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HYPERSONIC RESEARCH ENGINE

PHASE 2: CEE_IC_T KINETICS STUDY

_ SUPE_$CNIC CGE_CSTC_ _OE_L, DAT_ IT_V

54. 10 (_iResearch _fg. Co., TCS Angeles,

https://ntrs.nasa.gov/search.jsp?R=19750071953 2020-04-20T05:58:57+00:00Z

CTHISPAGEISUNCLASSIFIED t...

Nlg-qS2.ol

AIRESEARCH MANUFACTURING COMPANY

Los Angeles, California

HYPERSONIC RESEARCH ENGINE PROJECT-PHASE II

CHEMICAL KINETICS STUDY

FOR ASUPERSONIC COMBUSTOR MODEL(U)

DATA ITEM NO. 54.10

NASA CONTRACT NO. NASI-6666

Document No. AP-70-6319

Number of pages

Original date

243

20 May 1970

- "11_

Prepared by

v

EnqineeEin9 Staff

Edited by W. Platte

Approved by_

f

Revision Date Pages Affected (Revised,

EetO00C[O iT

NATIONAL TECHNICALINFORMATION SERVICE

¢5. DEPARIIW[NTOFCOIIllER¢/_RIilGFliLD, Vk Z2lil

Added, Eliminated)PI

leOmM23 77, A._'O J_'_

\

UNCLASSIFIED

FOREWORD

The analytical report contained herein is submitted to the NASA Langley

Research Center by the AiResearch Manufacturing Company of Los Angeles_

California 3 in accordance with the guidelines of Paragraph 5.7.3.2.13 NASA

Statement of Work L-49_7-B (Revised).

This report describes the chemical kinetic study for the Supersonic

Combustor Model which was performed by AiResearch in support of the combustor

program phase of the Hypersonic Research Engine Project.

_J AIRESEARCM MANUFACTURING COMPANY

LOS AnlpIItelk Call,_llUNCLASSIFIED 70-5319

Page ii

Sect ion

I

2

3

9

References

Appendix A

Appendix B

UNCLASSIFIED

CONTENTS

SUMMARY

INTRODUCTION

PARAMETRIC STUDIES

3.1 The Detailed Hydrogen-Air Chemical Kinetic Model

3.2 Results and Discussion

CHEMICAL KINETICS DURING THE IGNITION DELAY PERIOD

TWO-DIMENSIONAL EFFECTS IN A DIVERGING COMBUSTOR

COMPARISON WITH TEST DATA

6.1 Results

6.2 Chemical Kinetic Simulation of Two-Dimensional

AIM ANALYSIS .,..-

DISCUSSION AND RECOMMENDATIONS

8.1 Discussion

8.2 Future Work Recommendations

CONCLUSIONS

Run 238

Run 242

I-I

2-1

3-1

3-1

..3-2

4-1

5-1

b-I

6-3

6-11

7-1

8-1

8-1

8-1

9-1

R-I

_ AIRESEARCM MANUFACTURING COMPANYL_ Anll_l_ Cakfomw UNCLASSIFIED 70-6319

Page i i i

%

P

j,

Fiqure

3.2-1

3.2-2

3.2-3

3.2-4

3.2-5

3.2-6

3.2-7

3.2-8

3.2-9

3.2-10

3.2-1 I

3.2-12

3.2-13

3.2-14

3.2-15

3.2-16

3.2-17

3.2-18

UNCLASSIFIED

ILLUSTRATIONS

3-3

3-4

Effect of Initial Static Temperature on Combustor Length

Effect of Initial Static Temperature on Static Pressure

Effect of Initial Static Temperature on Chemical Efficiency 3-5

Species Concentration as a Function of Combustor Length 3-6for an Initial Static Temperature of 2200°R

Species Concentration as a Function of Combustor Length 3-7

for an Initial Static Temperature

Species Concentration as a Function of Combustor Length 3.8

for a Static Temperature of 1900°R

Effect of Initial Static Temperature on Total Ignition 3-9

Delay

Effect of Initial Static Pressure on Total Ignition Delay 3-13

Effect of Initial Static Pressure on Combustor Length 3-14

and Temperature

Effect of Initial Static Pressure on Pressure as a 3-15

Function of Combustor Length

Effect of Initial Static Pressure on Chemical Efficiency 3-16

as a Function of Combustor Length

Species Concentration as a Function ofCombustor Length 3-17

Effect of Initial Static Pressure on Ignition Delay 3-18

Effect of Initial Static Pressure on Temperature as a 3-19


Effect of Initia] Static Pressure on Pressure as a Func- 3-20

tion of Combustor Length

Effect of Initial Static Pressure on Chemical Efficiency 3-21

as a Function of Combustor Length

Effect of Initial Static Pressure and Temperature on 3-22

Ignition Delay

Effect of Equivalence Ratio on Ignition Delay 3-24

_ AIRE$1rARCM MANUFACTURING COMPANY 70--63 I 9UNCLASSIFIED Page iv

P

F--,

f

_

Figure

3.2-19

3.2-20

3.2-21

3.2-24

3.2-25

3.2-26

3.2-27

3.2-28

3.2-29

3.2-30

3.2-31

3.2-32

UNCLASSIFIED

ILLUSTRATIONS (Continued)

Effect of Equivalence Ratio on Static Temperatureas a Function of Combustor Length

Effect of Equivalence Ratio on Static Pressure asa Function of Combustor Length

Effect of Equivalence Ratio on Chemical Efficiencyas a Function of Combustor Length

Effect of Vitiation on Ignition Delay Time

Effect of IO-Percent Carriers on Static Temperatureas a Function of Combustor Length for Several InitialStatic Temperatures

Effect of IO-Percent Carrier on Chemical Efficiency as aFunction of Combustor Length for Several Initial Static

Temperatures

Effect of IO-Percent Carriers on Static Pressure as aFunction of Combustor Length for Several InitialStatic Temperatures

Effect of 2-Percent Carriers on Static Temperature as aFunction of Combustor Length for Several InitialStatic Temperatures

Effect of 2-Percent Carriers on Chemical Efficiency as aFunction of Combustor Length for Several InitialStatic Temperatures

Effect of 2-Percent Carriers on Static Pressure as a

Function of Combustor Length for Several Initial

Static Temperatures

Effect of Percentage of Carriers on Initial Static Tem-

peratures as a Function of Required Combustor Length andChemical Efficiency

Effect of Divergence on Static Temperature as a Functionof Combustor Length

Effect of Divergence of Chemical Efficiency as a Func-tion of Combustor Length

Effect of Divergence on Static Pressure as a Function

of Combustor Length

PaGe .

3-25

3-26

3-27

3-28

3-29

3-30

3-31

3-32

3-33

3-34

3-35

3-37

3-38

3-39

AIRESEARCH MANUFACTURL INJCOMPANI_y UNCLASSIFIED 70-6319Page v

C

f -

Figure

3.2-33

3.2-34

3.2-35

3.2-36

_.2-1

5.0-1

6.1-1

6.1-2

6. I-3

6. I-/_

6. I-5

6.2-1

6.2-2

6.2-3

6.2-_

6.2-5

6. 216

6.2-?

UNCLASSIFIED


Effect of Divergence on Static Temperature as a Func-

tion of Combustor Length

Effect of Divergence on Chemical Efficiency as a


Effect of Divergence on Static Pressure as a Function

of Combustor Length

Effect of Divergence on Ignition Delay as a Function

of Initial Static Temperature

Comparison of Theoretical and Experimental Ignition

Delay Times

Mainstream Compression by Burning in the Boundary Layer

Chemical Kinetics Simulation of Cookson's Experiment

Chemical Kinetics Simulation of Cookson's Experiment

Chemical Kinetic Simulation of Cookson's Experiment

Chemical Kinetic Simulation of Cookson's Experiment

Pressure Profiles for Cookson Combustor

Combustor Configuration Schematic

Second Stage Static Pressure Vibration in Two-

Dimensional Combustor at TTO = 3000°R

Second Stage Temperature Variation in Two-Dimensional

Combustor at TTO = 3000°R

Species Concentration_ Two-Dimensional Combustor at

TTO = 3000°R

Comparison of Calculated and Measured Static Pressures

for TWOlOimensional Combustor Test at TTO = 3800°R

Static Temperature Comparison for Two-Dimensiona]

Combustor at TTO = 3800°R

Chemical Efficiency Variation at TTO = 3800°R

3-A2

3-_,3

3-4/_

_-5

5-2

6-_

6-5

6-6

6-7

6-10

6-12

6-13

6-1&

6-15

6-16

6-1"/

6-18

_] AIRESEARCH MANUFACTURING COMPANY UNCLASSIFIED 70-6319Page vi

UNCLASSIFIED


/

Fiqure

6.2-8

6.2-9

6.2-10

6.2-11

6.2-12

6.2-13

6.2-14

6.2-15

6.2-16

6.2-17

7. -I

7. -2

7. -3

7. -4

7. -5

7. -6

7. -7

7. -8

7. -9

7, -I0

7, -II

7. -12

Species Concentration 3 Two-Dimensional Combustor Study

at TTO = 3800°R

Species Concentration_ Two-Dimensional Combustor Study 6-20

at TTO = 3800°R

Mixing Models 6-22

Measured Static Pressures - Tests 238 and 242 6-23

Geometric and Calculated Areas vs Axial Position 6-24

Mixing Efficiency vs Axial Position - Run 238 6-25

Chemical Efficiency vs Axial Position 6-26

Mixing Efficiency vs Axial Position - Run 242 6-28

Geometric and Calculated Areas vs Axial Position - 6-29

Run 242

Chemical Efficiency vs Axial Position 6-30

Static Variation at Mach 7 - AIM Combustor 7-3

Static Temperature Variation at Mach 7 - AIM Combustor 7-4

Species Concentration at Math 7 - AIM Combustor 7-5

Species Concentration at Mach 7 - AIM Combustor 7-5

6-19

Second Stage Chemical Efficiency at Mach 7 - AIM Combustor 7-7

Static Pressure Variation at Mach 6 - AIM Combustor 7-9

Static Temperature Variation at Mach 6 - AIM Combustor 7-I0

Second Stage Chemical Efficiency at Mach 6 - AIM Combustor 7-II




Comparison of Species Concentration for Different Mixed 7-15

Temperatures at Mach 6 - AIM Combustor

L_.._ AIRESEARCH MANUFACTURING COMPANYLot _w_ll_wl_ Cakfee_ UNCLASSIFIED 70-6519

Page vii

L"..__4

f

4.

,.''.

(

FiRure

7.1-13

7.1-14

7.1-15

7.1-16

7.1-17

7.2.1

7.22

7.2-3

7.2-4

7.2-5

7.2-6

8.2-1

UNCLASSIFIED


Page

Temperature vs Time - Second Stage 7-16

Static Temperature Variation at Mach 6 - AIM Combustor 7-18

Effect of First Stage Efficiency on Second Stage Temperature 7-20

Combustor Length vs Amount of First Stage Fuel Reaction 7-22

Combustor Length vs Amount of First Stage Fuel Reaction 7-23

Static Temperature in a Constant Area Section 7-25

Computed Pressure Profile 7-26

Concentration of OH 7-27

Effect of Ignition on Static Temperature 7-2a

Temperature Profile 7-29

Gas Stream Area Expansion 7-30

General Electric Test Data 8-3

_ AIRESEARCH MANUFACTURING COMPANYLot ,_alm_,, Caldemm UNCLASSIFIED 70-0319

Page v i i i

UNCLASSIFIED

TABLES

Tabl.._..._e

3.1-1

3. I-2

3,2-1

3.2-2

6,0-1

6.1-1

Hydrogen-Air Reactions

Reaction-Rate Constants

Mass Fractions of Reacting Flow

Mass Fractions of Reacting Flow with Initial Carriers

Reactions Used in the Shear Layer Combustion Program

Initia] Conditions Assumed for Cookson's Combustor

3-1

3-10

3-11

3-36

6-2

6-8

_ AIRESEARCH MANUFACTURING COMPANYLo_.Arq_ms, C_mo,mmUNCLASSIFIED 70-6519

Page ix

UNCLASSIFIED

I. SUMMARY

The problems of supersonic combustion in a diverging duct were examined

analytically_ and the results of this study were compared with test results

from the HRE two-dimensional combustor rig. The effects of temperature_ pres-

sure 3 duct divergence, amount of vitiation and initial concentration of

radicals on the chemical kinetics of the hydrogen-air system were investigated.

