0000 4 1.4113

77 0.3606 0.3827 0.4048 0.0000 0.0000 0.0000 7 1.4687

TION VELOCITY

(KM/S)

MP

1.4252 1.~

1.5121 1.4

1.4792 1.~

JB

4580

8284

4898

CHAPMAN-JOUGUET VELOCITY

(KM/S)

SOURCE

2 1.4391

2 1.4628

2 1.4733
Table C-3 (cont'd.)

Test Series #3 (cont'd.)

62

76

60

78

42

80

56

82

84

53

88

so

88

0.3990

0 .4751

0.5820

0.5848

0.8253

0.6738

0.7830

0.8701

0.9687

0.9828

1.4687

1.9618

2.9832

0.4213

0.4981

0.6059

0.6088

0.8501

0.6985

0.8085

0.8964

0.9957

1.0098

1.500

1. 9974

3.0077

0.4437

0.5212

0.6297

0 .6327

0.6750

0.7232

0. 8339

0.9226

1.0228

1.0369

1. 5313

2.0329

3 .0522

0. 0000 0.0000 0. 0000

0. 0000 0. 0000 0.0000

0.0000 0.0000 0.0000

0.0000 0.0000 0.0000

0.0037 0.0038 0.0040

0.0000 0.0000 0.0000

0.0000 0.0000 0.0000

0.0000 0.0000 0.0000

0.0000 0.0000 0.0000

0.0000 0.0000 0.0000

0.0000 0.0000 0.0000

0.0000 0.000 0.000

0.0000 0.0000 0.0000

S

7

5

6

5

4

5

6

5

4

1.4996

1.5851

1.6954

1.6904

1.7327

1. 7751

1.8688

1. 9418

1.9767

1.9585

2.0816

2.1375

2.2259

1.5160

1.6052

1. 7255

1. 7071

1.7491

1.8070

1. 8787

1.9507

1.9898

1.9865

2.0943

2.1555

2.2406

1. 5327

1.6259

1.7566

1. 7242

1. 7658

1. 8399

1.8886

1.9596

2.0032

2 .0153

2.1071

2.1738

2.2655

1

2

1

2

1. 5222

1.6103

1. 7154

1. 7180

1. 7514

1.7924

1.8700

1.9220

1.9695

1.9752

2.0911

2. 1508

2.2281

TEST SERIES #4

The 2S limits for T, Air Density for the entire series are:

387. < T (K) < 376.

40.9 < Air Density (moles/rn3) < 42.0

I-.

I-.

TEST EQUJIVALENCE RATIO STEAM MOLE FRACTION

LB

75 0.4713

79 0.5779

41 0.5829

61 0.5955

58 0.7857

54 0.9765

51 1.9369

MP~ Ue

0.4943 0.5173

0.6018 0.6258

0.6102 0.6374

0.6195 0.6435

0.8111 0.8386

1.0038 1.0308

1.9724 2.0078

LB

0.0903

0 .0898

0.0955

0.0919

0.0904

0.0901

0.0956

MP LIB

0.0975 0.1048

0.0970 0.1041

0.1033 0.1110

0.0990 0.1062

0.0975 0.1046

0.0972 0.1043

0.1026 0.1095

OBS.

7

4

4

4

4

DETONATION VELOCITY

(KM/S)

LB M L B

1.5297 1.5408 1.5520

1.6490 1.6588 1.6883

1.6607 1.6872 1.6737

1.5986 1.6653 1.7378

1.8212 1.8306 1.8401

1.9112 1.9303 1.9498

2.0179 2.0542 2.0919

CHAPMAN-JOUGL1ET VELOCITY

(KM/S)

SOUR~CE

2 1.6624

1 1.8662

1 1.6597

1 1.6704

1 1.8186

1 1.9191

1 2.0383
Table C-3 (cont'd.)

Test Series #4 (cont~d.)

81 0.6887 0.8932 0.7178

85 0.9753 1.0024 1.0295

90 0.8724 0.6989 0.7214

59 0.7930 0.8185 0.8440

55 0.9812 1.0082 1.0353

52 1.9350 1.9704 2.0057

39 0.7882 0.8167 0.8472

83 0.8742 0.9003 0.9285

89 0.8767 0.9028 0.9290

87 0.9751 1.0021 1.0291

57 0.9781 1.0051 1.0322

0. 1446

0. 1495

0.1792

0.1901

0. 1896

0. 1958

0.2415

0.2588

0. 2903

0.2892

0.2821

0.1514 0.1581

0.1582 0.1628

0.1858 0.1921

0.1965 0.2028

0.1960 0.2023

0.2018 0.2080

0.2483 0.2550

0.2624 0.2683

0.2959 0.3015

0.2948 0.3004

0.2877 0.2934

5

6

6

5

6

1.7029

1.8734

1.6849

1.7409

1.8099

1.9349

1. 7129

1.7350

1.7045

1. 7711

1.7583

1. 7144

1.8857

1. 6881

1. 7521

1.8497

1. 9549

1.7305

1. 7671

1.7146

1.7829

1. 7787

1.7261

1.8983

1.6712

1.7634

1. 8914

1. 9752

1.7484

1.8003

1.7248

1.7948

1.8016

1

1

2

1

1

1

1

1

1

1

1

1.6986

1.8834

1.8791

1.7579

1.8599

1.9258

1. 7198

1.7609

1.7384

1.7867

1,.7932

I-.'

N)

TEST SERIES #5

The 2S limits on T, Air density for the entire Series are:

290. < T (K) < 298.

41.0 < Air Density (moles/rn3) < 42.0

TEST EQUIVALENCE RATIO DETONATION VELOCITY CHAPMAN-JOU(IJET VELOCITY

#(KMw/S) (KM/S)

LB MPl U1B OBS. LB MP UB SOURCE

96 0.3709 0.3989 0.4270 5 1.4799 1.4978 1.5158 1 1.4878

95 0.4719 0.5011 0.5303 5 1.6178 1.6264 1.8331 1 1.6092

94 0.5733 0.6038 0.6340 5 1.7162 1.7292 1.7424 1 1.7113

93 0.7714 0.8038 0.8381 5 1.8894 1.9182 1.9480 1 1.86888

92 0.9771 1.0116 1.0481 5 1.9771 1.9879 1.9989 1 1.9081

91 1.9329 1.9776 2.0223 4 2.1520 2.1632 2.1746 1 2.1468
Table C-3 (cont'd.)

TEST SERIES #6

2S limits for EQR and P for the

0.446 < EQR < 0.511

100.1 < P (kPa) < 101.7

TEST TEMPERATURE

(K)#

LB MP Lie OBS.

46 285.6 287.6 289.6 3

47 321.1 323.1 325.1 5

48 371.1 373.1 375.1 4

49 370.1 372.1 374.1 5

entire series are:

DETONATION VELOCITY

(KM/S)

LB MP UB

1.5819 1.5885 1.5950

1.5748 1.5854 1.5961

1.5715 1.5776 1.5838

1.5903 1.5988 1.6073

CHAPMAN-JOUGUET VELOCITY

(I<M/S)

SOURCE

1 1.5836

1 1.5832

1 1.5773

1 1.5950

I-.

TEST SERIES #7

2S limits for EIQR and AIR DENSITY for the entire series are:

0.448 < EQR < 0.510

34.0 < Air Density (Moles/rn3) < 34.8

TEST TEMPERATURE DETONATION VELOCITY CHAPMAN-JOUGUFET VELOCITY

(K) #(KM/S) (KM/S)

LB MP UB OBS. LB MP U18 SOURCE

11 274.9 276.9 278.9 4 1.5314 1.5879 1.6488 1 1.5819

45 321.6 323.6 325.6 5 1.5850 1.5905 1.5961 1 1.5762

44 368.1 370.1 372.1 5 1.5847 1.5955 1.8065 1 1.5928
Table C-4

Initial Thermodynamic State

TEST SERIES #1

TEST TEMPERATURE PRESSURE AIR DENSITY EQUJIVALENCE RATIO STEAM MOLE FRACTION

11

12

13

14

15

63

64

65

66

67

68

69

70

71

72

LB

274.9

275.6

279.1

275.6

279.1

292.1

298.1

296 .6

299.1

292.6

297.6

296.6

300.1

297.6

301.6

(C)

MP

276.9

277.6

281.1

277.6

281.1

294.1

300.1

298.6

301.1

294 .6

299.6

298 .6

302.1

299.6

303.6

UB

278.9

279.6

283.1

279.6

283.1

296.1

302.1

300.6

303.1

296.6

301 .6

300.6

304 .1

301.6

30S.6

LB

99174.

99863.

97864.

97795.

97312.

100112.

100249.

100043.

100318.

100112.

100112.

100180.

100180.

100249.

100249.

(PA)

MP

99284.

99974.

97974.

97905.

97423.

100801.

100939.

100732.

101008.

100801.

100801.

100870.

100870.

100939.

100939.

UB

99394.

100084.

98084.

98016.

97533.

101490.

101628.

101422.

101697.

101490.

101490.

101559.

101559.

101628.

101628.

(MOLES)

LB MP

35.534 35.798

36.255 36.523

35.739 36.001

36.203 36.471

35.664 35.925

33.667 34.035

33.240 33.597

33.627 33.985

33.888 34.246

35.038 35.409

34.205 34.565

34.018 34.379

15.544 15.837

13.817 14.113

11.497 11.782

UB

36.062

36.792

36.262

36.739

36.185

34.403

33.954

34.344

34.604

35.779

34.925

34.741

16.130

14.408

12 .067

LB MP

0.4498 0.4792

0.4046 0.4334

0.3534 0.3813

0.3529 0.3812

0.3465 0.3743

0.4737 0.5037

0.4575 0.4867

0.4334 0.4623

0.3965 0.4248

0.3583 0.3868

0.3788 0.4071

0.4048 0.4335

3.5773 3.6647

4.3527 4.4655

5.5574 5.7129

U8 LB

0.5085 0.0031

0.4622 0.0037

0.4092 0.0038

0.4094 0.0027

0.4021 0.0028

0.5336 0.0000

0.5158 0.0000

0.4912 0.0000

0.4631 0.0000

0.4152 0.0000

0.4353 0.0000

0.4621 0.0000

3.7521 0.0000

4.5783 0.0000

5.8684 0.0000

MP

0.0031

0 .0037

0.0038

0.0027

0.0028

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

UB

0.0031

0.0037

0.0038

0.0027

0.0028

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

TEST SERIES #2

TEST TEMPERATURE

16

17

18

19

20

21

LB

283.4

275.0

281.2

277.8

284.5

289.5

(K)

MP

285.4

277.0

283.2

279.8

286.5

291.5

UB

287.4

279.0

285.2

281.8

2881.5

293.5

PRESSURE

(PA)

LB MP

106551. 106658.

106585. 106691.

106551. 106658.

106818. 106925.

106618. 106725.

106618. 106725.

UB

106765.

106798.

106765.

107031.

106831.

106831.

LB

35.01

34.8

30.6

26.9

27.9'

30.11

AIR DENSITY

(MOLES)

MP

34 35.337 35

46 35.104 35

74 30.897 31

23 27.124 27

53 28.155 28

53 30.367 30

EQUJIVALENCE RATIO

JB

.590

.362

.121

.324

.358

.580

LB MP

0.4589 0.4877

0.5672 0.5977

0.7227 0.7558

0.9953 1.0338

0.7983 0.8342

0.6863 0.7182

UB LB

0.5165 0.0406

0.6282 0.0409

0.7889 0.0912

1.0723 0.1428

0.8700 0.1425

0.7502 0.0914

MP

0.0500

0.0505

0.1000

0.1509

0.1505

0.0999

UB

0.0594

0.0601

0. 1088

0. 1590

0. 1585

0. 1085

C02 MOLE FRACTION
Table C-4 (cont'd.)

Test Series #2 (cont'd.)

C-)

22 294.5 296.5 298.5

23 283.9 285.9 287.9

24 288.4 290.4 292.4

25 292.5 294.5 296.5

TEST SERIES #3,4

TEST TEMPERATUJRE

(C) LB MP UB

39 367.1 389.1 371.1

41 367.1 389.1 371.1

42 366.1 388.1 370.1

50 371.1 373.1 375.1

51 370.1 372.1 374.1

52 369.6 371.6 373.6

53 369.6 371.6 373.6

54 369.1 371.1 373.1

55 371.1 373.1 375.1

568 370.6 372.6 374.6

57 371.1 373.1 375.1

58 370.6 372.6 374.6

59 370..1 372.1 374.1

60 370.1 372.1 374.1

61 369.1 371.1 373.1

62,370.1 372.1 374.1

73 371.1 373.1 375.1

74 369.6 371.6 373.6

75 370.1 372.1 374.1

76 370.1 372.1 374.1

77 370.1 372.1 374.1

78 368.6 370.6 372.6

79 369.8 371.8 373.8

80 369.1 371.1 373.1

106685. 106791.

106551. 106658.

106551. 106658.

106551. 106658.

106898. 32.945 33.174 33.403

106765. 28.703 28.911 29.118

106765. 29.158 29.386 29.574

106765. 31.986 32.210 32.435

0.5369 0.5652

0.7208 0.7559

0.8048 0.8379

0.6430 0.6723

0.5936

0.7909

0. 8709

0.7017

PRESSURE AIR DENSITY

(MOLES)

EQ.UIVALENCE RATIO STEAM MOLE FRACTION

LB

225113.