It was found that supersonic combustion of hydrogen-air in a diverging duct at

low mixed temperatures (around 2000°R) is very sensitive to chemical kinetics

effects. The ignition delay time decreased with increasing pressure but this

effect was reversed in the pressure range of I to 15 atm depending on the

initial temperature. The ignition process was enchanced by the presence of

free radicals_ but the relative effects diminished rapidly as the initial con-centration was increased.

A detailed chemical-kinetic simulation of the HRE two-dimensional com-

bustor test results indicated that low chemical efficiencies in the second

stage were not caused by chemical-kinetics but were due to.inadequate mixing.

This conclusion was further strengthed by tests reported by General Electric

(Reference I-I) in which low chemical efficiencies were observed when fuel was

injected into a constant-area duct followed by a divergence section_ with an

inlet static temperature as high as 2500°R.

It is postulated that intimate mixing requires turbulence with small but

high energy level eddies. The various injector geometries used in the two-

dimensional combustor tests probably did not cause sufficient turbulence in

the mainstream, evidenced by lack of sufficient flow separation. The low level

of turbulence could be due to the favorable pressure gradient in the diverging

duct and to the relatively high temperatures upstream of the second stage

injectors. Further exploration in this area is urgently needed.

The analytical simulation of the AIM engine indicated that the chemical-

kinetics effects will not adversely affect the second-stage combustion process

in the flight Mach number range of 5 to 8.

The results from the two-dimensional combustor tests lead to the prediction

of low second-stage combustor efficiencies in the AIM engine unless methods

for enhancing the mixing process can be devised. Turbulence could be generated

by a metallic coating on the combustor walls. This coating can be applied with

varying degrees of surface roughness to produce different levels of turbulence,

Currently_ five additional igniter stations are being installed in the

AIM combustor. The igniter jets are directed upstream to produce additional

sources of turbulence as well as ignition energy.

_ AIRESEARCH MANUFACTURING COMPANY

I

UNCLASSIFIED 7o- 3J9Page I-I

CUNCLASSIFIED

1

2. INTRODUCTION

(

The problems of supersonic combustion in a diverging duct were evident

in the HRE two-dimensional combustor component test program. In these tests

low chemical efficiencies_ in the order of 50 to 60 percent, were encountered

regardless of injector geometry_ equivalence ratios, and inlet total tempera-

ture. Various injector geometries and equivalence ratios aimed at improving

the mixing, and high inlet total temperatures (5800°R) which should enhance

the chemical reactions were tried. However, all attempts failed to improve

the combustor performance. A subsequent survey of the literature indicated

that low chemical efficiencies were also obtained by a number of investigators

(Reference I-I I-2, and 2-I) whenever a diverging duct was used. Cookson

(Reference 2-II found that a hydrogen diffusion flame could not be maintained

in a simple conical combustor of 0..75 deg divergence and 50 in. long. Com-

bustion was observed to occur after the Mach disc which was formed at the

combustor exit. Cooksonts experiments strongly suggest that chemical kinetics

have a significant affect on the problem. Therefore 3 an investigation was

initiated to study the various effects of chemical kinetics using existing

computer programs in order to obtain a better understanding of the problem.

The investigation was divided into four phases. First_ a parametric

study was conducted to obtain the basic understanding of the chemical kinetics

from the effects of various independent variables such as temperature, pres-

sure, divergence_ degree of vitiation_ and initial concentration of radicals;

second, the mechanism of ignition delay was examined in a simplified analytical

form in order to obtain the essential correlation parameters which otherwise

could not be obtained from computer programs; and third_ a comparison was made

between the computer program results and Cookson's experiments in order to

substantiate the validity of the kinetics programs. Fully-mixed and partially-mixed models were simulated in a shear-layer combustion program (Reference 2-2)

to try and analyze and compare with the results from the two-dimensional com-

bustor test program. Finally 3 a chemical kinetic analysis of the AIM engine

was performed. A brief examination of chemical kinetics using a two-dimensional

kinetics program was also made.

____J AIRESEARCH MANUFACTURING COMPANYLos _ Cale_rr_ UNCLASSIFIED

'2.

70-6,319

Page 2- I

UNCLASSIFIED

1/

3. PARAMETRIC STUDIES

An investigation of the chemical kinetics of a premixed hydrogen-airsystem was conducted. The investigation was directed toward clarifying theeffects of static temperature_ static pressure_ flow velocity, equivalenceratio_ vitiation 3 initial radical concentrationj and combustor divergence onthe chemical kinetics. These effects were determined through use of a one-dimensional chemical kinetics computer program (Reference 5-1).

3.1 THE DETAILED HYDROGEN-AIR CHEMICAL KINETIC MODEL

The reaction mechanism of the hydrogen-air reaction assumed to be com-prised of the II reactions is shown in Table 3.1-1.

TABLE 3.1-1

HYDROGEN-AIR REACTIONS

f (4)

(9)

(ll)

H2+M=H+H +M

02 +M =O+O+M

H2 + 02 = OH + OH

(chain-ini tiatin 9 steps)

(1)

(s)

H2 + OH = H20 + H

O+H +M =OH +M(chain-carrying steps)

(2)

(3)

(7)

(6)

H+O2=OH+O

O+H2=OH+H

H20 + 0 = OH + OH

HO2 + H2 = H202 + H

(thai n-branch in9 steps)

(5)

(_o)

H + 02 + M = HO 2 + M

H + OH + M = H20 + M

(chain-breaking steps)

[_ AIRESEARCH MANUFACTURING COMPANYLOll _lmelk ClktOm9

UNCLASSIFIED 70-6319Page :5-1

UNCLASSIFIED

L,

The symbol M represents a "third body" 3 i.e• 3 any chemical species. The

third body acts as an energy source or sink in chemical reactions. Steps 23

33 and 7 are branching reactions since two chain carriers appear in the

products while only one enters into the reaction• Steps 5 and I0 serve to

break the hydrogen-oxygen chain by removing (H) and (OH) from the mixture.

Thus 3 chain-branching reactions are responsible for the production of pro-

gressively larger concentrations of chain carriers. Unless the chain-branching reactions are balanced by chain-breaking reactionsj the reaction

rate will increase until it becomes sufficiently rapid to be classified as

an explosion.

The reaction rate constants are expressed in the standard Arrhenius form

given by

FKf = DT E exp. T

Kf

Kb =K_Q

KEQ = OCTEC exp. (FC/T)

where D 3 E_ Fj DCj EC and FC are the constants and are presented in Table 3.1-2•

The constant 3 D 3 for reaction (5) was multiplied by the weighted third body

efficiency factor 3 bW

3.2 RESULTS AND DISCUSSION

5.2.1 Effect of Static Temperature

Chemical kinetic calculations were made as a function of initial static

temperature for clean air as defined in Table3.2-1. In all of these calcula-

tions 3 the initial static pressure (P = I atm)3 equivalence ratio (¢ = 0.5)3

initial flow velocity (V = 4500 ft/sec) and combustor flow area were held

constant.

The results of these studies are presented in Figures 3.2-1 through 3.2-7.

In Figure 3.2-13 there appears a significant time delay before any appreciable

temperature rise is observed. This period is referred to as the ignition

delay period. During this period 3 little change occurs in hydrogen molecular

species but large changes in H20 _ O_ H3 and OH concentrations occur as shown

in Figures 5.2-43 3.2-53 and 3.2-6. The two body reactions are relativelyfast and lead to an overproduction of radicals. At the end of ignition delay

period 3 the third body reactions begin to play a dominant role leading to

recombination and depletion of radicals with the accompanying energy release,

The time for the process to proceed from the end of ignition delay to an

equilibrium state is referred to as the reaction time. Due to an inherent

difficulty of the computer program in reaching the equilibrium state_ the com-

putations were limited to 3 min of computer time; thereforej the final

equilibrium state was not reached in most cases.


Lo_ _ ¢=Uorm=UNCLASSIFIED 70 -L_319

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JS IN.

S-53889

Figure 3.2-2. Effect of Initial Static Temperature on StaticPressure

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COHBUSTER LENGTH_ CH

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Species Concentration as a Function of

Combustor Length for an Znitial StaticTemperature of 2200°R

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UNCLASSIFIED 70-6519

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TABLE 3•1-2 (REFERENCE 3-5)

REACTION-RATE CONSTANTS

D E F DC EC FC

I .23000+14

2 .10000+15

3 •12000+14

4 ,10000+22

5 •86000+154

6 .54000+12

7 .29000+15

8 .40000+19

9 .11370+26

iO •75000+20

II •25000+13

.00000

.00000

.00000

-.15000+01

•00000

•00000

.00000

-.10000+01

-.25000+01

-.10000+01

.0000

-.26200+046

-•80500+04

I-•46300+04

-.51900+05

.64400+03

-•12090+05

-.94000+04

.00000

-.59400+05

•00000

-.19630+05

•21592-01

•40779+03

• 18825+01

•26160+0 I

.69905-0 I

• 66604-00

• 87164+02

•51895-00

• 78438+03

• 59569-02

•76439+03

.28430-00

-.41058-00

.21810-01

.63998-02

.28001-00

-.46383-01

-.26247-00

.15772-01

-.42620-00

.27819-00

-.58806-00

..79253+04

-.86628+04

-.91546+03

-.52421+05

.25858+O5

-.76370+04

-.88387+04

.51506+05

-.60168+05

.60344+05

-.95775+04

• bw = 5.0 XH2 + 1.75 X02 + 2,5 XN2 + 1.00 XAR + 50.0 XH20

42.2 + 15 used in calculations reported in Section 6.

There are a number of quantitative definitions of the ignition delaytime which can be found in the literature:

(a) The time required for the concentration of OH radical to reach

10 -6 mole/liter (Reference 3-2)

(b) The time at which a point of inflection of atomic hydrogen isobserved (Reference 3-3)

(c) The location of the intersection of the slopes of the initial andmaximum temperature rise (Reference 5-4)

(d) The time at which a point of inflection of OH radicals is observed


Lo_ _lmes, CaktomiUNCLASSIFIED 70-6319

Page 3-10

@UNCLASSIFIED

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(e) The point of 0. I percent density decrease

(f) The time it takes for the temperature to increase 5 percent

of the total temperature rise (Reference 3-5)

All these assumptions in defining the ignition delay period are reason-

able and lead to the same conclusion (Reference 3-6). For convenlence 3

definition (a) is used in this report. The summarized results are shown in

Figure 3.2-7. As expected, the ignition delay increases with decreasing

temperature and does not ignite at all when temperature decreases to 1800°R.

The resultant pressure and chemical efficiency variations are presented in

Figures 3.2-2 and 3.2-3. The chemical efficiency is an approximation base_

on the percentage of reacted hydrogen molecules by weight. For complete

combustion, the percentage of unreacted hydrogen molecules increases with

combustion temperature. Thereforej the approximation of chemical efficiency

will be pessimistic, especially at high combustion temperatures. The approxi-

mation was used as a calculation convenience and is permissible because only

qualitative results are being sought.