177539.

160509.

236007.

260380.

291716.

181952.

200568.

225940.

171127.

254416.

189536.

212151.

160234.

177746.

149547.

147961.

146996.

171265.

154649.

148995.

159958.

177539.

165887.

(PA)

MP

225803.

178229.

161199.

236696.

261069.

292406.

182641.

201257.

226630.

171817.

255105.

190226.

212840.

160923.

178436.

150236.

148650.

147685.

171955.

155338.

149685.

160647.

178229.

166577.

.UB

226492.

178918.

161888.

237386.

261759.

293095.

183331.

201947.

227319.

172506.

255795.

190915.

213530.

161613.

179125.

150926.

149340.

148375.

172644.

156028.

150374.

161337.

178918.

167266.

LB

40 .955

41. 127

40.424

41. 220

41. 138

41. 218

41. 220

41. 162

41.053

41. 110

41. 109

41.052

40.920

41. 165

41. 117

40.958

41. 096

41. 253

41. 249

41. 275

41. 375

41. 219

41. 327

41.442

MP

41. 333

41. 487

40.745

41. 535

41. 454

41.534

41.6535

41.476

41. 366

41. 424

41. 423

41. 365

41. 233

41.480

41. 432

41.269

41. 413

41. 569

41. 565

41.591

41. 692

41.536

41.644

41.760

UB LB MP

41.711 0.7862 0.8167

41.847 0.5829 0.6102

41.066 0.6253 0.6501

41.851 1.9618 1.9974

41.771 1.9369 1.9724

41.849 1.9350 1.9704

41.851 0.9826 1.0098

41.791 0.9765 1.0036

41.680 0.9812 1.0082

41.738 0.7830 0.8085

41.737 0.9781 1.0051

41 .679 0.7857 0.8111

41.546 0.7930 0.8185

41.794 0.5820 0.6059

41.746 0.5955 0.6195

41.581 0.3990 0.4213

41.729 0.3526 0.3747

41.885 0.3355 0.3575

41.881 0.4713 0.4943

41.907 0.4751 0.4981

42.009 0.3606 0.3827

41.852 0.5848 0.6088

41.960 0.5779 0.6018

42.078 0.6738 0.6985

UB

0.8472

0 .6374

0.6750

2.0329

2.0078

2.0057

1.0369

1.0306

1.0353

0.8339

1. 0322

0.8366

0.8440

0.6297

0.6435

0 .4437

0.3967

LB MP UB

0.2415 0.2483 0.2550

0.0955 0.1033 0.1110

0.0038 0.0038 0.0038

0.0000 0.0000 0.0000

0.0956 0.1026 0.1095

0.1956 0.2018 0.2080

0.0000 0.0000 0.0000

0.0901 0.0972 0.1043

0.1896 0.1960 0.2023

0.0000 0.0000 0.0000

0.2821 0.2877 0.2934

0.0904 0.0975 0.1046

0.1901 0.1965 0.2028

0.0000 0.0000 0.0000

0.0919 0.0990 0.1062

0.0000 0.0000 0.0000

0.0000 0.0000 0.0000

0.0408 0.0498 0.0588

0.1419 0.1500 0.1581

0.0916 0.1001 0.1086

0.0396 0.0486 0.0577

I

0.3794 0.0000

0.5173 0.0903

0.5212 0.0000

0.4048 0.0000

0.6327 0.0000

0.6256 0.0898

0.7232 0.0000

0.0000 0.0000

0.0975 0.1046

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0970 0.1041

0.0000 0.0000
Table C-4 (cont'd.)

Test, Series #3,4

81370.3 372.3

82 389.8 371.6

83 371.3 373.3

84 370.3 372.3

85 370.9 372.9

88 370.5 372.5

87 372.3 374.3

88 370.3 372.3

89 372.3 374.3

90 372.0 374.0

(cont'd.)

374.3 195328.

373.6 176091.

375.3 238489.

374.3 181883.

374.9 216150.

374.5 209324.

376.3 258277.

374.3 290061.

376.3 250141.

376.0 204222.

196017.

176781.

239178.

182573.

216839.

210014.

.268968.

290751.

250830.

204911.

196707.

177470.

239868.

183262.

217529.

210703.

259656.

291440.

251520.

205601.

41.328 41.645

41.275 41.591

41.175 41.490

41.308 41.625

41.295 41.611

41.331 41.647

41.209 41.523

41.298 41.613

41.098 41.412

41.285 41.599

41. 961

41.908

41.804

41.941

41.928

41. 963

41.837

41. 929

41. 726

41.914

0.6687 0.6932

0.8701 0.8964

0.8742 0.9003

0.9687 0.9957

0.9753 1.0024

1.4687 1.5000

0.9751 1.0021

2.9632 3.0077

0.8767 0.9028

0.8724 0.6969

0.7178

0.9226

0.92865

1.0228

1.0295

1. 5313

1.0291

3 .0522

0. 1446

0.0000

0.256W

0.0000

0. 1495

0.0000

0.2892

0.0000

0. 1514

0.0000

0.2624

0.0000

0.1562

0.0000

0.2948

0.0000

0. 1581

0.0000

0.2683

0.0000

0. 1628

0.0000

0.3004

0.0000

0.9290 0.2903 0.2959 0.3015

0.7214 0.1792 0.1856 0.1921

I-.

TEST SERIES #6

TEST TEMPERATURE

(K)

LB MP LB

91 293.9 295.9 297.9

92 290.9 292.9 294.9

93 291.4 293.4 295.4

94 290.4 292.4 294.4

95 292.6 294.6 296.6

96 293.3 295.3 297.3

TEST SERIES #8

TEST TEMPERATURE

(K)

LB MPw LB

46 285.6 287.6 289.6

47 321.1 323.1 325.1

48 371.1 373.1 375.1

49 370.1 372.1 374.1

PRESSURE

(PA)

LB MP

186089. 188778.

143273. 143962.

134854. 135344.

126038. 126725.

122037. 122726.

117762. 118452.

LB

187488.

1448652.

138033.

127415.

123416.

119141.

AIR DENSITY

(MOLES)

LB MP LB

41.127 41.526 41.925

41.126 41.527 41.927

41.140 41.541 41.942

41.210 41.612 42.014

41.057 41 .468 41.855

40.948 41.343 41.741

LB M

1.9329 1.9776

0.9771 1.0116

0.7714 0.8038

0.5733 0.6038

0.4719 0.5011

0.3709 0.3989

LB LB

2.0223 0.0000

1.0461 0.0000

0.8381 0.0000

0.6340 0.0000

0.56303 0. 0000

0.4270 0.0000

MP LB

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

EQUJIVALENCE RATIO STEAM MOLE FRACTION

PRESSURE

(PA)

LB MP

100112. 100801.

100318. 101008.

100180. 100870.

100180. 100870.

LB

101490.

101697.

101559.

101559.

AIR DENSITY

(MOLES)

LB MP LB

34.554 34.932 35.309

30.625 30.988 31.352

26.815 27 .080 27.346

26.830 27.096 27.382

EQUIVALENCE RATIO STEAM MOLE FRACTION

LB MP

0.4506 0.4807

0.4480 0.4788

0.4481 0.4701

0.4606 0.4848

LB LB

0.5107 0.0043

0.5096 0.0050

0.4942 0.0030

0.5091 0.0000

MP LB

0.0043 0.0043

0.0050 0.0060

0.0030 0.0030

0.0000 0.0000
Table C-4 (cont'd.)

TEST SERIES #7

TEST TEMPERATURE

(K)

LB MP UB

11 274.9 278.9 278.9

44 368.1 370.1 372.1

45 321.8 323.6 325.8

PRESSURE AIR DENSITY EQUJIVALENCE RATIO

(PA) (MOLES)

LB MP UB LB MP LB LB MP LB

98595. 99284. 99974. 35.402 35.798 38.194 0.4480 0.4792 0.5103

127001. 127690. 128380. 33.978 34.269 34.561 0.4818 0.4853 0.5087

111212. 111902. 112591. 34.108 34.444 34.779 0.4468 0.4736 0.50W3

STEAM

LB

0.0031

0.0061

0.0074

MOLE FRACTION

MP UB

0.0031 0.0031

0.0061 0.0061

0.0074 0.0074

I-A

-J

APPENDIX D

ESTIMATE OF UNCERTAINTY BOUNDS

The uncertainty bounds associated with four measured quantities, detonation cell width, detonation pressure, detonation

velocity and thermodynamic state of the mixtudre will be discussed.

D.l DETONATION CELL WIDTH

Obtaining detonation cell size (or width) data from a smoked

foil still remains more of an art than a science, and hence, the

uncertainty of the measurement is difficult to estimate. In

fact, the long accepted postulate that there exists a single

dominant mode, or detonation cell width, for a given fuel-air

mixture has been recently questioned [D1]. A typical smoked foil

record from a detonation in a H2 -air mixture is shown in Figure

D-1. Casual observation shows a range or distribution of structure. If this range of structure is interpreted as representing

a detonation with a single dominant mode that is continually

being perturbed, then an estimator of the variability in size, or

width, of that mode has some meaning. If the range of structure

is interpreted as representing a detonation with multiple modes,

or length scales, then a single variance estimator is meaningless.

The exp eriments conducted in this report were not intended

to, address the question of detonation cell width distributions.

The currently accepted procedure, i.e., to select a single detonation cell width for a given mixture at a given initial thermodynamic state, is the approach taken for this report. The method

of estimating the uncertainty associated with the procedure is

discussed below.

D.1.1 Method of Estimating Detonation Cell Width

The method used to determine the detonation cell size is

termed the dominant mode method [D2]. The method is illustrated

in Figure D-1. Long-running parallel lines (relative to the

spacing between the lines) are used to determine the dominant

mode as in Figure D-l(b). Long parallel lines typically run

three to ten times the spacing between the lines. Unfortunately,

the lines are never perfectly parallel and appear to fade in and

out (change in contrast) along their length. Therefore, experimenter judgement is used to determine what degree of parallelness

and contrast in variation are acceptable in determining a long

running line. Typically, the space between three or four parallel lines is measured for each foil and averaged to determine the

most probable detonation cell width.

D-1
(b)

Figure D-1. Detonation Cell Width Measurement (a) Use of

High Contrast Individual Cells, (b) Use of

High Contrast Long Running Lines

D-2
Depending on how line length and contrast ratio are defined,

and the relative weight given to each criterion, different values

of detonation cell width can be selected. Since there is no

fundamental physical reasoning which yields the proper balance of

the two criteria, subjectivity is required. In other words,

there is no a priori reason that a detonation cell width selected

by one method over the other plays a more fundamental role in

determin 'ing the propagation properties, or is more representative

of the chemical-hydrodynamic coupling.

In general, one would expect that detonation cell width

measurements would be more accurate for near-stoichiometric detonations where the cells are small compared to the size of the

smoked foil. However, the advantage of a larger sample size is

offset by lower contrast on the foil (due to weaker transverse

structure) which makes the lines harder to distinguish. Because

of these competing effects, it is not clear that detonation cell

width can be more accurately measured for certain reactant concentrations than for others.

For the HDT tests, R. Knystautas of McGill University,

Montreal, P.Q., Canada instructed the authors in his version-of

the dominant cell method. Because of the complexity of the

pattern and the large change of length scales, the variability in

line length and contrast is large over the spectrum of mixtures

tested. For this reason it is not possible to assign quantitative values for the criteria used. Most of th e smoked foil

records have been independently reviewed by Benedick and Tieszen

as discussed in the next section. Where multiple observers have

reviewed a single foil, more than one detonation cell size is

usually selected. In many cases, a range is selected because it

is almost impossible to select a single value for detonation cell

width. Heavy weight was given to the measurements made by R.

Knystautas because of his experience in making detonation cell

width measurements in many different laboratories.

To select a single value from a range of detonation cell

widths, a technique commonly used by other researchers is used

[D3]. In using this technique, the ranges of detonation cell

width are plotted as part of a family of curves. Certain smoothness properties are assumed about the shape of the best fit curve

that is drawn through the data. It is this "best fit line" which

becomes the locus of detonation cell width values, called the

"most probable" values in this appendix. Figures D-2 and D-3

show the range of data and the best f it line which yields the

most probable detonation cell widths for test series #3 and #5.

The best fit line is established by appropriate weighting of

two criteria. The first criterion is that, for a given test, a

subjective confidence level is established for the data point by

each individual. Individuals who independently review the foil

may have low, medium, or high confidence -in their ability to

interpret the track spacing on the smoked foil based on their

D-3
I I I I

1000- :Benedick Individually

Idvdually

:Benedick/Tieszen

Team

+1- 25% of MP

Mos ý t P irobab' l e- -(W1

E

0

a

0

0

A

100-

/

/ A

10- I

U- -

3-T

0.3 1

I I

Equivalence Ratio-O

Figure D-2. Detonation Cell Width Measurements for HDT Test

Series #3 (H2 -Air, Pair = 41.6 moles/rn 3 , T=1000 C).

D-4
1000 -w * F a I I I

Benedick

Knystautas

A

I

LI

I

-c

4-'

0

C

0

4-.

0

C

0

4-.a)

0

Tleszen

--- +/- 25% of MP

Mosit Probabl~le (MPj)

' X'4 I

I

100-

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

a

r

I

10- a' - a'

I I I I I

0.3

Equivalence Ratio -

Figure D-3. Detonation Cell Width Measurements for HDT Test

Series #5 (H2 -Air, Pair = 41.6 moles/rn 3 , T=20*C).

D-5
experience and the complexity of the pattern on the particular

smoked foil. Additional weight was given to the estimates of R.

Knystautas due to his experience.

The second criterion is that the functional dependence of

detonation cell width on equivalence ratio is a smooth "U"-shape

curve. The smoothness property can be stated as:

aXis continuous and >0

For the case where 0<1, the gradient, awo is negative and

tends to zero. For the case where 0>1, the gradient is positive

and for 06=1, the gradient is zero.

The application of the second criterion requires that data

be examined as a whole while the first criterion examines each

data point individually. Subjective judgement is then used to

select the line through the data that best matches the two criterion. This is the method used to determine the most probable

values of detonation cell width.

This technique can only be applied with confidence if there

is a large number of points measured for a given family of

curves, and if the range of data selected by independent observations for any one test is smaller than the differences between

tests. Fortunately, detonation cell widths cover two to three

orders of magnitude in the H-DT. For those tests where it was

subjectively felt that there was not enough data to justify a

best fit function, weight was usually given to R. Knystautas's

measurement. The exact criteria used for each test series is

given in section D.1.3 following a discussion of uncertainty

bounds.

D.l.2 Uncertainty Bounds for Detonation Cell Width

Measurements

Establishing uncertainty bounds on the dominant mode detonation cell width is difficult because the definition of the

dominant mode is subjective. As discussed above, in using the

dominant mode method two criteria are applied (a) the length of

parallel running bands and (b) the contrast ratio. Depending on

the relative weight of these criteria different values of the

dominant mode can be selected. Because of this reason, uncertainty bounds that consider both variability and bias are extremely difficult to establish.

one method of estimating the uncertainty bound is to assume

that there is no bias error, i.e., the criteria used to select

the detonation cell width is correct and consistently applied.

A single observer will probably give more self-consistent

interpretations than will multiple observers because of bias.

D-6
Bounds obtained by this method are "relative" to the criteria

used by the individual observer. They are useful for determining

the significance of a change in detonation cell width as measured

by a single observer. A different observer with a different bias

may easily select detonation cell widths outside of the uncertainty bounds obtained by this method.

A bound estimator of detonation cell width that includes

both variability and bias must be made with multiple observers

making independent measurements. The multiple observers would

use their individual criteria of line length and contrast ratio

to determine the detonation cell width. This type of bound would

be wider than that on a single observer because of the broader

range of criteria application of the multiple observers. A bound

determined by this method may be quite large and may hide real

trends in the data simply because there is no accepted quantitative criteria available for the selection of detonation cell

width.

However, in spite of the difficulties in establishing meaningful uncertainty bounds, the authors feel that some variability

estimate is necessary to give safety analysts some qualitative

"feel" for the uncertainties involved. Bounds will be estimated

using a comparison between test apparatus, where the foil has

been read by a single observer and by multiple observers of

selected tests.

D.1.2.1 Comparison Between Test Apparatus

Figure D-4 shows a comparison between the detonation cell

width measurements made for test series #1 where those measurements overlap the measurements at McGill University [D3],. The

detonation cell width measurements in the HDT and at McGill

University were made by R. Knystautas of McGill University.

During test series #1, R. Knystautas instructed the authors in

measuring detonation cell width. An uncertainty bound estimate

of +/-25% of the McGill University data completely include the

HDT data. The range of equivalence ratio in this comparison is

not large, compared t6 the range covered in the HDT test series

but the range of detonation cell width covered is a substantial

fraction of the detonable range in the HDT, and as such, represents a fair comparison. This result suggestsý that relative

bounds (i.e., neglecting bias error) can be e-stimated to be

+/-25% of the data.

D.1.2.2 Multiple Observers

Figure D-5 shows the measured detonation cell width for all

tests in the HDT where more than one individual measured the

detonation cell width independently. The measured detonation

cell width by the individual author has been divided by the

measurement of R. Knystautas to normalize the data. For the

dozen or so tests where R. Knystautas selected a range of detonation cell width, the center of the range was used to normalize

D-7
800 I

* HDT Data

* McGill Data

+/- 25% of McGill Data 700+

E

0

CO

C:

0

'A

600+

A

500±

400+

300+

200±

100±

10.3750.400 0.425 0.450 0.475 0.500 0.525

Equivalence Ratio -0

Figure D-4. Comparison of Detonation Cell Width Data Between

the HDT and McGill University. (HDT Test Series

#1, P=1 atm, T=25*C).

D-8
000%. Benedlck/Tleszen

co ~ Teamn :Bonedick

-IndIvIdually E =Tleszen

1zIndivIdually

co

Eu

.j

0-3-

10 20 30 40 50 60 70 80 90 100

Test Number

Figure D-5. Normalized Detonation Cell Width (XAuthor/X Knystautas)

vs. HDT Test Number.
the other individual's measurement. Where the individual

selected a range, two symbols linked with a line are shown; where

the individual selected a single detonation cell width only one

symbol is shown. often when a range is shown, the detonation

cell width is not necessarily continuous across the range, but

may appear to the individual to be in discrete subranges. This

includes the cases where the individual decided the detonation

was either one end of the range or the other.

As expected, the variability in the data is higher than that

in the previous comparison between test apparatus where the

smoked foils were measured by a single individual. The horizontal lines in Figure D-5 represent a factor of 2 of the normalized

value. Most of the data only had two independent observations,

R. Knystautas and a joint observation by S. Tieszen and W.

Benedick, however, later tests had three independent measurements.

Some of the data haves been plotted in Figures D-2 and D-3

as a function of equivalence ratio. Relative bounds of +/-25%,

have been also been drawn. For the most part the +/-25% bounds

cover the measurements made by R. Knystautas. In most instances,

the measurements by S. Tieszen are higher than the values measured by the other individuals. This is an example of using

different criteria to select detonation cell width. In informal

discussion, it was found that S. Tieszen placed more emphasis on

contrast than the other observers.

D.1.3 Bounds on the HDT Test Series

The numerical values for the estimated detonation cell

widths (most probable, or MP values) and the corresponding estimates for the uncertainty bounds (LB and UB values) are listed in

Appendix C by test series. The subjective judgement used to

establish the most probable value of detonation cell width and

the corresponding uncertainty bounds is described below.

For the first test series, the most probable values of

detonation cell width is assumed to be the measured value of R.

Knystautas, except for test HT-15 where Tieszen & Benedick's

measurement is used. The uncertainty bounds are assumed to be

+/-25% of the most probable value as in Figure D-4.

For test series #2, the most probable value -of the detonation cell width is assumed to be the measured value of R.

Knystautas, except for test HT-23 where the high end of the

Ties~zen & Benedick range is used. The uncertainty bounds are

assumed to be +/-25% of the most probable value, or the range of

individual measurements, whichever is larger.

For test series #3 and #4, the most probable value of the

detonation cell width is assumed to be the value predicted by the

best fit function (described in the last section) through the

data. The uncertainty bounds are assumed to be +/-25% where the

D- 10
data are "dense" and many tests are used to define the most probable curve, that is for 0 • 1 and XH20 • 0.1. Elsewhere, if only

one individual measured the smoked foil, then the bounds are

assumed to be a factor of 2 of that reading. If more than one

individual measured the foil, then the bounds are assumed to be

+/-25% or the range of the individual measurements, whichever is

larger. Data from test series #3 is shown in Figure D-2.

For test series #5, the most probable value of detonation

cell width is assumed to be the value predicted by the best fit

function through the data for 0 • 1 and the value measured by

R. Knystautas for 0=2. The uncertainty bounds are assumed to be

+/-25% where the data is relatively dense for 0 ý 1, and the

range of the individual measurements for 0=2. Data f rom test

series #5 is shown in Figure D-3.

For test series #6 and #7, the most probable value of detonation cell width is assumed to be the value measured by R.

Knyst~autas. The uncertainty bounds are assumed to be +/-25% or

the range of the individual measurements, whichever is larger.

An emphasis has been placed on the +/-25% bounds for the

detonation cell width in selecting the above criteria. The

primary reason for emphasizing this criterion is that we feel

that factor-of-2 bounds artificially hide real trends that exist

in the data because there is no accepted way to select detonation

cell size. However, for safety analysis, the authors strongly

recommend that the factor-of-2 bounds be universally applied and

that the detonation cell width (MP value) be divided by 2 for use

in safety calculations. In some cases, this may be conservative

and in other cases it may not be, but it is necessary to reduce

the possible effect of observer bias.

D.2 DETONATION PRESSURE

Detonation pressure measurements are made with dynamic

piezoelectric gages made by two companies, Kistler and PCB. The

performance of the pressure gages to measure detonation pressure

is rather erratic compared to values predicted by Chapman-Jouguet

(C-J) values and, for this reason, pressures were not presented

in the main text. From decades of research, the expected values

of detonation pressure are 10 to 15% below those predicted by the

C-J theory. In the HDT, typical measured pressure-peak deviations from the Chapman-jouguet value are +/-20%. The sources of

variability in the. pressure measurements include the response

time of the gages, digitizing frequency, calibration of the

gages, excitation of the gages from the couplers, the effect of

temperature, and vibration in the gage mount.

The face of each transducer is perpendicular to the direction of propagation of the detonation front. The gage faces are

on the order of 2 mm in diameter. Since detonation cell width

for stoichiometric H2 -air mixtures is on the order of 8 -15 mm,

D- 11
the transducers should be able to resolve the pressure

distribution in a cell provided the rise time is sufficiently

fast. The Chapman-Jouguet pressure is related to the ave .rage

.pressure in a cell and should easily be resolved.

Detonations in H2 -air mixtures propagate on the order of

2000 rn/s. Since the transducer face is on the order of 2 mm, it

takes about 1 ,as to sweep the face of the transducer. The natural frequency of each type of transducer is quite high, 250 kHz

for the Kistler and 500 kHz for the PCB. The rise time for each

transducer is 1 #ss. This rise time is fast enough to respond to

the peak pressure averaged over the face of the transducer. The

signals from the transducers are recorded on Textronix 7612D and

BI RA digitizers. The digitizing rate on the 7612D's depended on

the test, either 10 14s or 1 14s per point (see Table A-5) while

the BI RA digitizers were fixed at 25 #ss per point. The data

digitized at 1 jus are sufficient to resolve the peak pressure

averaged over the face of the transducer, and hence, the average

pressure in a cell.

In addition to the standard uncertainty in the linearity and

hysteresis of a gage, which are given by the manufacturer as

<+/-l%, its calibration is sensitive to the input voltage provided to the gage by the couplers and the surrounding temperature. Sandia calibrations indicate that the manufacturers'

estimates of linearity and hysteresis is good. However, during

testing, the voltage supplied by the couplers was never recorded.

Kistler indicates that their gages have a 0.5%/volt sensitivity.

The PCB is assumed to have the same sensitivity, Voltage readings taken at random times during the testing, to verify that the

batteries in the couplers were not too weak, indicated that the

voltage ranged from 21V to 27V. Therefore, the calibration may

be in error by 3% due to voltage supply.

The effect of temperature on each type of gage is different.

On Kistler gages the sensitivity is -0.03%/0 F and on PCB gages

the sensitivity is +0.01%/*F. The temperature of the. gages is

assumed to be 1000C but the electronics in the back of the gages

which are also temperature sensitive may be at a different temperature. The calibrations used in assigning engineering units

to data plots have not taken the effect of the gage temperature

into account; however plots from the BI RA data clearly show a

negative drift for the Kistler gages and a positive drift for the

PCB gages over a period of milliseconds for gages where the RTV

face had decayed. It is assumed that data taken 6ver the period

of microseconds after the arrival of the detonation front are

unaffected by temperature.

The combined effect of linearity, low voltage and hysteresis

do not explain differences of +/-20% from the Chapman-Jouguet

values. Typical pressure traces from PCB and Kistler transducers

for tests with large and small cell width are shown-in Figs. D-6

through D-9. It is obvious from the figures that there are large

oscillations on the recorded pressure traces. These oscillations

D- 12
400

0~

CO,

0o(D

Q)

300

200

100

0

(~A~

-100

35.0 40.0 45.0 50.0

Time (Seconds)

55.0 *104

Figure D-6. Typical PCB Pressure Tr

(X = 5 mm, Test HT-84).

ace - Small Cell Width
400

300

(-

CO,

CL

(D

200

100

0

-100

-200

30.0 35.0 40.0 45.0

Time (Seconds)

50.0

-,4

Figure D-7. Typical Kistler Pressure Trace - Small Cell Width

(X = 5 mm, Test HT-84)
450 -I --

350+±

aY)

C',

CL

0)

250+1

I-. 150 4

/J \

.1

I

50 -

-50

45.0 ,50. 0 55.0

Time (Seconds)

60.0 65.0

*10-4

Figure D-8. Typical PCB Pressure Trace - Large Cell Width

(X = 400 mm, Test H-T-96).
450

CO)

LM

03

0.

350

250

150

50

I-.