TABLE 3.2-1

MASS FRACTIONS OF REACTING FLOW

(EQUIVALENCE RATIO = 0.5)

Clean Air

H 1.000-09

0 1.0000-09

N2 0.7569-00

H2 0.1440-01

02 0.2287-00

OH 1.0000-09

H20 1.0000-09

HO2 1.0000-09

H202 1.0000-09

5.05 Percent Vitiation

Static Temperature

2000°R

1.000000-09

1.000000-09

0.71959-00

0.14634-01

0.23228-00

0.545-06

0.33491-01

1.000000-09

1,000000-09

2300°R

1.0000-09

0.296-07

0.71981-00

0.14634-01

0.23206-00

0.3438-05

0.33491-01

1.0000-09

1.0000-09

49.25 Percent Vitiation

Static Temperature

2000°R

1.000000-09

1.000000-09

0.38336-00

0.17194-01

0.27292-00

0.116-05

0.52655-00

1.000000-09

1.000000-09

2300°R

1.00000-09

0.346-07

0.38348-00

0.17194-01

0.27279-00

0.116-04

0.32653-00

0.330-07

1.0000-09


Los Anlms,UNCLASSIFIED 70-6519

Page 3-11

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UNCLASSIFIED

3.2.2 Effect of Pressure

Chemical kinetics calculations were made for a hydrogen-air mixture at

a temperature of 1900°R for several initial pressures in a constant area duct.

The ignition delay times obtained from these calculations are presented in

Figure 3.2-8. At low pressuresj the collision rate of molecules is small due

to the low density of the mixture, thereforej the chain-branching reactions

are slow which results in long ignition delays. As the pressure is increasedj

more and more molecules collide per second and chain-branching reactions

become faster and faster resulting in shorter ignition delays. However 3 when

the pressure is further increased_ the ignition delay time reaches a minimum

point beyond which it increases with increasing pressure. This phenomenon is

caused by the following chain-breaking reaction:

H + 02 + M = HO 2 + M

where M represents any kind of molecules? such as H27 027 H203 N2, etc.

Ordinarily HO2 is a very unstable combination of hydrogen and oxygen because

more energy is released upon its formation than is required to bring about its

decomposition. However_ if another molecule is present to absorb the excess

energy released from the formation of H023 the latter may exit as an inter-

mediate product in the chain reaction. The "third body"_ M_ acts as an energy

acceptor and stabilizer to this reaction. This reaction serves to break the

hydrogen-oxygen chain reaction by removing the free hydrogen atom from the

mixture. As the pressure increasesj the concentration of "third body"increases and the effect of chain-breaking becomes greater than the effect of

chain-branching; thereforej it increases the ignition delay time.

Figures 3.2-9_ 3.2-10_ and 3.2-11 show the temperature_ pressurej and

chemical efficiency distribution along a constant area combustor with various

inlet static pressures. The concentration of species is given in Figure 3.2-12

at an inlet pressure of 25 psia.

The effect of pressure on ignition delay for an initial temperature of:

2200°R is presented in Figure 3.2-13. The ignition delay time decreases with

increasing pressure and no minimum point was observed up to a pressure of 65

psia. The reaction is slowed down slightly in the range of pressures from

65 to I00 psia. Figures 3.2-14_ 3.2-15_ and 3.2-16 show the temperaturej

pressure and chemical efficiency distributions_ respectively3 along the duct

with initial inlet temperatures of 2200°R.

Calculations were also made for other inlet temperatures which are shown

in Figure 3.2-17. As the static temperature is increased from 1900°K to

2200°R3 the pressure at which the minimum delay time occurs moves progressivelyto higher values and the curves become flatter. Thus_ at the higher initial

temperature of 2200°R3 ignition delay was not affected as much by staticpressure as at an initial temperature o_ 1900°R.

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significant. Therefore 3 at low initial static temperatures 3 vitiation caused

higher ignition delays. At initial static temperatures above 2200°R the

difference in ignition delay time for vitiated and clean air were less than

20 _sec and therefore can be considered negligible.

3.2.5 Effect of Initial Radicals (Carriers)

In order to see the effect of initial radicals or carriers on the

chemical reaction as a function of initial static temperaturej chemical

kinetic studies were made for two vitiated mixtures with initially non-

equilibrium free-radical concentrations (see Table 3.2-2). Results are

shown in Figures 3.2-23 through 3.2-28 as plots of temperature 3 chemicalefficiency 3 and pressure versus combustor length with different initial

temperatures for I0 percent and 2 percent of initial carriers. The percentof carriers indicates the amount of hydrogen consumed in a constant area

duct if the initial temperatures were 2200°R. As expected 3 the presence of

initial carriers accelerated the chemical reaction by the chain-branching

reactions of Table 3.1-13 steps 23 33 and 7. Initial carriers had the effect

of transposing the region of long ignition delay to lower temperatures. Theautoignition temperatures (those temperatures below which chemical reactionceased to occur) were lowered to 1600°R and 1400OR for the vitiated mixtures

of 2-percent and IO-percent reacted-chain carriers respectively 3 as comparedto 1800°R for clean air. Ignition delay could not be determined by the

previously used criterion of OH concentration because of the presence of

initial carriers. Results based on the chemical efficiencies of 80 percentand 40 percent for both vitiated mixtures and clean air are shown in

Figure 3.2-29. For a given combustor iength_ Figure 3.2-29 gives the

required initial static temperature to produce a given chemical efficiency.

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Figure 3.2-18. Effect of Equivalence Ratio on Ignition Delay

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Figure 5.2- 19. Effect of Equivalence Ratio on StaticTemperature as a Function ofCombustor Length

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MASS FRACTIONS OF REACTING FLOW WITH INITIAL CARRIERS

(EquivalePceRatio = 0.5)

f

H

0

N2

H2

O2

OH

H20

HO2

H202

2 Percent Carriers _

0.63844118-04

0.34675790-05

0.75690000-00

0.14104986-01

0.22605520-00

0.88783859-04

0.18617049-02

0.58i85451-05

0.12254745-06

I0 Percent Carriers _

0.50009155-05

0.16987557-02

0.75690000-00

0.12964130-01

0.21569500-00

0.44593853-05

0.9132556-02

0,28683717-02

0.64002613-06

ePercent carriers indicates the amount of hydrogen consumed in a constant-area

duct if the initial temperatures were 2200°R.

3.2.6 Effect of the Divergence

The effect of divergence was calculated for clean air as a function of

initial static temperature. The results for an initial temperature of 2500°R

are presented in Figures 3.2-30_ 3.2-312 and 3.2-32 for different values of

I dA (change of area ratio per unit length)Ai dx

Examination of Figure 5.2-50 indicated that ignition delay increased with

(idA /with increasing divergence Ai dx and that the reaction proceeded very slowly

at values of divergence greater than approximately I/I0 cm "I. The increased

ignition delay with divergence was due to the relative production rates in the

chain-branching and chain-breaking reactions. At low values of divergence_

the production rates in the chain-branching reactions were sufficient to offset

the production rates in the chain-breaking reactions. At large values of

divergence 3 the decreasing values of pressure and temperature effectively

quenched the chain-branching reactions and the production of chain carriers was

not sufficient to initiate the highly exothermic recombination reactions. For

example 3 to achieve a chemical efficiency of 80 percent within a combustor

length of _, cm_ the required initial static temperature would be 1670°R3

1910°R and 2/_lO°R for lO-percent_ 2-percent and O-percent carriers_ respectively.

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Calculations were also made for clean air at an initial static temperature

of 2200°R. The results presented in Figures 3.2-33_ 3.2-34_ and 3.2-35

indicated a trend similar to the higher inltial static temperature case with

the reaction essentially quenched for values of divergences greater than about

6/I00 cm-I.

Examination of Figure 3.2-33 indicated that ignition would occur in a

diverging duct when concentration of OH had reached 10 -6 moles/liter before

the temperature had decreased below about 1950°R.

I dAIn Figure 3.2-36_ the ignition delays plotted versus AT _ for initial

static temperatures of 2200°Rj 2350°R3 and 2500°R indicated that the effect ofdivergence on ignition delay decreased with increasing initial static tempera-ture. The effect of increasing divergence was to increase the length requiredfor combustion. This increased length was due to (I) the temperature andpressure effects on ignition delay_ and (2) increased flow velocity.

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4. CHEMICAL KINETICS DURING THE IGNITION DELAY PERIOD

Although more than a dozen chemical reactions are involved in a hydrogen-

air combustion process 3 not all reactions are significant at all times. In

the isothermal induction period the major change is in the buildup of the

atomic species (H) and (0) and the (OH) radicals. The significant reactions

are either mildly exothermic or endothermicj and the system is essentially at

a constant temperature. The production rates in reactions which involve large

activation energies are insignificant during this isothermal induction period.

The length of this period is affected both by the initial temperature and by

the pressure. For the HRE application_ the ignition delay must be considerablyless than one millisecond. Significant production rates occur in the following

reactions during the induction period=

i0 I0 15..__1.1 (Ref 3-4) (4-1)H + 02--_OH + 0 k I = 5.64 x e - RT

H + 02 + Mk'--_-"2H02 + M k2 = 8.6 x I08 e + 1.2.___88RT (Ref 3-5) (4-2)

k 3O+H 2 OH+H

9.__2 (Ref 3-4) (4-3)k3 = 1.2 x I0 I0 e - RT

H2 + OH k---_ H20 + H (Ref3-4) (4-4)k4 = 4.2 x 109d_ "e - RT

Where the reactance concentration is in units of mole/lite_ R is in kilo-cal/

mole °K_ T is in °Kj and the unit for time is seconds,

From the above equations the net production rates of (OH), (H) and (0)

can be readily written=

= ,.I.II0 ]+ I. ]IoI-d[H]

(4-5)

(4-6)

(4-;)

_ AIRESEARCH MANUFACTURING COMPANY UNCLASSIFIED 70-6319

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Observing the numerical solutions for more complete reactions in Section 33the relationship

[o][_

remained relatively constant for a given initial condition. Also during the

ignition delay period 3 the molecular concentrations did not change materially 3

and the ratio ofll___2defined" as 2_ could be considered constant. Therefore 3 in

order to simplify the solution the following quantity denoted by symbol Bj Willbe treated as a constant.

10 ]l.lSubstituting these two definitions into Equations (4-5)3 (4.6)3 and (4-7)

results in the following equations.

dEOH]dt= ai [Hi - a2 [OH] (4-e)

d[H] [OH] [H]dt = a2 " a4 (4-9)

d[O]dt= a3 [H] (4-)o)

w.ere: aI = 102lkI(i+8)

a3 --lOz]k,(,-.)(4-)i)

Equations (4-8) and (4-9) are coupled and are independent of the atomic

oxygen concentration. The solution of Equation (4-8) and (4-9) is

m I t m2t

[OH] : b I e + b z e (_mJ2)

a2b I mlt a2b 2 m t "a4t

[Hi = a4 + ml e + a4 + m2 e 2 + b3 e (4-13)

UNCLASSIFIEDLvq

70-6:319

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@ UNCLASSIFIED

.,,.-*.

\

where blJ b2 and b3 are constants to be evaluated_ and mI and m2 are

+ + )2 + 4a 2 _ )-(a 2 a4) + 4(a2 a4 (a I a4ml = 2 .(4-14)

f-/

/

m2 2

+ + )2 + 4a 2 . )-(a 2 a4) - V(a2 a4 (aj a4= (_-Is)

The term involving m2 has a large negative value and dissipates rapidly3

and only mI is of significance. For the range of temperatures and pressures

important to HRE operation_ (900°K < T < 1400°K and pressure = I ATm) the

values for al_ a2

T = 900°K

T = 1400°K

and a4 are:

¢ =0.5

a I = 2.55 x 104 (I + B)

a2 = 7.4 x 105

a4 = 2.3 x I04 (I -B) + 5.5 x I04

a = 4.8 x I05 (I + B)I

a 2 = 8.6 x I06

a4 = 4.8 x 105 (I - B) + 2.7 x I04

@= 1.0

Same as for ¢ = 0.5

i.48 x 106



1.7 x 107


For temperature exceeding 1400°K the ignition delay time will be inmicroseconds.

The value of B for the stated critical conditions is approximately 0.8.