-50

35.0 40.0 45.0 50.0

Time (Seconds)

55.0

*10.4

Figure D-9. Typical Kistler Pressure Trace - Large Cell Width

(X = 400 mm, Test HT-96).
can be attributed to the transverse waves in the threedimensional detonation structure. However, the oscillations

begin before the arrival of the pressure peak; therefore, the

most probable source of the oscillations is vibration of the gage

mount due to radial vibrations in the, tube caused by the detonation. Because these oscillations can be +/-50% of the signal

level, it was felt that spectral analysis would not completely

separate the noise from the transverse wave structure.

Further, a comparison of the PCB and Kistler data shows that

the PCB indicates a very large "overshoot." The overshoot can be

explained as the von Neumann spike; however, the Kistler gages

for the same test do not show this spike. Therefore, the most

probable source for this overshoot is loading of the quartz gage

face by the internal mount.

Because of the high degree of noise in the pres .sure data and

the possible large variations from the Chapman-jouguet 'value

which can not be explained by standard calibration uncertainties,

the peak pressure data taken during the tests are not reported.

D.3 DETONATION VELOCITY

Detonation velocity i's determined by taking the time of

arrival of the detonation as determined by the initial break in

slope of the pressure transducer data divided by the distance of

the transducer from a reference point. The variability of velocity measurements arises from the uncertainty in the location of

the transducers, the digitizing frequency and the resolution of

the break in slope on the data plots. The type, number and

digitizing frequency of the transducers for each test is given in

Table A-5 of Appendix A. Two types of recording devices were

used. Both are discussed in Appendix A. one type is called

CAMAC and the other is made by Tektronix (7612D).

The variability associated with determiningdetonation velocity from a single transducer is reduced by taking a linear

regression of all time of arrival vs. distance data. For the

analysis in this report, the independent variable was taken to be

the location of the transducer and the dependent variable was

taken to be the time of arrival. The slope of the linear regression line is the reciprocal of the detonation velocity. A standard deviation is calculated for the reciprocal of the detonation

velocity and 95% confidence bounds are calculated using a standard statistical procedure. The calculations were made using a

procedure from the SAS library [D4].

In the above analysis, the detonation velocity was assumed

to. be constant along the entire length of the tube, which it is

not. Since the detonation is started from a high explosive

charge, the detonation velocity is overdriven at the start.

Constant detonation velocity indicates a steady-state wave has

been reached. In test HT-11 through 72 the closest pressure

D- 17
transducer to the explosive initiator was placed no closer than

1.3 m from the explosive. In tests HT-73 through 96 more pressure records were taken and the first transducer was located

0.749 m from the explosive and the second transducer was located

2.273 m from the explosive.

The latter data were used to establish that the detonation

had reached steady state by 2.273 m from the explosive. A linear

regression fit to the data from each test was made for six cases.

Two different amounts of explosive were used to initiate the

charge, nominally 40 grams and 80 grams. For each of these

,Charge weights, three cases were considered. The first case used

all the data including the data from the transducer at 0.749 m.

The second case used all the transducer data except from the

transducer 0.749 m from the explosive, and the third case. used

all the data except for the transducers at 0.749 m and 2.273 m

from the explosive. The first transducer data used in the second

(third) case came from the port located at 2.273 m (4.407 m) from

the explosive.

Differences were taken of the detonation velocity between

cases #1 and #2, and between #2 and #3 for each of the charge

weights. The results are summarized in Table D-1. The difference in detonation velocity between cases #1 and #2 of 6.1 m/s

Table D-1

Effect of Initial Transient on

Detonation Velocity

Initiation ,Case Mean Difference STD Error

Charge in velocity of the

Weight (m/sec) Mean Diff.

grams) ___________(m/s)

80 DIFFi 6.1 3.1

80 DIFF2 2.5 2.7

40 DIFFi 2.4 1.1

40 DIFF2 -0.17 1.6

DIFF1 M Detonation velocity calculated with all data minus

detonation velocity with all data except for the

first transducer at 0.749 m from the initiator.

DIFF2 --:Detonation velocity calculated with all data except

for the first transducer at 0.749 m from the initiator minus the detonation velocity with all data

except the first two transducers at 0.749 m and

2.273 m from the initiator, respectively.

D- 18
for the 80 gram initiating charge and 2.4 m/s for the 40 gram

initiating charge show that the detonation had a higher velocity

at the first transducer, located 0.749 m from the initiating

charge, than at the remaining downstream transducers. These

differences are judged to be significantly different from zero.

The difference in detonation velocity between cases #2 and #3 of

2.5 m/s for the 80-gram initiating charge and -0.17 rn/s for the

40-gram initiating charge are judged not to be significantly

greater than zero. These results indicate that the estimated

velocity is statistically the same whether the data from the

second pressure transducer at 2.27 m from the initiator is included or excluded from the linear regression. Therefore, the

detonation has reached steady state by 2.27 m from the initiator.

Table D-2 lists the upper and lower bounds for the velocity

data for each test. These bounds are the the reciprocal of the

confidence bounds calculated for the reciprocal of the velocity.

Only data 2.273 m or farther from the explosive are used in the

table.

The data from the Tektronix 7612D's almost always have

smaller uncertainty bounds due to the higher digitizing frequency. Therefore, the data from the 7612D's were used when

available. In some instances, no 7612D data was available; in

these cases, the CAMAC data was used. The data with bounds are

listed by Test Series in Appendix C.

D.4 THERMODYNAMIC STATE

Six variables are used in this report to specify the initial

thermodynamic state of the gaseous mixtures. The six variables

are: the temperature prior to initiation of detonation, T; the

density of the air in the mixture, Pair; pressure prior to initiation of the detonation, P; the equivalence ratio, 0; the mole

fraction of steam, X1120 ; and the mole fraction of carbon dioxide,

XC02. For binary 112-air mixtures only three thermodynamic variables are required to specify the initial state. For ternary 112-

air-H2 0, or H2 -air-C02 mixtures four variables are needed to

specify the initial state. The variables chosen for each test

series is listed in Table D-3.

of the six variables used to specify the initial thermodynamic state of the mixtures, only two, the temperature and pressure prior to initiation of detonation, are measured directly.

The other variables are inferred from temperature and pressure

measurements. The relationships between various thermodynamic

variables are derived in Appendix E. Table D-4 lists the temperature and pressure measurements made for each test and defines

a numbered subscript for each measurement.

D- 19
Table D-2

Upper and Lower Bounds on the Detonation Velocity (kin/sec)

7612 CAMAC

Test Sample Lower

size bnd.

Vel. Upper Sample Lower Vel.

est. bnd. size bnd. est.

11

12

13

14

15

16

17

18

19

20

21

22

23

24

26

28

29

31

33

36

37

38

39

40

41

42

43

44

45

46

47

48.

49

50

51

52

53

54

ý1. 5314

1.5073

0.7918

1. 3707

1. 3964

1. 4533

1. 6040

1. 6057

1.6708

1. 5571

1. 6085

1. 5299

1. 5219

1. 6980

1. 6659

1. 9085

1. 8325

1. 5850

1. 8357

1. 9743

1. 7868

1. 7285

1.7129

0. 7797

1. 6607

1. 7327

1. 6148

1. 5847

1. 5850

1. 5819

1. 5748

1. 57 15

1. 5903

2.1375

2. 0179

1. 9349

1. 9585

1. 9112

1. 5879

1. 5287

0. 8478

1. 4523

1. 4103

1. 4766

1. 6321

1. 6437

1.6845

1. 5949

1,~6156

1. 5682

1. 5567

1. 7115

1. 6969

1. 9291

1. 8468

1. 6009

1. 8492

1. 9833

1. 7993

1. 7645

1: 7305

0. 8351

1. 6672

1. 7491

1. 6198

1. 5955

1. 5905

1. 5885

1. 5854

1. 5776

1. 5988

2.1555

2. 0542

1. 9549

1. 9865

1. 9303

1.6488

1. 5507

0.9 123

1. 5443

1. 4245

1. 5007

1. 66 12

1. 6836

1. 6985

1.6347

1. 6228

1. 6086

1. 5931

1. 7252

1. 7290

1. 9500

1. 86 14

1. 6172

1. 8628

1. 9924

1. 8119

1. 8021

1. 7484

0. 8989

1. 6737

1. 7658

1. 6250

1. 6065

1. 596 1

1. 5950

1. 5961

1. 5838

1. 6073

2.1738

2. 0919

1. 9752

2. 0153

1.9498

1. 5099

1. 5074

0. 7962

1. 3242

1. 3953

1.4590

1. 6028

1. 6076

1. 5633

1. 5995

1. 6078

1. 5421

1. 5288

1. 6745

1. 6171

1. 8657

1. 8249

1. 2853

1. 6286

1. 9460

1. 7779

1. 7388

1. 7143

0. 7783

1. 6403

1. 7294

1. 6031

1. 5583

1. 5795

1. 55.24

1. 5783

1.5381

1. 5656

2.,1414

1. 9273

1. 9352

1. 9028

1. 8880

1. 5756

1. 5261

0. 8506

1. 4434

1. 4178

1. 4716

1. 6322

1. 6603

1. 6707

1. 6226

1. 6098

1. 5606

1. 5606

1. 7032

1. 6759

1. 9274

1. 8494

1. 5961

1. 8070

1. 9943

1. 8173

1. 7779

1. 7322

0. 8358

1. 7077

1. 7361

1. 6358

1. 5910

1. 5879

1. 5993

1. 5975

1. 5654

1. 6395

2.1619

2. 0285

1. 9529

1. 9803

1. 9425

Upper

bnd.

1. 6473

1. 5453

0. 9130

1. 5863

1. 4411

1. 4844

1. 6627

1. 7165

1. 7939

1. 6463

1. 6118

1. 5796

1. 5936

1. 7329

1.7391

1. 9933

1. 8745

2.1050

2. 0292

2. 0450

1. 8585

1. 8188

1. 7505

0. 9024

1. 7429

1. 6698

1. 6252

1. 5963

1. 6492

1. 6170

1. 5937

1. 7207

2. 1828

2.1409

1. 9709

2. 0643

2. 0002

D-20
Table D-2 (cont'd.)

Upper and Lower Bounds on the Detonation velocity (km/sec)

7612 CAMAC

Test Sample Lower

size bnd.

Vel. Upper Sample Lower Vel.

est. bnd. size bnd. est.

55

56

57

58

59

60

61

62

63

64

65

616

67

68

69

70

71

72

73

74

75

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

1. 8099

1. 8688

1. 7563

1. 8212

1. 7409

1. 6954

1. 5986

1. 4996

1. 6487

1. 5896

1. 5707

1. 5007

1. 4516

1. 5040

1. 5307

2. 2435

2. 2091

2. 2281

1. 6490

1. 7751

1. 7029

1. 9418

1. 7350

1. 9767

1. 8734

2. 0816

1.7711

2. 2259

1. 7045

1. 5947

2.1520

1. 9771

1. 8894

1. 7162

1. 6178

1.4799

1. 8497

1. 8787

1. 7787

1. 8306

1. 7521

1. 7255

1. 6653

1. 5160

1. 6539

1. 6099

1. 5749

1. 5447

1. 4758

1. 5086

1. 5496

2. 26 10

2. 2757

2. 2782

1. 5056

1. 4300

1. 5520

1. 6354

1. 4881

1.* 6586

1., 8070

1. 7144

1. 9507

1. 7671

1. 9898

1. 8857

2.:0943

1. 7829

2. 2406

1.7146

1. 6821

2.1632

1. 9879

1. 9182

1. 7292

1. 6254

1. 4976

1. 89 14

1. 8886

1. 8016

1. 8401

1. 7634

1. 7566

1. 7378

1. 5327

1. 6591

1. 6307

1. 5791

1. 5914

1. 5009

1. 5131

1. 5690

2. 2788

2. 3464

2. 3305

1. 6683

1. 8399

1. 7261

1. 9596

1. 8003

2. 0032

1. 8983

2.1071

1. 7948

2. 2555

1. 7248

1. 7798

2. 1746

1. 9989

1. 9480

1. 7424

1. 6331

1.5 158

1. 8061

1. 8630

1. 7267

1. 8221

1. 7240

1. 6894

1. 6032

1. 4955

1. 5867

1. 5788

1. 5261

1. 4554

1. 4372

1. 5063

1. 5126

2.1766

2. 2457

2. 2332

1. 4113

1. 3939

1. 5297

1. 5851

1. 4687

1. 6904

1. 6468

1. 7892

1. 70 18

1. 9219

1. 7398

1. 9720

1. 8610

2. 0878

1. 7683

2. 2275

1. 6850

1. 6649

2.1170

1. 9758

1. 8793

1. 7057

1. 6111

1. 4882

1. 8419

1. 8750

1. 7663

1. 8331

1. 7543

1. 7283

1. 6454

1. 5062

1. 6223

1. 5911

1. 5702

1. 5154

1. 4633

1. 5231

1. 5434

2. 2267

'21,2764

2. 2757

1. 5121

1. 4252

1. 5408

1. 6052

1. 4792

1. 7071

1. 6586

1. 8028

1. 7080

1. 9394

1. 7486

1. 9843

1. 8828

2.1039

1. 7719

2. 2351

1. 7008

1. 6681

2. 1555

1. 9904

1. 8938

1. 7174

1. 6184

1. 4943

Upper

bnd.