From the above table 3 a 2 is an order of magnitude larger than a I or a4,

The exponent mI is then approximated

a2 (aI -a 4)

I a 2 + a4

=" a I - a4(4-16)

I= JOzJlkI + e)-k= -B)+k2[M]j

[ AIRESEARCH MANUFACTURING COMPANYC_ Anqle_ C_dornm

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The [OH] concentration is then given by

10_]I_,_-_ I_[OH] = [OH]i e (4-_7)

Using the definition of ignition delay as the time for the [OH] radical

to achieve a concentration of I0-6 mole/liter_ then

Or

,0.6 [02112k8-k2c._l__i = e I

10-6

In [OH] i

T =

I°_I_I_,_ _ t_I

C4-18)

Equation (4-18) was plotted in Figure _.l-I for pressures of 1/23 13 and2 atmospheres for the temperature range between 900°K and 1400°K,

Also shown in Figure 4.1-1 were the shock tube experimental results taken

from Ref 4-1. The definition of ignition delay used in Ref 4-1 was based on

the sharp rise in temperature observed by the infra red optical system. If

this sharp temperature rise occurs near an [OH] concentration of 10-6 moles/

liter 3 then the agreement between theory and experiment is reasonable.

The oxygen concentration and the molar concentration [M] of the mixture

can be replaced by pressure in Equation (4-18).

I

aSP - a6p2

where :0.0037 Bk I cm2

a 5 =10 -6 sec gm

T 1.t-c_i

1.7 x 10"5 k2 cm2

a6 = 2 10 -6 sec gm

T in_i I

P in units of gm/cm 2

T in°k

_ AIRESEARCH MANUFACTURING COMPANY UNCLASSIFIED5_

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@ UNCLASSIFIED

tO °3

/fl

i0 "4

l-

h

iO -5

\

____ 0.43

1.0

_THEORETICAL

----EXP. AVERAGE -"2.0FROM REF.4-!

10-6

900 I000 I100 IZO0 1300 1400 1501

TEHPERATuRE, • K

S-53947

Figure 4.1-1. Comparison of Theoretical and ExperimentalIgnition Delay Times

AIRESEARCH MANUFACTULRJNG _COMC_,P,AtNnY

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@UNCLASSIFIED

Equation (4-19) has a minimum when the pressure is varied.

d_ a5 " 2abp_ _ 0

dp [a5P . a6p212

or

a5 109 Bk I

P = _ = k2 T

/

-16.58/RT= 7100 BTe

For B = 0.8 the minimum delay time occurs at the fo]iowing pressures.solutions from numerical integration are also listed for comparison.

Simplified NumericalSolution Solution

T__ P/ atm Pz arm

I000 1.45 I

1140 4.4 2.7

The

The disagreement between these two methods may be attributed to theignorance of the third body effects of water vapor in the simplified solution.

The ignition delay is also affected by the initial [OH] concentration.The influence of this factor can be deduced from equation (4-18) as follows:

'r = (log I0 "6 - !o9 [OH]i)

Increasing the initial [OH] concentration will reduce the i_nition time.A typical initial [OH] concentration is I0-10 mole/liter at IO00UK. A tenfoldincrease of this value produces a 25 percent reduction of the delay time whilea IO0-fold increase results in a 50-percent reduction as calculated below:

Ti0 fold [OH] -6 - (-9)

-io - -e- (-io) =• [OH] i = I0

TI00 fold [OH] -6 - (-8) I

: -e- =T[OH] i = I0


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The increasing ignition delay in the second explosion limit is clearly

illustrated by Figure 4,1-1. For an initial temperature of IO00°K or iessjthe ignition delay time increases with pressure. This phenomena has been

known for some time and is due to the formation of the [H02] radial by

reaction 2 which is (H + 02 + H - HO2 + H). This reaction removes the atomic

hydrogen without the benefit of producing a new active species. Since it is a

three-body-collision process_ its rate is proportional to the second power of

the pressure as compared with the two-body-collision process which is propor-tional to the first power of the pressure. The ignition delay time will

increase with increasing pressure when the rate of reaction 2 increases fasterthan reaction 3.

The initial rate of [OH] production is primarily given by the molecularcollision denoted by the reaction

H 2 + 02---_20H

At time zero 3 it is assumed that the production rate of [OH] in the above

reaction balance the [OH] consumption rate of reaction 4.

t It =0

2k 5

[OH]i : 4"_

-- 2k5I"211°2]-k,I"2]Io.]

1°2}

= 0

The calculated data presented in Figure 4.1-1 were computed based on theinitial [OH] concentration given by Equation (4-20).


Page 4-7

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f

5. TWO-DIMENSIONAL EFFECTS IN A DIVERGING COMBUSTOR

A few exploratory calculations were made in order to investigate two-

dimensional effects in supersonic combustion of a premixed gas in a divergin 9

combustor. Since this effort was very limited in scope_ only a brief qualita-tive discussion will be given here.

Numerical solutions were obtained using the method of characteristics with

finite chemical kinetics in an axisymmetric combustor. The computer programdescribed in Reference 5-1 and 5-2 was used to obtain these solutions.

The hot portion of a boundary layer can give beneficial effects in theinitiation of combustion (assuming that there is fuel in the boundary layer).

Ignition and combustion in the boundary layer can produce an expansion of the

boundary stream tube. Compression waves are induced in the main flow where

the stream tube begins to expand. Farther downstream_ when combustion is

nearly complete in the boundary layer_ expansion waves appear in the main flow,

This situation is depicted schematically in Figure 5,0-1. At the duct center-

line the pressure waves appear downstream of the start of the compression

surfaces. For typical AIM Mach numbers this distance is of the order of the

duct height.

Compression heating of the mainstream 3 caused by combustion in the boundarylayer stream tube_ was predicted in Reference 5-5 using a quasi-two-dimensional

model which assumed a uniform pressure across the combustor_s height. The

"overshoot" (See Figure 5,0-1) predicted by the truly two-dimensional solution

has an effect on combustion which is usually benefica] and which is not pre-

dicted by the quasi-two-dimensional approach,

Howeverj the beneficial effect of a high initial temperature in the

boundary layer can be offset. When a diverging portion of the combustor is

reachedj the boundary layer stream tube is the first to be turned (expanded).

This can result in quenching of combustion in the boundary layer.

Alsoj choking can occur in a single stream tube 3 possibly leading to a

disturbance which propagates upstream in the combustor and causes an adjust-ment in the air flow. Such a disturbance cannot be predicted using the

existing steady-state model. However 3 this phenomenon could conceivably occur

in a real combustor and be a factor in boundary-layer separation.


LOS L_I_ C_kfomm UNCLASSIFIED55

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/,f_

O.

,J

W

Q.

6O

50

40

50

20

I01

0

i= 40.0 PSIA

P = 30.0 PSIA

P = 20.0 PSIA

_= 0.5

dA--=0.0dX

V = 4500 FT/SEC

T. = 2200°RJ

CLEAN AIR

P = I0.0 PSIA

4

Figure 5.2-15.

8 12 16 20

COMBUSTORLENGTH1 CM

S-53895

EFfect of Initial Static Pressure onPressure as a Function of CombustorLength

_ AIRESEARCH MANUFAU'I"UL_I_:I_CO_PAI_NY UNCLASSIFIEDZI.

70-63 19Page 3-20

©UNCLASSIFIED

L

: 0.50

dA_--_= 0.0

V = 45O0 FT/SEC

CLEAN AIR

T. = 2200°RI

/

u

>:¢Jzu.II,-I

(_1

14.1,I.IJ

II

fJ

=:MJ-rIJ

1.0

0.8

0.6

0.4

0.2

00

20.0 PSIA 7

30.0 PSIA

40.0 PSIA

14.7 PSIA

10.0 PSIA

t8 12 16

COMBUSTORLENGTH,_ CMS-53896

Figure 3.2-16. Effect of Initial Static Pressure on

Chemical Efficiency as a Function of

Combustor Length

AIRESEARCMMANUFACTURINGCeq,wLOMPANc._Y UNCLASSIFIED70-6319

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o,.

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8O dAdx " o.o+. 0.50V - _500

CLEAN AIRFT/SEC

6O

20 _" II_OIR

0 _0 80 120 160 200 2&0

T[O, _ SEC.

S-53929

Figure 3.2-17. Effect of Initial Static Pressure and

Temperature on 19nitlon Delay

: AIRESEARCH MANUFACTURING COMPANY

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3.2.3 Effect of Equivalence Ratio

Chemical kinetics were calculated as a function of equivalence ratio with

clean air. Results presented in Figures 3.2-18 through 3.2-21 indicated that

ignition delays are essentially constant for the range of equivalence ratios

investigated.

3.2.4 Vitiation Effects

Precombustion of hydrogen with oxygen replenishment as a means of perheated

air is denoted by the term "vitiated air." The effect of this vitiated air on

the ignition delay time of the H2 -air reaction was investigated.

Clean air at several initial total temperatures was precombusted at a

pressure of 20 atm with varying amounts of hydrogen at room temperature. The

combustion products were then expanded to a pressure of I atm in order to

obtain their equilibrium compositions. Note that in the precombustion 3 oxygen

was added to preserve the same 02 mole fraction as in clean air. The percent

of vitiation or percent of fuel by weight (fuel considered as H 2 and 02 with

the weightlOf). 02 12.2 times that of H2) was varied from 0 to 50 percent (seeTable 3-2-

Chemical kinetic calculations were then made starting with the vitiated

equilibrium species concentrations at I arm pressure. Hydrogen at an equiv-alence ratio of 0.5 was allowed to react at constant area with the vitiated

air. The initial conditions consisted of a static pressure of I arm and a

velocity of 4500 ft/sec at several initial static temperatures from 1850°R to

2300°R. The results of these calculations are presented in Figure 3.2-22.

Ignition delays were determined from the time required for the OH concentra-tion to reach 10 -6 moles/liter. The dotted lines are the estimated values.

Examination of Figure 3.2-22 indicated that the degree of vitiation had

a strong effect on ignition delay time at 1850°R and 2000°Rj but a negligibleeffect at 2300°R. Even small amounts of vitiation at 1850°R caused the

ignition delay time to increase very rapidly and for all practical purposescaused chemical reactions to cease. Chemical reactions also ceased at 2000°R

initial temperature near 25 percent vitiation.

As the amount of vitiation increased_ so did the amount of water vaporand OH. The initial concentrations were shown in Table 3.2-1. The water

vapor acts as a very efficient third body (third bodies act as energy sourcesor sinks in chemical reactions) as shown in the reaction:

H + 02 + M = HO 2 + M

This reaction removed H from the mixture causing a quenching of the

chain-branching reaction. At low temperaturej the chain-breaking reaction

H + 02 + M = HO2 + M predominated. At the higher temperaturesj the thermal

dissociation of H20 and chain-branching HO2 + H2 = H202 + H then became

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6. COMPARISON WITH TEST DATA

Considerable attention has been given to the theoretical chemical kinetics

of premixed hydrogen-air supersonic combustors. However, little of this work

has been done for diverging combustors of specified geometry. In this type

of combustorj conditions can occur in which the expansion waves cause the

temperature and pressure to decrease from their entrance values with combustor

length. By contrast 3 if constant pressurej constant area, or constant Mach

number is assumed 3 the temperature never decreases appreciably (unless largewall heat losses are considered).

Because the rates of the elementary chemical reactions in the hydrogen-

air combustion system are strongly dependent on concentrations and temperaturej

it seems plausible that under some conditions divergence of a supersonic com-

bustor could lead to significant adverse effects on the chemical kinetics even

though the initial temperature is above the autoignition temperature.

Experimental results reported by Cookson 3 Flanagan 3 and Penney (Reference

2-1) provide an example of conditions under which a small change in divergence

angle had a dramatic effect on combustion.

Cookson et al. report that for a combustor inlet air total temperature of

approximately 1900°K and at Mach 1.98_ a flame was initiated in a combustor

which consisted of a 5-in.-1ong constant-area section followed by a 25-in.-

long conical section diverging at a l-deg angle; howeverj with the same inlet

conditions no combustion took place within a completely divergent ductj even

with a divergence angle as small as 0.75 deg.