1. 8793

1. 8871

1.,8078

1. 8442

1. 7857

1. 7690

1. 6900

1. 5171

1. 6596

1. 6036

1. 6170

1.5805

1. 4905

1. 5404

1. 5755

2.2793

2. 3079

2. 3198

1. 6284

1. 4580

1. 5520

1. 6259

1. 4898

1. 7242

1. 6706

1. 8165

1. 7141

1. 9572

1. 7574

1. 9966

1. 9052

2.1202

1. 7755

2. 2427

1. 7169

1. 67 12

2.1953

2. 0053

1. 9086

1. 7294

1. 6257

1. 5005

4

4

5

6

5

5

6

6

5

5

6

3

.4

5

5

5

5

5

D-21
Table D-3

Variables chosen to Specify the

initial Thermodynamic State of the Mixture

Test Series Variables

1 , , 2 O,XCO2 ,T,P

3 0,T,Pair

4 O,XH20ITPair

5 0,T,Pair

6 XH2, T,P

7 XH2,T,Pair

Table D-4

Measured Variables

Variables For CO2 tests, For all other tests,

Measured variable measured for variable measured for

T2 , P2

TA 7P3

Ambient Air

Air only in HDT

C02 -Air in HDT

H2 -C02 -Air in HDT

Prior to initiation

Ambient Air

Air only in HDT

H2 -air in HDT

H2 0-H2 -air in HDT.

Prior to initiation

D-22
The technique used to establish uncertainty bounds f or the

reported variables is referred to as "Single Sample Uncertainty

Analysis" [D5,D6]. The technique is used to estimate uncertainty

bounds for test data where no repeat tests were conducted. The

technique consists of the following procedures: The first step

is to estimate the standard deviation of the measured variables,

in this case the appropriate temperatures and pressures. The

estimate is made by engineering judgement based on prior performance and calibration data. Next a Taylor series expansion is

made of the. relationship between the inferred (dependent) variables, such as equivalence ratio, and the measured (independent)

temperature and pressure variables. The first term of the expansion is retained. An estimate of the variance of the inferred

variable is the sum of the variances of the measured variables

times the square of the gradient of the measured variable with

respect to the inferred variable, i.e..

given an inferred variable, V, that is a function, g, of the

measured variables', Xi, or,

V=g(Xl,X2 , . XN) (D-1)

then the mean of V is approximated by,

A'V 90g(41442, 14.~/N) (D-2)

and the variance of V is approximated by,

C 12 I 2( +..+ 2 )

UX ax I A-1 i1-42 ''" ./NJ X. 6 X~ N 1A12f .

(D-3)

Upper and lower bound estimates are established on the. six

initial thermodynamic state variables and are calculated to be

twice the standard deviation of the variable, i.e. an estimate of

2o- limits.

In single sample uncertainty, the estimator, R. , of the

mean of each of the measured variables /,ti, is taken to be the

actual measurement of the variable. Thus, the estimated mean is

.based on a sample size of one. For example, the mean v Ialue of

temperature, /AT, is estimated to be the actual temperature measurement, T. The estimator, si, of the variance of each of the

measured variables, aj, is determined by engineering judgement of

the accuracy of measurement.

D.4.1 Variance Estimat es for Measured Variables

The, measured thermodynamic variables for each test are the

temperature and pressure of the mixture after the addition of

D-23
each component gas. The measurements are point measurements

taken to reflect the average value in the gas volume. The variability in each of these measurements arise from the variability

in the measurement itself and the uniformity and time variability

of the mixture. Table D-5 summarizes the temperature and pressure standard deviation estimates. These estimates are based on

engineering judgement which is discussed below.

Table D-5

Summary of

Standard Deviation Estimates of Measured Variables

(Using Engineering Judgement)

-Test Series Tests 5T (OC)- 6P (psi) 6(AP) (psi)

1 11-15 1 0.008 0.005

63-72 1 0.05 0.025

2 All 1 0.008 0.005

3 All 1 0.05 0.025

4 All 1 0.05 0.025

5 All 1 0.05 0.025

6 All 1 0.05 0.025

7 11 1 0.008 0.005

44,45 1 0.05 0.025

D.4.1.1 Temperature Standard Deviation Estimate

The temperature measurement device and recorder for each

test is listed in Table A-2, 3 in Appendix A. Early tests used

an average of the surface temperature measurements made by the

thermocouples used to control the temperature of the tube. The

thermocouple tips were calibrated using ice and boiling point

temperatures, but the electronic reference junctions were. not

cal-ibrated. Sixteen thermocouples use a Kinetics Corp. Model

,1991 reference junction while 32 thermocouples terminate in a

Sandia designed, temperature monitored, constant temperature

block.. The discrepancy between readings of nominally the same

temperature are on the order of 1*C.

After test HT19, a K-type ungrounded tip thermocouple in a

3 mm (1/8 in) sheath was used to measure the gas temperature.

The thermocouple was inserted through the Heated Detonation Tube

wall in port 6 and protruded only 3 mm (1/8 in) to prevent the

D-24
detonation from destroying the tip. At this depth, the thermocouple is subject to conduction effects from the tube wall. This

influence is assumed to be minimal bec'ause the temperature is

uniform in the tube wall and steady state is reached before the

temperature measurement is taken. After test HT73, the thermocouple was inserted farther into the tube to a depth of approximately 2.5 cm (1 in). The fitting was removed after test HT96

and the thermocouple was found to be bent at the fitting in a 450

angle due to the pressure loading of the detonation wave. It can

not be determined if the strain induced by the bend affected the

calibration of the thermocouple.

For tests HT19 to HT79, the reference junction for the

thermocouple was a Fluke Model 8024B Handheld DMM with a reference junction for a K-type thermocouple. The manufacturer's

uncertainty estimate for the device is +/-3*C with a resolution

of +/-1*C. After test HT79, the reference junction used is a

Digitec model 2831. The manufacturer's uncertainty is +/-0.3*C

with a resolution of +/-0.1*C.

The thermocouple and reference Junctions were not calibrated

prior to testing. An ice point and boiling point calibration w~as

conducted after test HT96. using the Fluke reference, the

reading alternated between 0 and 1*C for the ice point and read

960 C at the boiling point (95.0*C at the time the calibration was

taken). Using the Digitec reference, the ice point reading was

0.2*C and the boiling point reading was 95.6*C. No attempt was

made to correct the data for the fixed error, and no estimate of

thermocouple aging can be made.

Comparison of- the average temperature of the thermocouples

used to control the tube temperature and the thermocouple used to

measure the gas temperature showed a variation of +/-1*C. Based

on 'this information and the post test calibration, a reasonable

estimate of the standard deviation is +/-l*C for each temperature

measurement in each test.

D.4.1.2 Pressure Standard Deviation Estimate

The pressure gage(s) used to record the predetonation gas

pressure are listed in Tables A-2, 3 in Appendix A. For tests

prior to test HT31, a Wallace & Tiernan 0-800 mm Hg absolute gage

was used. This gage was calibrated by Sandia Standards and the

uncertainty is given as +/-0.8 mm Hg with a least division of

1 mm Hg. The +/-0.8 mm Hg uncertainty in calibration can be

taken as a two sigma estimate, and therefore, the standard deviation is taken to be +/-0.4 mm Hg.

Tests HT31, 32 and 33 used the Wallace & Tiernan gage for an

atmospheric reference and a Heise 0-100 psig gage was used for

measuring the pressure in the tube. The Heise gage was calibrated by Sandia and has an uncertainty of 0.1 psig with a least

division of 0.1 psig. -The standard deviation of the Heise gage

is estimated to be +/-0.05 psig.

D- 25
For tests after HT33, a Wallace & Tiernan 0-50 psia gage was

used. The gage was calibrated by Sandia Standards Lab and was

assigned an uncertainty of 0.4 psia over the entire range of the

gage. The gage was used in a range above 4 psia; below this

value, the calibration error becomes large. In this limited

range the uncertainty of the gage can reasonably be assumed to

have a standard deviation of +/-0.05 psia. The gage has a least

division of 0.05 psia.

Due to the high linearity of the pressure gages used, it is

assumed that the relative uncertainty between any two pressure

measurements is less than the absolute uncertainty which may

contain some zero bias. The standard deviation for a relative

pressure measurement in the tests prior to HT31 is assumed to be

+/-0.25 mm Hg and after test HT33 it is assumed to be +/-0.025

psia. For tests HT31, 32 and 33 the standard deviation is assumed to be the square root of the sum of the squares of the two

standard deviations or +/-0.05 psia.

D.4.1.3 Uncertainty in the Uniformity of the Gas Mixture

The temperature and pressure measurements are point measurements which may be affected by spatial nonuniformity of the gas.

No compositional measurement is taken; composition is inferred

from the temperature and pressure measurements.

Uniformity of Temperature - Temperature uniformity in the

tube is maintained by 15 independently controlled sections of

heaters on the tube. For details of the heating system see

Appendix A. An analytical estimate of the nonuniformity of the

inner surface of the wall in Appendix G predicts that the nonuniformity is +/-0.7 0 C. Typical variation in temperature at steady

state at 100 0 C between the hot and cold measurements on the outer

surface of the tube is +/-3*C excluding the endplates.

The temperature of the endplates varied with the ambient air

temperature and date of test. The removable insulating endcaps

lost their sealing quality with use and allowed ambient air to

circulate around the endplates. For most elevated temperature

tests, the endplates were lower in temperature than the rest of

the tube, typically 50C but sometimes as much as 20*C.

Attempts to introduce a steam mole fraction to produce saturation corresponding to the average tube temperature resulted in

a mole fraction corresponding to saturation at a temperature

approximately 5*C lower than the average tube temperature.

sufficient steam was introduced to produce condensation somewhere

in the system. The secondary piping used to circulate the mixture is heated over most of its length. The only unheated

segment is from the outlet port at the foil end of the tube,

through the filter, pump, and a couple meters of pipe to where

the secondary piping runs under the heating tapes along the main

tube. The secondary piping is insulated along its entire length,

D-26
but the unheated portion is assumed to be the coldest point in

the system.

While the largest temperature excursions of the tube wall

and secondary piping are large compared to the point temperature

measurement standard deviation of +/-l*C, these excursions are

assumed to be confined to very narrow regions in the boundary

layer of the gas and the temperature variability of the core

region is assumed to be adequately characterized by +/-10 C.

Uniformity in Pressure - The pressure in the tube is uniform

prior to the initiation of the detonation because there is no

flow in the tube. Pressure measurements made between the addition of gases are made with the circulation pump running. The

flow rate of the pump is 142 slm (5 cfm). This flow rate produces a velocity of approximately .15 mm/s (3 ft/mmn) in the

detonation tube. The pressure drop is minimal and the measured

static pressure can be considered the total pressure within the

standard deviation of the point estimates.

Uniformity of mixture - The gas mixture is made homogeneous by

continuous circulation of the gases in the tube during and after

gas addition. At least one tube volume of gas is allowed to

circulate through the secondary piping while gas is being added,

and at least one additional tube volume of gas is allowed to

circulate before adding additional gas or initiating the detonation. Since no compositional measurements are taken, there is no

method of directly establishing the uniformity of the mixture.

D.4.1.4 Steady State Criteria

The temperature and pressure measurements which define the

composition of the mixture are made only after steady state is

obtained. Steady-state is defined by two criteria. The first is

that there is no detectable change in temperature or pressure

over a period of 15 minutes. This period is chosen because it is

the time-constant of the tube with respect to a sudden change in

temperature as discussed in Appendix B. (Pressure equilibration

in the gas is very fast compared to this time scale.)

The second criterion is that the gas mixture be uniform.

The circulation rate of the pump is 5 scfm ~verified by a calibration test) and the tube volume is 1.92 J~.A circulation of

one tube volume of gas occurs every 13.5 minutes. To obtain

uniformity in the gas mixture at least two tube volumes of gas

are allowed to pass through the secondary piping. This is

equivalent to waiting at least 27 minutes between the additions

of gases.

Typical procedure was to wait approximately 1 hour between

adding gases and a half an hour after the last gas was added to

initiate the detonation. Using these times to achieve equilibrium, it is assumed that the time rate of change in temperature

and pressure is minimal.

D-27
D.4.2 Standard Deviation Estimates Of Pair, 4O, XH2Q, and XCO2

Equation D-3 is used to estimate the standard deviation of

Pair, O, XH12Q, and XCO2, given the standard deviations of the

measured variables established in the last section. The functional relation, g, for each of the variables is given below.

The discussion of the equations will be divided into two categories: 1. H2 -air and H2 -air-H20, and 2. H2 -air-C02. This is

necessitated because the order of gas entry for the C02 tests was

air-C02 -H2 while the gas entry for the other tests was air-H2- H20.

The following relations are based on the use of dry air.

For tests prior to HT-49 ambient air containing some humidity was

used. In all cases the final mole fraction of H20 due to humidity in the ambient air is less than 0.01. The manuf acturers

estimate of the standard deviation of the humidity measuring

device is +/-3%. In some cases, air from a compressor was used

to boost the air density up to its required value. The

compressor draws in ambient air, and therefore, the total air

mixture in the HDT is assumed to have the same humidity as the

ambient air.

The calculation of steam mole fraction requires interpolation of the steam tables. The estimated uncertainty in interpolation is +/-2% for a combined standard deviation of +/-3.6%

for the humidity contained in the ambient air. This standard

deviation is included in the final value of the standard deviation given for the mole fraction of steam for the appropriate

tests where ambient air was used by taking the square root of the

sum of the squares with the standard deviation for steam developed below.