Axial injection was used in Cookson's experiments. This eliminates com-

plicating effects associated with cross-stream injection and makes the experi-

ments more amenable to one-dimensional analysis.

In an attempt to explain Cookson's results_ chemical kinetic calculations

were made using two different computer programsj each using a different set of

chemical kinetic rate constants. The first program used (Zupniks) is described

in Reference 5-I.; the second (Frey's) in Reference 2-2. The chemical reactions

and rate constants used in the two programs are listed in Tables 6.0-I and

5. I-2. For initial calculations the higher frequency factor listed in Table

3.1-2 was used for reaction 5.

Because the analytical models used were one-dimensionalj there was some

question as to what initial conditions were appropriate. In the Cookson

experimental work the fuel and air started out unmixed at the combustor

entrance. For the chemical kinetic calculations_ premixing was assumed. A11

initial parameters were kept constant except the initial temperature 3 the

_ AIRESEARCH MANUFACTURING COMPANYLos _Igl C_W_

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TABLE 6.0-I

REACTIONS USED IN THE SHEAR LAYER COMBUSTION PROGRAM

React t on

H2+M = H+H+M

02+M = O+O+M

H2 + 02 = OH + OH

H20 + H = OH + H2

OH ÷ M " 0 + H + M

02 + H = OH + 0

H2 +0 - OH+H

H20 + 0 - OH+OH

H202 + H = H2 + HO2

HO2 + M = H + 02 + M

H20 + M = H + OH + M

N2 + M ,, N + N + M

NO+H = N+O+M

03 + M - 02 + 0 + M

H202 + M = OH + OH + M

NO + H - N + OH

N2 + 0 - NO + N

N2 + 02 = NO + NO

NO + 0 - 02 + N

H202 _" H = OH + H20

H20 + OH :" H202 + H

H20 + HO2 = H202 + OH

7.5 x I018

1.9 x 1016

1.6 x 1013

6.0 x I011

2.0 x I0 I§

3.2 x I011

121.4 x I0

1.06<)6 x I013

129.6 x I0

1.59 x IOISbW

I. 17 x 1017

i016

6 x 1016

1018

148.4 x I0

IIS.3x I0

131.5 x tO

1013

I. 8 x 108

135.6 x I0

3, 18 x 1014

10 I_

Backward rate constantk_ s

b =w

-BAT "N • R'_

5.0 + I 75XH2 • X02

N B

1.0 0.0

0.5 0.0

O. 015 49. 2644

-O.S 5.0

1.0 0.0

-0.47 O. I

0.0 5.19

0.013_ 0.96671

0.0 24.0

0.0 1.0

0.0 0.0

1.0 0.0

0.5 0.0

1.0 0.0

0.0 5.3

-0.5 2. 832

0.0 0.0

0.0 40.0

-I.5 3.020

0.0 77.9

0.0 9.0

0.0 1,8

Reference

6-5

6-5

6-5

6-5

6-5

6-5

6-5

6-5

6-1

6-1, 3-5

6-3

6-5

6-5

6-6

6-1

6-5

6-5

6-5

6-5

6-1

6-1

6-1

+ 2.15 XN2 + 1.00 XAR + 30.0 XH20

AIRES£ARCH MANUFACTURING COMPANY

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combustor 9eometryj and the equivalence ratio. Cookson reports an air total

temperature of approximately IBTO°K (5366°R) and an air Mach number of 1.9B at

the combustor inlet. The air and fuel static temperature apparently were about

1176°K (2117°R) and 290°K (523°R) respectively. Preliminary calculations were

made using ¢ = 0.50. This is slightly above the highest value (¢ = 0.45)

given by Cookson.

5.1 RESULTS

At an initial mixed fuel-alr temperature of 1150°Kj the calculations

indicated a chemical efficiency of over 60 percent in the 0.75 degree all-diverging combustor. At an initial temperature of i130°K the chemical effi-

ciency calculated was less than I percent for the same geometry.

For the 30-in. duct with a 5-in. constant-area section and al-deg diver-

gence angle 3 the calculated chemical efficiency was 60 percent or greater fortemperatures of 1115°K and above. This indicated that the calculations with

initial temperatures in the band of approximately 1115°-1155°K (2007°-2054°R)

agreed qualitatively with Cookson_s results in one respect; combustion

occurred in the duct having a 5-in. constant-area section, and did not occur

in the all-diverging combustor.

To avoid choking in the theoretical model at an equivalence ratio of 0.5_

the initial temperature had to be more carefully selected. Raising the

initial temperature just a few degrees above 1115°K could lead to choking in

the divergent portion following the constant-area section.

A few calculations were made for an equivalence ratio of 0.33 using both

Zupnik's and Frey's programs_ with an initial temperature of 1115°K and thetwo different sets of rate constants listed in Table 5. I-Z and 6.0-1. The

initial conditions are listed in Table 6.1-1. Both programs again predicted

the result found by Cookson--that combustion would occur in the combustor

with a constant-area section followed by a I-deg divergence 3 but not in the

combustor having a constant divergence angle of 0.75 deg. Furthermorej when

a constant-area combustor was specified 3 the calculation indicated choking.

This apparently is in agreement with Cookson's observation that a shock wouldform in the constant-area combustor.

The computed axial temperature profiles for the two diverging combustor

cases are shown in Figures 5,1-1 and 6,1-2. In the case with no combustion

(Figure 5.1-2) the temperature profiles from the two programs were very

nearly identical and only one curve is shown.

Disagreement between the results from the two computer programs is due tothe differences in rate constants which were used rather than the differences

in mathematical method. The curves are labeled with the program name only forconvenience.

One of the conspicuous features of the case with no combustion is the

decrease in (OH) concentration which occurs in the results from both programs

and begins well along the combustor length_ as shown in Figure 5,1-3. (Adecrease in (0) concentration begins farther downstream; see Figure 5,1-4.)

UNCLASSIFIED 7o-63,9_ A_,_ _-_., Page 6-3

@ UNCLASSIFIED

34.0OO

/

0i

X

o

,J_DI--

M.I

I--

32.000

30.000

28.000

26.000

24.000

22.000

20.000

18.0000.000

COHBUSTOR:5 IN. LENGTH CONSTANT AREA

--BY I ° DIVERGENT SECTION

• = 0.33

FOLLO

FREY PROGRAM

I

ZUPNIK PROGRAMa

• . l/j/////

5. 000 I 0.000 30. 000

/I

/

15.000 20.000 25.000

Z DISTANCE, IN.

/35.000

S-53943

Figure 6.1-1. Chemical Kinetics Simulation of Cookson's

Experiment

_ AIRESEARCH MANUFACTURING COMPANYLOS AniliNe. Ca_locnba

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f

21.000

20.000

.-,. 19.000

0

Xv

o

,R

I-,

I,U

I'-'

18.000

17.000

16.000

COHBUSTOR

DIVERGENT

= 0.33

0.7S °

CONE

15.000

O. 000 5.000 I 0.000 15.000 20.000 25,000 30.000

Z DISTANCEj IN,S-539_

Figure 6.1-2. Chemical Kinetics Simulation of Cookson's

Experiment

_l AIRESEARCHMANUFACTURING COMPANY

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[

(

,o!

3.000

2. 500

2.000

om

X

i. s000

1.000

0.500

CO0_,S_ PHI = 0.35 0.75 DEG CONE

ZUPNIK PROGRAMT_

0.000 5.000 IO.O00

I

-FREY PROGRAH

--...15.000 20.000 25.000 50.000

DISTANCE, IN.$-53906

Figure 6.1-3. Chemical Kinetic Simulation of Cookson's ExperimentHole Fraction OH vs Z

_ AIRESEARCH MANUFACTURING COMPANYL_ _ _I_

UNCLASSIFIEDGz.-

70-6519

Page 6-6

@ UNCLASSIFIED

l'

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3.000

2.500

2.000

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• = 0.33

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S-539&5

Figure 6.1-4. Chemical Kinetic Simulation of Cookson'sExperiment


LO_ AnB4eS C&lee_


Page 6- 7

UNCLASSIFIED

TABLE 6. I-I

INITIAL CONDITIONS ASSUMED FOR COOKSON'S COMBUSTORMASS FRACTIONS

Species Zupnik Program Frey Program

H

0

N2

H2

02

OH

H20

HO2

H202

No

N

05

i0 "9

10 .9

0.761

0.00958

0.250

i0 -9

10.9

i0 -9

i0 -9

Not Applicable

Not Applicable

Not Applicable

0.0

0.0

0,761

O. 00958

0. 230

0.0

0.0

0.0

0.0

0.0

0.0

0.0

Velocity 3 ft/sec = 4215Static pressure_ psia =¢ = 0.55

12.81

Reaction rates from the Frey program indicate that the reversal .in the time-derivative of (OH) concentration occurs when the rate of the OH-destroyingreaction

OH + H2 - H20 + H (6-I)

outweighs the combined rates of the two dominant OH-producing reactions

02 + H - OH + 0 (6-2)

H2 + O - OH + H (6-3)

UNCLASSIFIED 70-6319_ A_,_c,_=_ Page 6-8

UNCLASSIFIED

/ .

The (OH) reversal is apparently only a symptom and not the basic cause of the

quenching of combustion in the analytical study. Exploratory calculationsshowed that when the rate of Reaction (6-1) above was suppressed by lowering

its rate constant, the destruction of (OH) was accomplished by the reaction

OH + OH - H20 ÷ 0 (6-4)

Similarly, when in a further calculation Reactions (6-I) and (6-4) above were

both suppressed 3 two more reactions took their place to cause net destruction

of (OH).

It is believed that the quenching observed in the computer programs is

due to a decrease in the rates of all the reactions_ which is caused simply by

the lowering of static pressure and temperature associated with expansion of

the gas. The OH reversal seems to be a part of the adjustment of the chemical

process to the slower rates. Changing the rate constants of the OH-destroying

reactions changes the overall process ratej but apparently does not change themechanism.

The pressure profile reported by Cookson for _ = 0.35 and those computed

by the two chemical kinetic programs for the geometry in which combustion

occurred are shown in Figure 6.1-5. Computed profile forms in disagreement

with the experimental profile is not surprising; the heat release was spread

out due to finite-rate mixing in the experiments_ but in the theoretical pre-mixed model the heat release occurred over a short axial distance. Agreement

in the constant-area section would probably be improved by considering the

effects of mixing and of wall friction.

As previously mentioned_ a high frequency factor was assigned to the rate

constant for reaction 5 in using the Zupnik program. This frequency factor

was about 2.5 times greater than that in the original reference (see Table

5.1-2). Decreasing the frequency factor of this reaction has the effect of

increasing the overall heat release rate. When the lower frequency factor in

Table 3.1-2 was used 3 the heat release was accelerated enough to cause choking

in the combustor having a constant-area section although the calculation for

the conical combustor still indicated no heat release. Thus for a marginal

case the results can be very sensitive to the rate of the H + 02 + M reaction.

This rate constant is believed to be known within a factor of two (Reference

6-I).

The temperature chosen for obtaining qualitative agreement with Cookson'sresults was about IlO°R, or 5 percent lower than the unmixed air inlet static

temperature. This is not considered a serious discrepancy in view of the

assumption of premixing in the model and the uncertainties in the chemicalkinetic rate constants.

It is believed that the qualitative agreement between theory and experi-

ment in this case is sufficient to indicate that the O.75-deg divergence of

the combustor used by Cookson et al. may have had a serious effect on the

chemical kinetics_ leading to the observation of little or no burning insidethe combustor.


Page 6-9

UNCLASSIFIED

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UNCLASSIFIED70-6519Page 6- IO

@ UNCLASSIFIED

6.2 CHEMICAL KINETIC SIMULATION OF TWO-DIMENSIONAL COMBUSTOR TESTS

Combustion tests were conducted with a two-dimensional 3 constant-width

combustor having a length of 29 in. 3 an inlet cross section of 0.6 by 6 in. andan exit-to-inlet area ratio of 2.6. The tests were conducted at various test

temperatures and injector geometries. Fuel was injected in two stages; the

first in a constant area 3 the second in a diverging area as shown in Figure

6.2-I. High chemical efficiencies were obtained in the first stage (about 90

percent) while second-stage efficiencies were lower (about 60 to 70 percent).

A study was made to determine if the second-stage combustion was chemical-

kinetics }imited or mixing limited. The Zupnik computer program (Reference

3-I) was used in the second-stage combustor to investigate the chemical kineticsj

and the Frey computer program (Reference 2-2) was used to investigate both

chemical kinetics and mixing in the first- and second-stage combustors.

The first case studied was at a test total temperature of 3000°R with

¢ = 0.68 injected in the second stage. Entrance conditions to the second stage

were calculated from a one-dlmensiona] data reduction program using equilibrium

chemistry. In this case 3 second-stage entrance conditions were determined

assuming complete combustion in the first stage.

The Zupnik computer program (Reference 3-1) was used to evaluate second-

stage combustion. The calculated air static temperature (from the data reduc-

tion program) was averaged with the 1500°R H 2 temperature and resulted in a

2100°R mixed fuel-alr temperature at the second stage entrance. Results in

Figures 6.2-2 through 6.2-4 indicated no second stage combustion. The OH

concentration reached a maximum of 1.47 x I0"B moles/liter or about I00 times

lower than that used to indicate ignition delay_ Figure 6.2-4.

Two cases at 3800°R total test temperature were run in a manner similar

to that at 3000°R. This time an equivalence ratio of 0.25 was injected in the

first stage and _ = 0.38 and 0.78_ respectively3 were injected in the second

stage. Results are shown in Figures 6.2-5 and 6,2-6. In both cases 3 the fuelstarted burning about I-in. from the second-stage entrance.

The static temperature distribution computed for complete mixing was

higher than that calculated from the data reduction program. This hi9her

temperature arises because more fuel reacts as shown by the chemical efficien-

cies in Figure 6,2-7. AIso_ cooling losses are not accounted for. The maxi-

mum reaction rate occurred (Figure 6.2-7) at a point about 2-in. downstream

of second-stage injection, a chemical efficiency of 80 percent was attained

5-in. from injection. Several species are plotted in Figures 6.2-8 and 6.2-9

for the stoichimetric and fuel lean cases, respectively. In both cases there

was a rapid increase in the concentrations of H 30_ OH and HO2. About 1,5 to

2.5 in. downstream of injection the production rate of OH3 HO2 and H began to

decrease.

Therefore with the assumption of complete and instantaneous mixing and no

second-stage air-fuel injection disturbance_ the second stage fuel reacted

(;7


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CO,MBUSTOR LENGTH, CN

S-55948

Figure 6.2-4. Species Concentration, Two-Dimensional Combustor

ac TTO = 3000°R


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70-6519

Page 6- I 5

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12 16 CH

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S-53912

Figure 6.2-7. Chemical EfFiciency Variation at TTO = 3800°R

''4


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7_70-6319

Page 6-18

@ UNCLASSIFIED

==

0.1 x 10"1

0.1 X 10"20

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t H20

H20

H0.1 X 10

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IO 12 IH

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S-559/_9

Figure 6.2-8. Species Concentration_ Two-Dimensional Combustor

Study at TTO = 5800°R


Lot Anl_et, Ca_,to_n,a

UNCLASSIFIED75

70-6519

Page 6-1 9

UNCLASSIFIED

1.0

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Figure 6.2-9.

COe'IBUSTOR LENGTH_ CM

Species Concentration,

Combustor Study at TTO

Two-Dimensional- 3BOOOR

S-53950

_ AIRFSEARCH MANUFACTURING COMPANYLOf,AnlleI,M.Csl*tor_

UNCLASSIFIED"76

70-6519

Page 6-20

UNCLASSIFIED

rapidly at 5800°R total temperature and did not react at all at 3000°R total

temperature. At 5800°R about 80 percent of all fuel injected reacted which

was higher than that calculated from the one-dimensional data reduction program.

A more realistic study atboth temperatures was made With another computer

program. Measured static pressures_ cooIing_ mixing_ and friction losses were

included in the model. The results of that study follow.

Two of the two-dimensional combustor tests were simulated in the Shear

Layer Combustion Computer Program (Reference 2-2) developed by Dynamic Science.

This program permits the analysis of complex chemical kinetic systems with

arbitrary gas phase reactions and species using a one-dimensional (area or

pressure defined) stream-tube model. Unique features of this program are (1)

its ability to integrate the differential equations governing the chemical

kinetic system with complete numerical stability using an implicit integration

technique (Reference 6-2)3 and (2) its ability to add (or extract) mass momen-

tum_ energy 2 and species at any position along the stream tube.

The simulation of the tests was based on the assumption of two limitingconditions. The first of these conditions assumed that the combustor effi-

ciencies calculated from test data represented chemical efficiencies (100percent mixing efficiency). The second assumed that the combustor efficiencies

represented the mixing efficiencies.

The several mixing models used with the two limiting conditions were

implemented by the concept of an inert hydrogen molecule denoted by the symbol

HZ 2. This inert hydrogen molecule participated in the flow dynamics_ but

was not permitted to dissociate or react with other species. Mixing was done

by replacing inert hydrogen (HZ 2) with active hydrogen (H2) using the species-

addition feature of the computer program.

The three basic mixing models are shown in Figure 6.2-10. Model I pro-

duced early mixingj Model 2 produced a maximum mixing rate at the mid-point

of the mixing length_ and Hodel 5 produced late mixing, Further variationwithin each mixing model was obtained by varying both the mixing length and

the amount of hydrogen mixed at the injectors.

The two tests chosen for this simulation are listed in Table 6.2-1 along

with their nominal test parameters.

TABLE 6.2-1

Run

258 242

Time (sec) 520.30 682.55

0.6049 1.0267

TT (°R) 2858 3575

T (OR) 1897 2158

Combustor Efficiency 60 percent 60 percent


_ AnleWHL _l,_c*,ew_J

UNCLASSIFIED

Station 7.5

7770-6519

Page 6-21

UNCLASSIFIED

WH 2

dX

MIXING LENGTH

MODEL I

I Il IxIN0'ENOT II MODEL 2 I

Figure 6.2-10. Mixing Models

L

MIXING LENGTH

MODEL 3

The chemical kinetics calculations were started at Station 7.3_ just ahead of

the first stage injectors_ using equilibrium concentrations of the species.

The energy and momentum defects due to heat transfer and wall friction were

distributed linearly along the combustor_ While the energy_ momentum 3 and mass

addition due to fuel injection were input at the appropriate injectors. The

pressure-defined stream tube model was employed using measured static pres-

sures from the two tests (see Figure 6.2-11).

The results obtained from imposing the two limiting conditions on the

simulation of run 258 in the Shear Layer Combustion Computer Program are pre-

sented in Figures 6.2-12 through 6.2-14_ where the areasj mixing efficiencies 3

and chemical efficiencies were plotted as a function of axial position. In

all cases I00 percent mixing efficiency (_m) was assumed in the first stage

combustor using mixing model 2 with 50 percent mixing at the injectors and

complete mixing at station 12. Examination of the calculated areas in

Figure 6.2-12 indicated a reasonable blockage (50 percent) in the constant-

area portion and reattachment of the flow near the entrance of the divergent

portion of the first stage combustor. The first stage results demonstrated

chemical efficiencies of 95 percent at station 13 and nearly lO0 percent

beyond station 17 (see Figure 6.2-14).

The first limiting condition (I00 percent overall mixing efficiency) was

imposed on the second-stage combustor using both a 50-percent local mixing

efficiency at the injectors with mixing Model 2 and a 0 percent local mixing

efficiency at the injectors with mixing Model 5. An overall mixing efficiency

of I00 percent was set at station 29 with both mixing models-- the former

simulating early mixing; the latter_ late mixing.

----'1 AIRESEARCH MANUFACTURING COMPANY UNCLASSIFIED 70-6519

Page 6-22

UNCLASSIFIED

0

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UNCLASSIFIED70-6319

Page 6-23

UNCLASSIFIED

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RUN 238 (_ = 0.60_,912

I I I I II00_ MIXING EFFICIENCY

II -- MIXING LENGTHS

I0--

+ IST STAGE

+ 2ND STAGE

02ND STAGE

TIME = 520.30

I 1

5.5 IN. 'r/ = 1.00C

7.82 IN. i/ = 0.92--C

8.2 IN. I/ = 0.82

9 --60_ MIXING EFFICIENCY

2ND STAGE MIXING LENGTHS

8 -- A 4.0 IN. ii = 0.97C

[] 8.2 IN. 1/c = 0.96

7 I I I

6

5

GEOMETRIC AREAS-_

÷

_e+ + + 4+++

c

/

I

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2

6 8 I0 12 14 16 18 20 22 24 26

X_ IN.

28 30

S-539 l&

Figure 6.2-12. Geometric and Calculated Areas vs Axial Position

-'-(_] AIRESEARCH MANUFACTURING COMPANYLOs Anlql_¢ Cald_rnl UNCLASSIFIED 70-6319

Page 6-24

UNCLASSIFIED

1.0

0.8

0.6

0.4

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06

RUN 238 = 0.6049 TIME = 520.30

/I/

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INJECTORS

50

0

50

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X2 IN.

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8 IO 22 24 26 28 50

S-53915

Figure 6.2-15. Mixing Efficiency vs Axial Position -Run 258


Lm,_ CaW_mmUNCLASSIFIED 70- 6319

Page 6-25

UNCLASSIFIED

1.0

O.B

RUN 238 _6 = 0.6049

I00_ MIXING EFFICIENCY

MIXING LENGTHS

+ IST STAGE

+ 2ND STAGE

0 2ND STAGE

60_ MIXING EFFICIENCY2ND STAGE MIXING LENGTHS

Z_ 4.0 IN. _/ = 0.97C

D 8.2 IN. 9c = 0.96

TIME = 520.30

3.5 IN. R = 1.00C

7.82 IN. _c = 0.92

8.2 IN. _/ = 0.82C

÷÷+ _ + +'P-

0.4

0.2

÷

÷

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+

0 ' _ , +6 8 I0 12 14 16 18 20 22 24 26 28 50

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S-53916

Figure 6.2-14. Chemical Efficiency vs Axla] Position

_ AIRESEARCH M A N U FACTUL_IANG CO Mc_IPAwNNY" UNCLASSIFIED 70-6519

Page 6-26

UNCLASSIFIED

Examinations of the calculated areas (symbols + and 0) in Figure 6.2-12indicated a reasonable blockage (15 percent) at the second-stage injectors 3however both mixing models eventually required flow areas greater than thegeometric areas. Since such flows would be impossible to attain with themeasured pressures from run 258_ the assumption that the combustor efficiencyequalled the chemical efficiency with IO0-percent mixing was in error. Thisargument was further substantiate_ from the chemical efficiencies in Figure6.2-14 where values were 92 percent for early mixing and 82 percent for latemixing_ compared with the value of 60 percent required to match the test data.

Therefore 3 the other limiting condition (combustor efficiency = mixingefficiency) was imposed on the second-stage combustor. A 50-percent localmixing efficiency at the injectors with mixing Model I (early mixing) wasassumed. An overall mixing efficiency of 60 percent was set at 4.0- and 8.2-in. downstream of the injectors (second stage) as shown in Figure 6.2-13.

Again 3 as shown in Figure 6.2-12, the calculated flow areas indicated areasonable blockage in the vicinity of the second-stage injectors, with theblockage gradually decreasing to zero as the flow approached the combustorexit. The mixing length of 4 in. produced flow areas which closely matchedthe geometric areas and resulted in a chemical efficiency of 97 percent.

The two limiting conditions were imposed on the simulation of run 242using the same mixing models as in run 238 with the exception that time didnot permit the late mixing case to be run. The flow areas, mixing efficien-ties 3 and chemical efficiencies were plotted as a function of axial distanceand presented Ln Figures 6.2-15 through 6.2-17. Examination of the areas inFigure 6.2-15 again indicated that the first limiting condition (chemicalefficiency = combustor efficiency, I00 percent mixing) was in error and thatthe flow areas resulting from the second limiting condition more closelymatched the test conditions. The fluctuating flow areas near the exit of thecombustor (Figure 6.2-15) were due to pressure fluctuations (see Figure 6.2-10).