H2 -air and H2 -air-H20 Tests - As mentioned above, the mean

value of a given variable, #ij, is estimated by the measurement of

that variable for a given test. The following mean value estimators are defined:

Air

Temperature: T1 Pressure: P1

H2 -air

Temperature: T2 Pressure: P2

H2 -air-.H20

Temperature: T3 Pressure: P3

Further, define a mean difference in pressure estimator as:

APH2 P2 -P AP21

APH20 P3 - P2 AP3 2

D-28
The standard deviation estimator for each measurement is given in

Table D-5. The symbol used in this appendix to identify a standard deviation estimate is 6; i.e. , standard deviation in pressure: 6P, standard deviation in temperature: 6T; standard deviation in relative pressure: &AP. Using these def initions the

standard deviation in the air density, equivalence ratio, and

steam mole fraction is as follows:

.Temperature:

T = T (D-4)

6T = 6T 3 (D-5)

Air density:

P1 (D .-6) Pair -RT 1

Taking the Taylor expansion of the air density and retaining the

first term gives,

p P 

( D -7

6Pair - RT RT ITI D

1 11 [1Ti

Taking square root of the sum of the squares, the standard deviation

is,

P ai RT 1

15TJ ] 2 + I p ,

T J P p1

(D-8)

D-29
Equivalence ratio:

=S X H (see Appendix E)

air

let S = 2.38691

Substituting (D-6) gives,

(D-9)

nair

S

P 2 P1

]RT 2 RT 1

P 1

RT1 ] (D-10)

Rearranging, and introducing relative pressure

S[AP2 P1 P1 P

Rearranging, the equivalence ratio is

= [T (l[AP21 +1 1

(D-11)

(D-12)

D-30
Taking the Taylor series and retaining the first term,

30 = s I

"P2 1 + __1] P 1 TT~ 2

A21+1 i

P II [Ti

aT 2

T2

+[JaA; 21 T1 AP21Cp 1] (D-13)

Taking the square root of the sum of the squares of each term,

the standard deviation is,

S T

Ti1 2

iP 21 + p 1 + 1j)2 [t. 2 + [62 ]2

1 2P, 2[+ ( 5E 2'1]/~2

p 1AP 2 21 2 1-i

Steam mole fraction: X - 2

H2 0 ntotal

Substituting (D-6) gives

= RT 3 - ~2

HO [P3)]

(D-14)

(D-15)

(D-16)

D-31
Rearranging,

X H 0 1(- P T (D-17)

Introducing relative pressure, the steam mole fraction is

( (T3[ 1P31] (D-18)

Taking the Taylor series expansion of the steam mole fraction and

retaining the first term,

ax H 0 T1P

-~ T[ ( T3 )[AP32 ) jP CA~ (D-19)

Taking the square root of the sum of the squares, the standard

deviation is,

2 2

[+ P ] 2 32 + [ 1P3)2111/2 (-0 P 3 P J2 P 3 J

D-32
Upper and lower bound estimates on the initial thermodynamic

state variables can be taken as +/-25. The numerical values for

the bounds are listed in Appendix C.

H2 -air-C02 Tests - The mean value of a given variable, pij, is

estimated by the measurement of that variable for a given test.

The following mean value estimators are defined:

Air

Temperature: T1

C02 -Air

Temperature: T2

H2 -air-CO2

Temperature: T3

Pressure: P1

Pressure: P2

Pressure: P3

Further, define a mean difference in pressure estimator as:

APCo2 P2 -P AP21

APH2 P3 - P2 A32

Define standard deviation as 5; i.e., standard'deviation in pressure: 5P; standard deviation in temperature: 5T; standard deviation in relative pressure: 5AP. Using these definitions the

standard deviation in the air density, equivalence ratio, and

carbon dioxide mole fraction is as follows:

Temperature:

T = T (D-21)

5T = T 3 (D-22)

Air density:

P 1

Pair -RT 1

(D-23)

Taking the Taylor series expansion of air density, and the square

root of the sum of the squares of the terms, the standard deviation is

D- 33
6oi RT1 5T( ) 2 + [: ,p 2?/ (D-214)

Equivalence ratio:

Using (D-6) and (D-9), the equivalence ratio is:

nair RT3

(D-25)

Rearranging, and introducing relative pressure

S[ j J A[P32 +P1 + P1 AP21 +P

P 1 T ~3T2

(D-26)

Taking the Taylor series expansion, and the square root of

the sum of the squares of each term, the standard deviation is:

=~~ -) ~ 2 )2 ,_ 

2+ ~~2 2

(P 3 ~(T T T 2 T

+ 3 L( T3J)2 (P1 -P 3 P2 + P 1 2(51]

+ P 21 AP2 j2 21 2[ 1 ] P2+ 2 ]1/2 (D-27)

D- 34
CO2 mole fraction: X O2

2 O2 n total.

Substituting (D-6) gives

(D-28)

X C0 2 CRT 1 (D-29)

Rearranging and introducing

fraction is,

relative pressure, the steam mole

x 0 = ~*][ T A P32

P 3

(D-30)

Taking the partial derivative of the C02 mole fraction, and

taking the square root of the sum of the squares, the standard

deviation is,

_ 21F _AP 2 1 1)2 [[6T2 1

2 +r[6TJ ~1

2

c5X C T1 [ 1 P 1 T J + LTJ

+ P j2[ 2 . 2 [:511 ] 2( 1/2 (D-31)

Upper and lower bound estimates on the initial thermodynamic

state variables can be taken as +1-26. The numerical values for

the bounds are listed in Appendix C.

D-35
D.4.3 Standard Deviation Estimates of Detonation Cell Width

and. Velocity Due to Initial Thermodynamic State

The variance in detonation cell width and velocity due to

the variance in thermodynamic state can be estimated by using the

same technique used to establish the variance in the initial

thermodynamic state variable described above. 'Estimates of the

detonation cell width and velocity gradients with respect to the

thermodynamic state variables can be estimated from the data.

For,

X=f(T, Pair, 0, XH20 or XCO2)

(D-32)

VD =g(T, Pair, 0, XH20 or XCO2)

the first term of the Taylor expansion is,

dX,V D= a8 xIv D ] dPair +

pairT,O~ XH 0

2

CXID 1dT

"ýV Pair'~X

C H 20

(D-33)

(3X DIdo +

(30 air TXH 20 I:

axIV D 1dXH0

2 p air TOP

The standard deviation estimate is,

c5Xv VD[ (3xV D 2 5P2 + a ai ,Oxair

H20

kLD ~ 5T 2

aX' )air' HO2

(D-34)

+ ( axD)D 2 2+ a, ao .Pair T, XHO 0 + aj D 1 11/2

D-36
As the mixture approaches the lean limit, the gradient of

detonation cell width with respect to equivalence ratio approaches infinity. Equation D-34 shows that the standard deviation in the detonation cell width also approaches infinity due to

a finite standard deviation in equivalence ratio multiplied by

the infinite gradient. The effect of the standard deviation in

the remaining thermodynamic variables can be estimated from their

respective gradients. The standard deviation in detonation velocity due to standard deviation in the initial thermodynamic state

can be estimated by using C-J theory to predict the gradients of

detonation velocity with respect to the gradients in the thermodynamic variable. Assuming that the detonation velocity does not

deviate significantly from C-J theory, none of the gradients are

large.

D.5 REFERENCES FOR APPENDIX D

Dl. Moen, I. 0., Funk, J. W., Ward, S. A.,Rude, G. M. and

Thibault, P. A., "Detonation Length Scales for Fuel-Air

Explosives," AIAA Progress in Astronautics and Aeronautics,

Vol. 94, 1984, pp 55-79.

D2. Moen, I. 0., Murray, S. B., Bjerketvedt, D., Rinnan, A.,

Knystautas, R., Lee, J. H., "Diffraction of Detonation From

Tubes Into A Large Fuel-Air Explosive Cloud," 19th Symp.

(Int'l.) on Combustion, The Combustion Institute,

Pittsburgh, PA, 1982, pp 635-645.

D3. Bull, D. C., Elsworth, J. E., Shuff, P. J., "Detonation

Cell Structures in Fuel/Air Mixtures," Combustion and

Flame, V. 45, 1982, pp 7-22.

D4. Ray, A. A., Editor, "SAS Users Guide: Statistics," SAS

Institute Inc., Cary N. C., 1982 Ed.

D5. Kline, S. J. and McClintock, F. A., "Describing Uncertainties in Single-Sample Experiments," Mechanical Engineering,

Jan. 1953, pp 3-8.

D6. Moffat, R. J., "Contributions to the Theory of SingleSample Uncertainty Analysis," Trans. ASME, Vol. 104, June

1982, pp 250-260.

D-37
FIGURES

D-1 Typical Smoked Foil Record f rom the HDT with

Large Cells (HT-96).

D-2 Detonation Cell Width Measurements for HDT Test

Series #3 (H2 -air, Pair=4 1 .

6 moles/rn3 ,

T=100-C).

D- 3 Detonation Cell Width Measurements for HDT Test

Series #5 (H2 -air, Pair= 4 1 .6 moles/rn 3 , T=200 C).

D-4 Comparison of Detonation Cell Width Data

Between the HDT and McGill' University. (HDT

Test Series #1, P=1 atm, T=250C).

D-5 Normalized Detonation Cell Width (X Author/X

Knystautas) Vs. HDT Test Number.

D-6 Typical PCB Pressure Trace - Small Cell Width

(X = 5 mm , Test HT-84).

D-7 Typical Kistler Pressure Trace - Small Cell

Width (X = 5 mm , Test liT-84).

D-8 Typical PCB Pressure Trace - Large Cell Width

(X = 400 mm , Test HT-96).

D-9 Typical Kistler Pressure Trace - Large Cell

Width (X = 400 mm , Test HT-96).

D- 38
APPENDIX E

THERMODYNAMICS AND CELL SIZE

For binary H2 -air mixtures three independent variables are

required to specify the initial thermodynamic state. An

additional variable is needed for each diluent, such as steam or

CO2. The purpose of this appendix is to develop relations

between the variables used in this report and a few of the other

commonly used variables. In addition, the general thermodynamic

relationship between detonation cell width and the thermodynamic

variables is developed and the relationship of cell width vs.

temperature for various thermodynamic processes is discussed.

E.1 THERMODYNAMIC RELATIONS

Thermodynamic variables are related by the equilibrium

equation of state. For simplicity a perfect gas relation is

used:

P nRT =-0-RT (E-1)

mw

where P =pressure

n =molar density

R =universal gas constant

T =temperature

p =mass density

mw =molecular weight

This relation is very good except at high steam concentrations at high pressures and relatively low temperatures.

An additional relation is necessary for multicomponent

mixtures, and that is that the sum of the mole fractions add up

to unity:

X.ai + X H2+X H =1 (E-2)

where X. is the mole fraction = ni

I n

The composition of air is taken to be

20.95% 02

79.05% N2

E-1
The equivalence ratio, 0, can be related to the air and fuel

mole fractions by its definition:

nH 2/ n.

air

Hn nair Istoichiometric

(E-3)

nH

where stoichiometric 2n

air

is given by:

H2 + 1 0o + 3.77382NJ I~ H2 + (3.77382N2 )

(E-4)

Let -

n air soc 1./2 (.1 + 3.77382)

or S = 2.38691

where S is defined simply for convenience.

Previous researchers have expressed detonation cell width as

a function of %H2 in dry H2 -air in place of equivalence ratio.

It is useful to derive the relation between these variables and

equvalence ratio, and the mole fractions of the diluted mixture.

Superscripts. 'will be used to identify whether the variable is

defined for a diluted, Xd, or undiluted, Xu, mixture. From

equation 3, the equivalence ratio, ~,is invariant to the

addition of diluent.

For undiluted mixtures., the H2 and air mole fractions sum to

unity:

Xu + u

air H 2

- 1 (E-5)

where Xau. and X u are the undiluted mole fractions.

E-2
U n__H_2 By definition X H2 = n.ar+ 2

H H

So -2 - 2

nair l-XHu

(E-6)

(E-7)

Therefore, 0 = S

XH2

1-XHu I XH

air

(E-8)

or Xu= 0(E-9)

H 2 + S

and from (Eq. E-5)

U _ -S (E-l0) air +

To get in terms of the diluted mole fractions, Eq. E-2 is

used. The relations are developed for steam dilution but are

general for any diluent. Note that the H2 to air molar ratio is

the same in each mixture, or

nH 

2

n.air

diluted nH 

2

nair

undiluted

(E-11)

By dividing by the appropriate total densities (Eq. E-l1)

becomes

XdXH2

Xd

air

XHu

air

(E-12)

E-3
Substituting (Eq. E-12) into (Eq. E-2) to elimnat XH gives

air

Rearranging (Eq. E-13) and using (Eq. E-5) gives

xd. x u di"xd (E-14) air air[H 2 Oj

Similarly, *substituting (Eq. E-12) into (Eq. E-2) to

eliminate Xair gives, with rearranging,

2 d = (E-15)

Substituting (Eq. E-15) into (Eq. E-8) gives

I xd d

- X H 2 S xd. (E-16)

if H 2air 2 

Substituting (Eq. E-9) and (Eq. E-10) into (Eq. E-15) and

(Eq. E-14) gives

x d = -x d~ (E-17) H 2 + S iH 20

air - + S 0

(Eq. E-18) can be used to give the relationship between

total molar density and air density, i.e.,

E-4
n d -= n d( S J (-4 d (E-19) air + 2 0

Since n d

mw

d(M air) S - (E-20)

~air = (mwmix) 2

E.2 GENERAL FUNCTIONAL RELATIONSHIP

Choosing air density, temperature, equivalence ratio and

.mole fraction of steam as the four independent variables gives

X = f(Pair T, O'XH 2o0 (E-21)

The change in cell width with respect to a change in any/all

of the independent variables can be def ined by the integral of

the total derivative of (Eq. E-21) with a defined reference

state:

Xo= f(Pair 0 To 'Oo'XHO 20 (E-22)

The total derivative is,

dX = 6Xdp + T OdT

L~ i Pa Pair I XHO0

~~air 0(E-23) T~tPXH 

+r(0 XdO +r [ ax X dXHO

)Pair. T,XHO 2 XHO 2 20 ,

air 2 Pair'T~

E-5
Integrating (Eq. E-23) gives

x-xO {air P (3 M

f~air IPair T,1,X H 0

I+ ý- dT

T BTiP air I OXH 20

(E-24)

+ [ ]~ do JX 2O 8 X~ 'd

P0airITIH20 XHO2 2 0H J 2 O

0

E.3 EFFECT OF TEMPERATURE

To isolate the effect of temperature, consider a process

where 0 and XH o are constant, such as a premixed set of gases

undergoing hea ing. Consider this heating taking place in three

different ways, at constant air density, at constant total

density, and at constant total pressure.

Constant air density Pa = C 1

- C2

- C3 X H 20

(Eq. E-23) gives,

dX = ( AT ) dT

aTPair'O'XH 20

B) Constant total density

(E-25)

p 1

SC 2

X H 20 = C 3

E-6
For X =f(pITI,,X H 2 )

dX = )x dT

B T IO I H 20

(E-26)

(E-27)

Note, however, that f or f ixed 0 and XH2O, constant p f rom

(Eq. E-20) implies constant$[Ol3O6srair and hence,

[ ST, PIPXH 20 = t Ia~ )PairOI~XH20

(E-28)

Therefore, at constant composition, the effect of

temperature is the same whether the process occurs at constant

air density or constant total density.

C) Constant total pressure

For X f fP,T,O,X H 0)

dX 3 X1 dT

S T P,O,XH 0

P 1

2

(E-29)

(E-30)

E-7
In this case,

( aTP,O,X H 0 ( 11')P,9oXH 20

The relationship between the temperature effect at constant

pressure and constant density can be determined by differentiating (Eq. E-29) for constant composition and density, and

relating that to the equation of state (Eq. E-1) and (Eq. E-27).

For constant 0b, X H 0

dX = aX ) dP ap T,O,X H 0

+ ( T )dT

P,O,x H 0

(E-31)

Differentiating (Eq. E-1) gives,

dP = dp RT- + PRdT

mw mw

Substituting (Eq. E-32) into Eq. 31) gives

dX 6X ) [dp ý-T+ R dTl + Fq ) dT ap 20~xm mw 8~ T PI,OXH HT 2 0 H 20

Equating (Eq. E-33) with dp = 0 and (Eq. E-27) gives

(E-32)

(E-33)

( II + (+'8) dT= ap TO~xMW S ,~ THO 2I 0XH 20

( 6 )]

ST 1,)'X 20

(E-34)

E-8
Noting from (Eq. E-1) that P= P T mw

( 81)P,1OXH 20

= _ P + ( ) I

T,HOx H 6 aT 0 ,~ 2 PIH2

(E-35)

Using (Eq. E-28) gives,

r CaxT a r O X = (' ~ TIJQ H 0a P, 1IXH 0 2 2

(E-36)

Finally, rearranging gives,

IIa x )

STPO~ 0 = a RT, )PairI 'hIXH 20 T, IXH20

(E-37>

Data for cell width measurements has established that both

( ax )

aT Pair 'OPIXH 20 and ( ýa~ ) ,~

are negative.

E-9

APPENDIX F

ANALYSIS OF THE TEMPERATURE DISTRIBUTION

AND THERMAL TRANSIENT RESPONSE OF THE HDT

To estimate the temperature non-unif ormity and the rate of

heating of the HDT using heater strips, a one dimensional transient model was developed. The model assumes that the HDT tube

wall acts as a one dimensional fin between the heater tapes. The

fin length is half the distance between heater tapes and is

assumed to be insulated at the tip. The inside surface of the

tube is assumed to be insulated due to symmetry and the low heat

capacity of the gas, while the outside surface loses heat to the

environment. The heat loss is approximated by a constant, q.

The heating occurs in two stages. In the first stage, the heating tapes are at full power. The second stage starts when the

temperature of the heaters reaches a set reference temperature,

Tr, such as 1000 C.. During this stage the heaters are held at

this temperature. In the HDT this temperature is held by computer controlled feedback of the thermocouple temperature unddr

the heater tape.

F. 1 NOMENCLATURE

English

Ac Cross--sectional area of fin (tube wall)

A p Surface area of fin (tube wall)

A Constant to be determined

B. Constant to be determined

C Specific heat

d,e,f Constants to be determined

H Width of fin

J Conveniently defined constant = Q/2kL

k Thermal conductivity

K Conveniently defined constant = q/kw

L Length of fin (1/2 distance between heaters)

q Heat loss per unit area through insulation

F-1
Q Heat gain per unit area from heaters

s Laplace variable

S Laplace transform of temperature distribution

S p Particular solution to Laplace ODE

S 9 General solution to Laplace ODE

Si,# First subscript ref ers to the term in the Laplace

transform. Second subscript refers to the pole at

which s is to be evaluated for inverse transformation

t Time, zero time begins when heaters are first

turned on

t Time when heaters reach set-point temperature,

usually 100 0C and begin to cycle

t2 Time, t-t *, zero time begins when heaters reach

set-point temperature

T Temperature distribution (x,t)

Tl,# First subscript refers to term in Laplace transform

that was inverse transformed. Second subscript

refers to the pole that was evaluated.

Tr Set-point temperature of heaters (usually 1000 C)=

T *(L,t*)

T* Temperature distribution at t * = T(x,t*

X Distance. Zero at tip of fin (midway between

heaters), L at heaters.

Greek

a Thermal diffusivity = k/pc

Xm convenience variable (m - 1/2 )7r/L

p Tube wall density

F-2
F.2 DERIVATION OF THE MODEL

Fig. F-i yields,

A- " A k-3 + qHAx =pcA Ax 8

volume in

(F-1)

Retaining first order terms gives,

A k 2 Ax+ qHx pA AxýT a 2 x~cAat- axCC

Dividing through by Ax gives,

(F-2)

82 + kA p )aT ax2 kAC k t (F-3)

Defining areas and noting the definition of thermal conductivity,

A~ LW Ac HW ,a pck

The governing equation becomes,

(F-4)

C 1 a T

ax 2 +kW a aat

(F-5)

with boundary conditions,

0;aT 0 = 'ax

(F-6)

x = L either aýT _ Q

ax k Problem #1 - Heaters Full On

Tr T - Tr = 0 Problem #2 - Heaters at Constant

F-3
HEATED DETONATION TUBE

q

if.- I L --mw

'It

I-.-

H

/

wi I I x

AX

Figure F-1. Control Volume for the 1-D Unsteady Fin Model.
The heat loss per unit area from the surface, q, and the heat

gain from the heaters per unit area, Q, are assumed to be

constant.

The initial conditions are,

T(x,O) = 0 Problem #1 - Heaters Full On

(F-7)

T(X,t*) = T*(x,t *) Problem #2 - Heaters at Constant Tr

where t * is the time at which the heaters

reach Tr.

T*(x,t) is the temperature distribution

at t *. Note: T*(L,t *)=Tr

A method of solution to the governing equation (Eq. F-5) subject

to the initial and boundary conditions (Eq. F-6,7) is the Laplace

Transform, L(T),

S =oo e-st T(x,t) .dt = L(T) (F-8)

The transform of a time derivative is

L ( 6T )1= SS - T(X,0) (F-9)

F.3 SOLUTION TO PROBLEM #1 - HEATERS FULL ON

For convenience, define K =q kW

Taking the Laplace transform of the governing equation (Eq. F-5),

d 2S + K=s

dx 2 s a

(F-10)

(I

F-5
The Laplace transform of the boundary conditions is,

dS = 0 at x = 0

dx

(F-11)

-s at x = L dx sk

Equation (F-l0) is a second order ordinary differential equation

in S which has:

particular solution S - aK2i

5

(F-12)

general solution

Sg SR xAin + Bcosh ~x+ S sn Tai a !p (F-13)

Using the boundary conditions (Eq. F-l1) yields,

dS =0at x = => A= 0

Fs 

aK

S Bcoshs2x

(F-14)

(F-15)

Solving for B, using the second boundary condition,

B= 1

sinh I3 L

(F-16)

F-6
The Laplace transform of the solution to (Eq. F-10) is

S Q

sk F as

cosh{ x +aK

sinh S L

(F-17)

which is of the form S = S1 +S

Finding the inverse transform; T = T1 + T

Second term has pole of order 2 at s = 0

C

T a~ t = qt Iý 2 kW PCW PCW A

This term is the lumped mass cooling d

insulation.

First term has poles at s = 0, sn=-

J It (F-18)

ue to heat loss through the

L22

For s ý 0

S =-P s q(s) Residue at s = sn for simple pole

p(sn) ep(snt)

dg (sn)ep

dsn

F-7
cosh S2n

Ia

k sn sn

a

.exp (sft)

Sn

a

L cosh s nL

- 2L cs (~rx Jexp (snt)

kn2 7r2 cos (n7r)

Inverting (Eq. F-19) gives,

(F-19)

T Q 1, n kL

n= 1

2(-1) L cos nr x JePan 7r tj (F-20)

This term is initial transient response of the tube wall.

For s = cosh S x

10ks s sinh L

(F-21)

Expanding S~ 1 ___a

1,0 k S sa[i

1,0 kL s2 i 2.

2 2 4

+ s x +s x+

a 2! a a4! - J

sL 2

+

6a -- 0 ( s 2) Ii (F-22)

F-8
Inverting gives,

1,0 gkL + 6kL Q 1 3x 2 _U 2 (F-23)

The first term is the bulk heat gain from the heaters while

the second term is the long time temperature distribution.

Combining terms gives the complete solution to problem #1,

q A

poc(WA ) II 1pc(LAc)J I 6 kL 3x 2_ L2

+ 2QL

kir 2 ~ cosn~r Jexp( ~an 7r t/LJ

n= n

(F-24)

F.4 SOLUTION TO PROBLEM #2 - HEATERS AT CONSTANT TEMPERATURE, Tr

For boundary and initial conditions,

Match conditions from Problem 1

Assume transient term in Problem #1 has died away

T3 t k 2_-- 2)~ 

pc(WA pp(L)) k

Define t * such that T at L is Tr at time of matching

=* qA '1 *Ac [ ]1 t*+ ~Q~ (2L 2

pc(WA p) Ip(AC k (F-25)

F-9
The reference temperature, Tr, is typically 100 0C.

Define t 2 =t -t

where time t is zero at the beginning of

problem #1 and t2 is zero at the

beginning of problem 2.

Define a new variable 8 = T - T*

at time 0 in problem 2 t t*

The initial conditi~on becomes,

B(x,O) = Q (x2_ L 2)

ak (F-26)

The boundary conditions become,

.ay

6- (0,t2 ) = 0

(F-27)

B(L,t 2 ) = 0

and the governing equation becomes,

a88 + C= 1 C)

3x2 kW a ýt

For convenience define

K = ,q j kW 2kL

(F-28)

(F-29)

F-10
The Laplace transform of the governing equation (Eq.F-28) is,

22 

a S K =1 - J(x 2 L2

IX2 s a .L)

Rearranging gives,

d 2S _ s

dx 2 a

Jx2 +12 K

a a a (F-30)

solving the ordinary differential equation in S gives:

Particular solution: S =fx 2 + ex + d

p

Substituting into the differential equation (Eq. F-30),

(F-31)

2ffX + ex + d) 2

s a

Solving for d, e, f,

e= 0

f J

5

d a [ 2J+K _

s Ls sa =a (K + 2J) 1 2

2 s 5

Therefore, S p is

J 2 + a (K +2J)

S=-xs SL Jx 2 _L2 )+a(K +2J)

s - 2 5s (F-32)

F-11
The general solution is,

S 9= A sinh is-/a x + B cosh I-s/a x + S p(x)

Using the Laplace transformed boundary conditions give,

as (0,s) = 0 => A =0

S (L,s) = 0 => 0 = Bcosh I-s/aL + S p(L)

Therefore,

B = F P(L)

cosh T's-l L

the transform of the solution is,

(F-33)

S =-. (x 2-_L 2) + 2-

5 s

(K + 2J){1l cosh T's/ax

cosh -s-/aL

(F-34)

which is of the form S = S1 + S

Inverting, there are poles at s = 0, and s =nir/2

For s ý 0

The second term has a simple pole at cosh fi~ 3etc n = 1,3,5 etc

or, when

FlaL = (m - 1/2)7r 1'22 s=-a(m - 1 2) L 2 ,mn 1,2,3,

F-12
define Xm = (m - 1/2)7r/L m m

Pole has form S2m 1_ P (s) a( +2J cosh is/a L

Inverting gives,

(F-35)

00

T2, Xm .2, 4

m=1 XAm

p(aXM2J eax 2 t 2

aQ (aXM 2 ) m (F-36)

where aQ/as is evaluated as,

ds ds

ds 2

am

I cosh i-S/aL ] = ( sinh I-s/aL)

L

- L *jsh -'1 = L (-1) m"

2a~m 5 ~' tJ2aXm

T 2,Xm = -2(K + 2J)

00

M= 1

m+1 -ax 2 t

(-1) e _ mt2

3 Xcos X X

m

(F-37)

This term is the initial temperature transient

For s = 0

To evaluate the second term of S it is necessary to expand the

cosh terms to evaluate,

F-13
2 2 4

cosh T--l x = 1 + S X + S X .+ ... 2 a 242

coh - + 2) _ 2 (x2 2)5KJ(x 2 L2 )

coh -L2a 24a

caash i

1-cosh Fs-7 s (x2 Li2) + 0(s2)

cosh Tsla L 2a

Therefore, at s = 0, S becomes;

S =i ( 2_ 2 +(K +2J) ~1&2, - (x-L 2

-s(x2_ L 2) + O(s 2)

2 (F-38)

Inverting,

T K (X2 _L2 (F-39) 1 & 2 r 0 2~(

This term is the steady state temperature distribution in the

tube wall.