While it appeared that the second limiting" condition_ i.e._ incompletemixing produced the correct flowfields_ the true condition could be foundsomewhere between the two limiting conditionsj quite close to the second. If

the chemical efficiency is denoted by _c combustor efficiency by _ and, mixing

efficiency by _m3 the relationship.

= " (6-5)

could be used to iterate on a mixing efficiency to produce flows which would

more closely match the test results. For example, the next value of mixingefficiency in the iteration for run 258 would be obtained from

_n + I) _ 0.60

= _ = 0.97 - 0.62

__.,,_ AIRESEARC H MA N U FACTU Rd NGCOUcapAt_Ny UNCLASSIFIED 2.-3

70-631 g

Page 6-27

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Page 6-29

UNCLASSIFIED

1.0

0.8

0.6u

0.4

0.2 !

06

I I-- RUN 242

8 I0

/

i

12

I00_ MIXING EFFICIENCYMIXING LENGTHS

+ I ST STAGE 3.5 IN. _/ = 0.98C

+ 2ND STAGE 8.2 IN. _/c = 0.8660_ MIXING EFFICIENCY

MIXING LENGTHS

A 4.1 IN. _ ; 0.96C

[3 8.2 IN. _1 = 0.95C

I I I I I I ,,I

14 16 18 20 22 24 26

Xl IN.

I

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28 30

S-53919

Figure 6.2-17. Chemical Efficiency vs Axial Position

rill AIRESEARCH MANUFACTURING COMPANY UNCLASSIFIED 70-_319

Page 6-30

f

UNCLASSIFIED

The results from the above test simulations support the conclusion that

the low combustor efficiencies experienced in the two-dimensional combustor

tests were due to poor mixing in the second stage.

The detailed results from the chemical-kinetic simulation of runs 258

and 242 are presented in Appendixes I and 2.

/


LOS ,e,_l[,Me_ CsklommUNCLASSIFIED 70-6519

Page 6-51

This rna__ntains info_tfecting

the natio_kl ._ State • within

the m,e,nin_of t_., Title 18,

• =io= or revel_],_ *h/ch in_h K to

an unauthc_mff_person is prohibited bylaw.

7. AIM ENGINE

7.1 ANALYSIS

In the AIM combustor_ fuel is injected from several locations as

shown below: Ib i

Ic 2cla

/

The first stage injectors (la_ and Ib) are located in a slightly diverging

section; the second stage injectors (Ic3 4 and 2aj 2c) at greater divergence.

Fuel flow requirements in the first stage are set to prevent inlet unstart

and thermal choking. The second stage fuel flow schedule was to be determined

from cycle analysis and mixing studies.

A simulation of both stages was made in a two-dimensional combustor

test. Testing demonstrated high chemical efficiency (near 90 percent) for

the first stage injectors. The second stage injectors_whlch were located

in a diverging area_ gave much lower efficiencies (near 60 to 70 percent).

A study was made of the present AIM combustor to see if these low efficiencies

were inherent in the design due to chemical kinetics.

It was assumed that combustion would be temperature-controlled. Thus

complete mixing was assumed. The Zupnik computer program was used to de-

termine whether the second stage combustor could have a high chemical

efficiency.

The first case studied was Math 7 total temperature at I000 psia total

pressure to simulate test conditions for Future AIM tests. It was assumed

that an equivalence ratio of 0.4 would be injected from the first stage

and that the second stage would begin midway between injectors 2a and 2c.

A chemical efficiency for the first stage was based on two-dimensional tom-

buster test results which indicated that at ]east 80 percent chemical el-

ficiency should be obtained in the first sta9e combustor at an equivalenceratio of 0._.

The engine cycle program was used to determine second-stage entrance con-

ditions. This program uses equilibrium chemistry. Using the output static

_J AIRESEARCH MANUFACTURING COMPANYLo__NI_ C=k_

70-6519

Page 7- I

temperature from the engine cycle program and assuming 900°R H2 fuel at an

equivalence ratio of 0.6 gave a mixed fuel-air temperature of 5000°R. This

H2 temperature included second stage cooling losses. Using this mixed tem-

perature at 19 psia and 4800 ft/sec as the first stage exit conditions, the

static pressure and temperature profiles for the second stage combustor were

calculated in the Zupnik chemical kinetics program as shown in Figure 7.1-I

and 7.1-2. Examination of these profiles indicated a very short ignition

delay period at mixed temperature of 3000°R. At a distance of 2.7 cm down-

stream of the second-stage entrance, the flow thermally choked after 85 percent

of all fuel injected in both stages (¢ = 1.0) had reacted. Instantaneous

complete mixing was assumed at the second stage entrance. Actually, mixing

will take some finite length with mixing and reaction occurring simultaneously

over a portion of the combustor. Therefore_ whether choking would actually

occur cannot be determined using this model. However, with the assumption of

complete and instantaneous mixing it does appear that at Mach 7 conditions

there will be no chemical kinetics problem in the second stage combustor of

the AIM engine. When the first stage chemical efficiency was reduced to

50 percent, which produced a mixed temperature of 2_O0°R, the fuel reacted

less rapidly as indicated in Figure 7.1-2. In this case, a chemical ef-

ficiency of 83 percent was attained at a distance of 8.3 cm from the second

stage entrance. Since the Mach number was about 1.6 at this point_ it is

improbable that thermal choking would have occurred had the calculation been

continued.

Combustion occurred when species H and OH produced from first stage com-

busion were removed at the second-stage entrance (see Figure 7.1-2). There

is, howeve_ a |arge ignition delay with about 53 percent of the second-stagefuel reacted 19.2 cm from the entrance. This case is not very realistic_

but was conducted to demonstrate that 3 at Math 7_ there is no combustion

problem due to temperature alone.

An idea of how the mole fractions of several species varied with combustor

length is presented in Figures 7.1-3 and 7.1-4. At a mixed temperature of

3000°R (see Figure 7.1-3) the concentrations of H, O, OH and HO 2 increased

rapidly, but after I cm the concentrations of H, O, and HO2 decreased. The

buildup of OH and H20 became less rapid after I cm, and OH started to de-

decrease just before thermal choking occurred. Similar trends were observed

at a mixed temperature of 2_O0°R (see Figure 7. l-L). It appeared that the

production rate of H20 started to decrease at 6 cm of combustor length and

that the reaction of H2 proceeded very slowly beyond 7 cm. In the AIM com-

bustor there is about 5-times as much length compared with the two-dimensional

combustor so slower reaction should not be a problem. The variation of second

stage chemical efficiencies are shown in Figure 7.1-5. The chemical efficien-

cies were approximated from the change in weight fraction of H2. This is not

exact since even if the chemical reaction were to go to equilibrium3some H2

would remain. It does indicate, though_ a rapid increase In chemical ef-

ficiency near 80 percent with a slow rise thereafter.

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The second case simulated Mach 6 flight conditions. The manner in which

the study was conducted was the same as at Mach 7. This time an equivalence

ratio of 0.2 was assumed For the first stage with a chemical efficiency of 80

percent at a point midway between injectors 2a and 2c. The second-stage

equivalence ratio was 0.8, and several fuel temperatures from 900°R to I500°R

were used. The results obtained from the finite kinetics program are shown in

Figures 7. I-6 and 7.1-7. At a fuel temperature of 900°R_ the mixed fuel-air

temperature was 2150°R and no temperature rise was observed; at I500°R fuel

temperature or 2270°R mixed fuel-air temperature the fuel burned rapidly.

A mixed temperature between these two was run (2200°R) and in this case the

fuel also reacted. Thus using species concentrations based on equilibrium

chemistry for second-stage entrance conditions showed that a change of 50°R

mixture temperature would produce a go or no-go situation. When the H and OH

produced from the first stage combustion were removed at a mixed temperature

of 2200°R, no temperature rise was observed_ as shown in Figure 7.1-7. This

was not the case at Mach 7 at a mixed temperature of 2400°R. At a mixed tem-

perature of 2270°R, about 70 percent of all fuel injected (_ = 1.0) reacted

before thermal choking occurred, while at 2200°R mixed temperature 60 percent

reacted before computer cut-off time was reached (flow did not choke). The

chemical efficiencies for these cases are shown in Figure 7.1-8. When the

fuel reacted it did so rapidly. The chemical efficiencies continued to rise

at both mixed temperatures.

Several species were plotted in Figures 7. I-9 to 7.1-12 for cases with

fuel reacting and without fuel reacting. The OH concentration for a mixed

temperature of 2150°R reached a maximum of 2 x I0"7 moles/liter at about 6 cm

downstream of the second stage injection as shown in Figure 7.1-II. At this

point the static temperature had dropped to about 1950°R with a static pressure

of 20 psia. The parametric studies seemed to indicate that once the static

temperature became less than about 2000°R in a divergent duct and the OH con-

centration had not reached I0-6 moles/liter by then, combustion did not occur.

Thus, results from chemical kinetics simulation of the AIM configuration were

consistent with the parametric study in Section 3 of this report. For the

cases with combustion(Figures 7. l-9 and 7. I-10) an OH concentration of #0-6

moles/liter was always reached before the static temperature was reduced to

2000°R. As shown in Figure 7.1-12, the 50°R difference in static temperature

between the go and no-go cases caused an increased production rate of OH start-

ing at about 0.05 cm from the second stage entrance. Thus the OH concentration

was able to reach 10-6 moles/liter before the temperature became too low due to

divergence.

For a mixed temperature of 2200°R, an OH concentration of 10 -6 moles/liter

was reached in about 3 cm. This corresponded to an iqnition delav time of

about 25 _sec. By this tlme the temperature had dropped to 2100°R.. If one

had assumed expansion with friction at a mixed temperature of 2150°R, the

variation of static temperature with time would have been as shown in Figure

7.1-13. With a friction coefficient of 0.006_ at 25 _sec, the static temper-

ature would be close to 2100°R. Thus_had friction been included in the modeI_

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S-57120

Figure 7.1-13. Temperature Vs Time,Second Stage(U)

_ AIRESEARCHMANUFACTURING COMPANY 70-6319

Page 7- 16

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combustion at a mixed temperature of 2150°R would probably have occurred.

Also 3 the model did not Include any temperature rise from fuel disturbance

which would have helped initiate combustion.

The above study indicated that second stage combustion was very sensi-

tive to the first-stage chemical effic!ency_ fuel temperature 3 and skin friction.

Second-stage entrance conditions (including the concentrations of ali

major species) were determined from an engine cycle program which used equilib-

rium chemistry, Therefore 2 a study was made to determine whether application

of a chemical kinetics solution in both stages would affect the combustion

characteristics of the second stage. The results showed that iE would.

The first-stage entrance static temperature at Mach 6 is about 1300°R.

At this temperature the finite kinetics program would indicate no combustion,

To simulate the air shock due to fuel injection_ an air static temperature of2000°R was chosen as the first stage entrance condition. An equivalence ratio

of 0.2 was assumed and combustion at a constant area was specified to insure

that the fuel would react. In this manner it was hoped that at the same amount

of fuel reacted (in a constant area)_ static temperature_ pressure and velocity

would match that from the engine cycle computer program, Thus the only dif-ference in second stage entrance conditions (if any) would be the concentration

of the individual species.

The first stage was defined to be halfway between injectors Ic and 4 at

a chemical efficiency of 50 percent. With 900°R H2 fuel_ the mixed fuel air

temperature was 1800°R. As shown in Figure 7.1-14_ reaction took place al-

most immediately_ and the flow choked about I cm downstream of injection.In this case the initial concentration of OH at the entrance of the second

stage combustor was 3 x 10 -5 moles/liter_ or 30-times that concentration used

to define the ignition delay time. This OH concentration was also I00 timesthat obtained from the cycle program output which used equilibrium Ehemistry

(Figures 7.1-9 to 7.1-12). As shown in Table 7.1-1_ the values of carriers

O_ H_ HO2 and H202 also changed significantly.