Adding the terms,

T(x,t) = T 0+ T2,

Noting that,

K = q/kW, J = Q/2kL, and Xm = (m - 1/2)L mL

F-14
*

and t 2 =t -t

The solution is,

8(x,t) q (X 2 _ L2) 2[ _q_ + pI

00 m+1 aX 2 t

(-1) e mt2

3 ~Cosx

m=1 m

(F-40)

for t > t*

F.5 COMPARISON BETWEEN THE MODEL AND THE HDT

The location of the Heaters are listed in Appendix A. The

model is compared to the heater sections on the sides and bottom

of the long pipes. Table F-i lists the numerical values for the

parameters used in the model. The heat loss ,q, is estimated

from an assumed 800C temperature drop across the insulation. The

heat gain is estimated from the heater power and area of heat

transfer to the fin. The length of the f in is taken as 1/2 of

the length between the midplane of the heater area in contact

with the fin.

Table F-i

Numerical Values of the Model Parameters

Parameter Description and units Numerical Value

q

k

W

a

Q

L

Heat Loss out Insulation (W/m2 )

Metal Conductivity (W/m0 C)

Tube Wall Thickness (m~

Thermal Diffusivity (m Is)

Heat Gain from Heater (W/m2 )

Half Length Between Heaters (in)

-47.3

17.

0.0127

4. 73E-06

3875.

0.112

Figure F-2 shows the comparison between the model and actual

thermocouple measurements from test HT-53 (Test Series #3). The

initial temperature value used in the model is 170C and the set

point temperature used 101 0C. The model predicts temperatures at

three locations that correspond roughly to the location of the

three thermocouples in heater tape section #5 that are shown in

Figure F-2.

The initial transient dies out in approximately 15 minutes

leaving a steady increase in temperature. The model predicts the

time decay of the transient quite well. However, the temperature

difference between the hot and the cold values are much higher

F-15
120- I

100-

280-

E 60-

C0340-

Hot Model

Medium Pred.

20 .... ~~~~~ H .o t ..H .D T I.D at a

o Medium

A Cold

0 2500 5000 7500 10000 12500 15000 17500 20000 22500

Time (seconds)

Figure F-2. Comparison of Temperature Distribution and Transient Response of the HDT

and 1-D Unsteady Model.
for the HDT data than the model. The model does predict that the

intermediate thermocouple is closer in temperature to the cold

thermocouple than to the hot thermocouple as is the case in the

data. The model also does an adequate job of predicting the time

at which the heaters reach the set point temperature of 100*C.

Because of the under-prediction of the temperature difference between the heater temperature and the tube wall temperature

midway between the heaters (tip of the fin in the model), the

model also predicts a much shorter time to reach steady state

than the data shows. If the temperature difference predicted by

the model was, greater at the time the set point temperature of

1Ol*C was reached, then the time to reach steady state would also

be longer. The model makes an adequate prediction of the final

steady state temperature distribution.

F-17
Figures

F-i. Control Volume for the 1-D Unsteady Fin Model.

F-2. Comparison of Temperature Distribution and Transient

Response of the HDT and 1-D Unsteady Model.

F-18
APPENDIX G

DATA ACQUISITION SYSTEM DETAILS

The data acquisition system used to acquire time of arrival

(pressure) signal in the HDT tests is a general purpose system

developed originally for another test apparatus, FLAME [Gl]. The

hardware consists of a Digital Equipment Corp. LSI 11/23 computer

using an IEEE-488 (GPIB) communication bus to control two

independent transient digitizer setups, Tektronix 7612D's and a

CAMAC (Computer Automated Measurement and Control) rack. The

software to control the systems and process the data was custom

written. Relevant details of the hardware and software are

described in this appendix.

G. 1 HARDWARE

The data acquisition system hardware can be divided into

three sections corresponding to separate tasks. During a test,

data is recorded by two independent transient digitizer systems.

The primary system is Tektronix 7612D's transient digitizers with

the CAMAC system used as backup. Post-test, the data is transferred from the volatile memory storage onboard the digitizers

and transferred to permanent storage.

G.1.1 Tektronix 7612D Transient Digitizers

The HDT uses three Tektronix 7612D's with each unit having

two channels. The 7612's provide signal amplification, analog to

digital conversion, and volatile memory for each channel. The

input voltage range is 40 mV to 40 V full scale for the 7A16A

plug in amplifiers currently being used. Each voltage range is

converted to 256 digital steps (or "grey levels"). The 7612's

can sample as fast as a 5 ns/sa' ile to as slow as 1 s/sample with

a total recordable sample size of 2048 samples. The time between

samples (or sampling frequency) can be programmed to change at

pre-set sample locations. (Note: The period in which the 7612

s amples is set at 5ns. If samples are taken every lO0ns, the

sample is not the average value over the 100 ns.)

For use in the HDT, the 7612's were originally setup to

sample every 10 jss/sample. From test HT-51 through HT-96, the

sampling rate was preprogrammed for each channel to increase to 1

jss/sample at the expected time of arrival of the detonation front

.(as predicted by Chapman-Jouguet theory). For the f irst two

channels closest to the initiator, the sample rate at the time of

arrival of the detonation was set to 0.5 ,ss/sample.

It should be noted that the 7612's have high impedance inputs

and the cable length to the heated detonation tube f rom. the

G~ 1
digitizer is -100 m (300 ft). The cable is RG-58 coaxial cable

with a wave travel time of -1.5 ns/ft. Therefore, the cable

resonance period is on the order of 1 /is.

G.1.2 CAMAC Transient Digitizers

The term CAMAC is a generic term for a set of standards for

data acquisition and control systems. In the system used as

backup for the HDT, no signal amplification is needed. The

analog to digital conversion is done by Bi Ra Inc. Model 5908

transient digitizers. These digitizers have variable performance

parameters depending on the number of channels of data being

used. For the HDT, two to three units are used, each with four

channels. The highest sampling rate is 25 jus/sample. The Bi Ra

digitizers do not have internal volatile storage, but use

separate Bi Ra 5903 external memory units. one unit is used in

the HDT tests with a corresponding maximum number of recordable

samples per channel of 8192. The digitizing frequency can be

changed by an external clock to lower frequencies but this

feature is not used for the HDT. The input voltage range is

internally selectable and is set at +/-5 V and the analog signal

is divided into 4096 grey levels.

In the CAMAC standard, the Bi Ra digitizers cannot communicate directly with the IEEE-488 bus. In the setup for the HDT

tests, a LeCroy 8901 bus controller is used for communication

between the LSI 11/23 computer and the Bi Ra digitizers.

G.1.3 Storage/Processing Hardware

During a test in the HDT, data is digitized and stored in

temporary volatile memory in the digitizers. This data is transferred to permanent storage and further processing by a DEC LSI

11/23 computer. The permanent storage devices are a DSD Inc.

,Model 880 Winchester hard disk and two DEC double density floppy

disk drives. The computer can be addressed, and data plotted, on

a Tektronix's 4010 display terminal with a hard copy unit. A

Datamedia DT80 is also used as a display terminal.

G.2 SOFTWARE

The software to control the HDT, and to acquire, store and

initially process the data is custom written using Tektronix's

SF5 BASIC language. The language is tied to DEC LSI 11 hardware

is currently has a limited 32K words of program memory.

G.2.1 HDT Control Program

The temperature of the HDT is controlled by a program that

interrogates the HDT temperature from a CAMAC temperature monitor

G-2
(see Appendix A for hardware details) and compares it to userselected limit or set-point temperatures. * The interrogation,

comparison, and relay closure cycle for all 16 measured temperatures occur once every 20 seconds. During each cycle, the program also interrogates a CAMAC clock and the user can select a

time interval between printouts. The program can operate in a

delayed start mode where only the clock is interrogated. The

interrogated time is compared to a user-specified turn-on time.

When that time is reached, the program reverts to its normal

cycle. This feature is used to begin heating the HDT at night.

The computer also communicates each cycle with a watchdog timer

device that will open circuit the power if not contacted every 64

seconds. This feature protects the HDT in case of a computer

failure.

G.2.2 Data Acquisition Programs

Two data acquisition programs have been written, one to

acquire data from the Tektronix 7612D's and the other from the

CAMAC system. The first communicates through a Tektronix custom

driver which talks only to Tektronix equipment. The second

.program communicates through a more standard IEEE-488 driver.

The programs are used to setup the programmable settings on the

hardware as well as retrieve the data. The programmable settings

are stored for processing the data.

G..2.3 Data Storage Formats

Tektronix SPS basic provides three storage formats. Data

from the 7612D's is stored with the WRITE command format which is

a BCD format with special data descriptors (which make it uncompatible to be read by any other language except SPS basic). Data

from the CAMYAC system is stored with the WRITEU command format

which is a record addressable BCD format. The third format is

the PRINT command format which stores ASCII output. This format

is used to transfer data *to other computers for further

processing.

G.2.4 Data Processing Programs

only simple data processing is done on the LSI 11/23 with SPS

basic. Engineering units are assigned to the data and plots are

made of both the raw and processed data. This facility is sufficient for obtaining the time of arrival data measured in the HDT

experiments.

*The program then tells a CAMAC relay module to open or close

(switching power to the HDT).

G- 3
G.3 REFERENCES FOR APPENDIX G

G1. Sherman, M. P., Tieszen, S. R., Benedick, W. B., Fisk, J. W.,

and Berman, M., "The FLAME Facility - The Effect of Transverse Venting on Flame Acceleration and Transition to Detonation," SAND85-1264, NUREGXX-XXXX, (to be published).

G-4
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"Mc FORM 2n US. "WI&Aa SGAKA?@UV COM4 '"oo"' NUMB" "WdA9US 7AC S- Val N&~

30.32BIBUOGRAPHIC DATA SHEET NtTREG/CR-4905

ate Odcvlow ON. mI "EVERse SAND85-1263

2. TITLE AND SIATII 3 LAVE 411111.4%

DETIONABILITY OF H 2 -AIR-DILUENT MIXTURES

4 DATE U~OfiOR COMPLETED

1ONT. "EAft

SAUT..OVISI MARCH 1987

Sheldon R. Tieszen, Martin P. Sherman 6 41 D01E 549Q1 essul9

William B. Benedick, Marshall Berman JUNE" 1 8

701 RENFORMING O04Q.ANZATtOft NAME AND MAILING ALOOSSS lff a~ CgR.w 0 UOJIECT MASK %VO4K UNIT NUMPES

Sandia National Laboratories

Reactor Safety Research Department 9 41%0 GRANT kuMIEB1

Severe Accident Containment Response Div. A-1246

Albuquerque, NM 87185

10 SPONSO0ING OAGANIZATION NAME Sf0 MAILING ADDRESS CUIil IIc~dZ VYE of ftE"OT

Division of Reactor System Safety Technical

office of Nuclear Regulatory Research_____________

Accident Evaluation Branch .nocvao,-~

U.S. Nuclear Regulatory Commission --

Washington, DC 20555 ____________

12 S4JMLEMENTAftV NOTES

13 ABSTAACT LM? w-* w ftul

This report describes the Heated Detonation Tube (HDT).

Detonation cell width and velocity results are presented f or H2 - air mixtures, undiluted and diluted with CO2 and H2 0 for a range

of H2 concentration, initial temperature and pressure. The

results show that the addition of either CO2 or H2 0 significantly increases the detonation cell width and hence reduces the

detonability of the mixture. The results also show that the

detonation cell width is reduced (detonability is increased) for

increased initial temperature and/or pressure.

14 DOCIJ'.E9T ANALYSIS. KEYWOAOS1OESCIVTOStS 16 AVAILABILITY

Unlimited

46 S4Cu.1TYCLASS.PICATO..

a O(T04F1S'~tC-doo TamsUnclassifieý

212

to 'fl'Ct

*U.S. GOVERNMENT PRINTING OFFICE: 1987-773-049/41050


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