Therefore with finite rate kinetic chemistry_ second stage combustion

occurred at a mixed temperature of 1800°R_ whereas with equilibr|um chemistry

a mixed temperature of 2200°R was required for combustion. This indicated

that at Hach 6_ second stage combustion would not be chemical kinetics-limited.Thus at both Hach 6 and 7 there should be no combustion problem if complete

mixing is assured.

Since combustion was shown to be very sensitive to initial specie con-

centration_ an investigation was made varying the percent of fuel reactedin the first stage in order to determine the effect on combustor length. To

simplify results the first stage was run at constant area and the second stage

at a constant divergence. An equivalence ratio of 0.2 was used in the first

stage at 2000°R_ 20 psia and 4400 ft/sec mixed conditions. An equivalenceratio of 0.8 was used for the second stage. The effect of varying the per-

centage of first stage fuel reacted on combustor length is shown in Figure 7.1-15.

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TABLE7.1-1

COMPARISON OF INITIAL MASS FRACTIONS USED IN AIM

STUDY AT SECOND STAGE ENTRANCE* (U)

Specie

H

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Finite Kinetics

Chemistry Ist Stage

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In a length of I0 cm, 2 percent of the first stage fuel reacts while it takes

about 18 cm for 97.8 percent of the fuel to react. Mixing the temperature of

output alr with 5&O°R fuel shows that about 25 percent of the first stage fuel

must react in order for combustion to occur in the second stage at a divergence

(dA/AldX) of 0.03 cm"I. No combustion occurred in the second stage for values

of less than I0 percent of fuel reacted in the first stage. However_ the

overall combustor length does not necessarily decrease as the percentage of first-

stage fuel reacted increases. The reason is that first stage combustor length

increases much more rapidly than the second stage length. This is more clearly

shown in Figure 7.1-16. In fact a minimum occurs near 60 percent of first stage

fuel reacted. The overall length is shown at a constant H2 mole fraction of

0.15 or at a constant overall chemical efficiency of about 55 percent. This

efficiency was the highest reached without choking the second stage with 97.8

percent of fuel reacted in the first stage. A similar minimum occurred when

the divergence was doubled to 0.06 cm -I (Figure 7.1-17). This indicated that

making the first stage of the combustor less efficient might decrease the

overall combustor length.

In summary,

(=) Equilibrium chemistry and finite kinetics chemistry in the

first-stage combustor did not predict the same combustion

characteristics for the second stage of the AIM combustor.

(2) Finite-rate chemistry assuming complete mixing indicated

no second stage combustion problems at both Mach 6 and 7.

(3) Shorter combustor lengths might occur with less efficient

first stages.

7.2 AIM KINETICS AT MACH 6

Model T inlet test data indicate that at Mach 6 the static temperature

for undisturbed flow at the first injecti.on station of the AIM will be

approximately 1290°R, the local Mach number being about 2.8. This static

temperature is too low for autoignition. Some exploratory chemical kinetic

calculations were made_ using the Shear Layer One-dimensional Combustion

Program, (Reference 2-2) to ascertain what strength of flow disturbance might

be needed at the first injection station in order to initiate combustion. A

further calculation was made for the second stage with no flow disturbance

other than that from simple mass and energy addition (no boundary layer sep-aration).

For all these calculations certain constant conditions were assumed.

The first-stage total equivalence ratio was set at 0.2, the fuel being

equally split between the two first stage injectors (la and Ib). The second-

stage total equivalence ratio was 0.83 split equally between _njectors 2c

and 2a. The igniters, about I in. downstream of the first-stage injectors,

were assumed to contribute 0.0413 lb/sec of hydrogen-oxygen combustion products

0

10770-6319

Page 7-21

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AMOUNT OF FIRST STAGE FUEL REACTEDjPERCENT

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Figure 7.1-16. Combustor Length vs Amount of First Stage FuelReaction (U)

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S-57119

Figure 7. l-17. Combustor Length vs Amount of First Stage FuelReact ion (U)

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Page 7-23

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at an overall igniter equivalence ratio of 1.6. The igniters' combustion

efficiency was taken to be 23 percent_ giving a mixed igniter exit gas tem-perature of 3050°R. The composition of the igniter gases was taken from quasi-

equilibrium calculations using the above chemical efficiency.

A uniform frictional force of 18.7 Ibf/in. along the combustor's length

was assumed. Estimated local heat losses were used; these varied between I09

Btu/in. sec. and 234 Btu/in. sec. and were specified as a function of axial

distance.

The fuel temperature was assumed to be 1440°R, and the total air flow was

taken to be 34.6 lb/sec. The fuel and the igniter gases were assumed to be

injected normal to the engine axis_ and to mix completely and instantaneouslywith the main flow. The fuel was injected over a length of 0.2 inches at each

injector.

The disturbances assumed for the flow ahead of the first injection station

corresponded roughly to those produced by two-dimensional flow over a wedge.

Thus the strength of the disturbance can be described by specifying a wedge

angle.

Results

Assuming a 15-deg wedge angle ahead of the first injection station gave

a Mach number of 2.1i a static pressure of 47 psia_ and a static temperature

of 1740°R just upstream of the first injector. An effective flow area reduction

of 47 percent was used in order to satisfy continuity. In the first calculation

using these conditions_ the effective flow area was kept constant for a distance

of 2 in._ then linearly increased to the actual duct area at.a point 8 in. down-stream of the first injector. Fuel injection and igniter gas injection pro-duced static temperature rises in the constant-area section (see Figure 7.2-1),

but the maximum temperature was less than 1800°R. Ignition did not occur.

The computed pressure profile is shown in Figure 7.2-2, and Figure 7.2-3 shows

the concentration of OH.

A second calculation was made using the same initial conditions but with

the assumption that the pressure along the combustor was constant. In this

case fuel injection produced a slight drop in static temperature, and theeffect of the igniter on static temperature was negligible (see Figure 7.2-4).

Again, ignition did not occur.

Increasing the wedge angle to 20 deg gave an initial static temperature

of 1940°R, a pressure of 61.7 psia 3 and an effective area reduction of 51

percent. A chemical kinetic calculation using constant pressure indicatedcomplete combustion in the first stage. The temperature profile is shown in

Figure 7.2-5. The area expansion of the gas stream at the equivalence ratio

of 0.2 (see Figure 7.2-6) was not sufficient to fill the actual cross-sectionalarea of the AIM duct. Consequently_ the calculation was re-started at a point

near completion of first stage combustion (Z = 45; see Figure, 7.2-5). From

this point on_ an assumed effective flow area (rather than constant pressure)

was specified. The initial area was that determined by the first stage constant

_ AIRESEARCH MANUFACTURING COMPANYLOS A_llt4 _ CsM/oet_6

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II_70-6319Page 7-30

pressure calculation; the effective area was then increased linearly unti| it

matched the actual duct area just downstream of the first injector of the

second stage. At the entrance of the second stag% the computed gas temperaturewas over 2300°R. The calculatlon indicated that the Fuel from the first

injector of the second stage would burn in a very short distanoe and cause

choking of the flow.

7.3 DISCUSSION

Time ]imitations prevented the investigation of any mixing model other

than instantaneous mixing for the AIM. With respect to the mixing model, the

calculation must be considered optimistic. Also, it is not known whether any-

thing approximating a constant-pressure profile can be sustained over a length

of 4.5 in. in the AIM's diverging first stage geometry.

The strength of the flow disturbance (pressure ratio of almost 4 to I)

required to produce combustion in the theoretical calculations is probably

excessive; it is unlikely that this pressure ratio can be induced in the AIM

(at some equivaIence ratio) without unstarting the inlet. However, it may be

possible to initiate combustion with smaller disturbances because of localized

igniter effects.

Treating fuel and igniter gas injections one-dimensionally undoubtedly

neglects some of the most beneficial effects of these processes. The igniter

gases, for instance, are known to be poorly mixed; the igniters' design is in

Fact based on film cooling by unmixed oxygen. The core of the igniter streams

therefore contains zones which have higher temperatures, and correspondingly

higher concentrations of labile species, than indicated by the fulIy-mixed

igniter model.

The effectiveness of the igniters is also considerably increased because

the hot gases mix only with part of the mainstream. The assumption used in

the calculations, namely that mainstream gas is mixed with igniter gases in

a mass ratio greater than 800 to I, leads to the unrealistic result that the

igniters' effect on local static temperature is negligible. For Mach 5 test

conditions the igniter used in the two-dimensiona] combustor was effective

with a static temperature (before boundary layer separation) of approximately

lO00°R. The undisturbed static temperature in the AIM is 1290°R; hence, it

seems possible that combustion can be initiated in the AIM by use of the

igniters even if the flow disturbance is small. Als%the prediction of choking

at the second injection station might be negated by use of a reasonable Finite-

mixing model.

The conclusion from this AIM study is that with instantaneous mixing and

for the conditions assumed in the 20 deg wedge angle case, the second stage of

the AIM would not be klnetically limited at the Mach 6 test condition.

_ AIR£SEARCH MANUFACTULRJN GCe,p_O,MJAj I

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8. DISCUSSION AND RECOMMENDATIONS

8,1 DISCUSSION

The analytical studies have indicated that chemical kinetics problems

wou]d not be present in the AIM engine at Mach 6 and 7 f]ight conditions.

Inadequate mixing was considered to be the major contributing factor for thelow combustor efficiencies in the two-dimensional combustor tests. In order

to substantiate these theoretical findings, it is recommended that future

research programs be directed to better understanding the mixing process, par-

ticularly in a confined, favorable pressure gradient system.

As discussed in the fifth oral review_ Reference 8-1j the mixing process

in a supersonic combustor may be classified in three distinct phases; (I) jet

penetration, (2) turbulent mixing, and (3) molecular diffusion. Among these,the turbulent mixing is least understood. The function of jet penetration is

to properly distribute the fuel sources into the combustor by means of jetmomentum. The turbulence either existing in the airstream or generated by jet

penetration and combustion is to break up the fuel sources into many small

lumps stirring up the fuel and air. Finally3 mixing is completed by moleculardiffusion which brings hydrogen and oxygen molecules into intimate contact.

The molecular diffusion process is slow_ therefore, in order to shorten the

mixing length, it is necessary to generate strong turbulence and small eddiesat the molecular level to reduce the distance in which the molecules diffuse

for complete combustion.

Since turbulent mixing theory is still in an early stage of development_it cannot be applied to the solution of this problem at present. Therefore,future solution of this problem will have to rely on experiment.

8.2 FUTURE WORK RECOMMENDATIONS

The following items are recommended for future work to extend and com-

pliment present efforts in solving potential problems in supersonic combustion.

8.2.1 Analytical Approach

The analytical study may be best summarized by Swithenbank's paper,Reference 8-2. In general, the low-wave-number end of the turbulent energyspectrum depends on the geometry of the turbulence-producing device, while thehigh-wave number region of the spectrum is almost isotropic and independentof the source of eddy formation. The smalier eddies are very important in theturbulent mixing process in which two gases are stirred together, to the mole-cular level. Since the high-wave-number eddies contain about 80 percent of thetotal turbulent energy J the ability of different systems to achieve mixing

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will depend largely upon the total turbulent energy in each particular system.

In general 3 the ability of a turbulent mixin 9 system to mix two gases willdepend upon

(a) Intensity of turbulence

(b) The scale of turbulence

(c) Mixing region length

(d) Lateral distances through which the injected fluid must travel

(e) Velocity of gas through the mixing system.

To obtain a semi-quantitative analysis of the mixing process 3 we need to

know the relation between these five various quantities 3 and the effect of

the chamber 9eometry.

The analytical study should provide guidance in conducting a well defined

experimental effort.

8.2.2 Experimental Approach

The fuel mixing process is strongly influenced by the levels of intensity

of turbulence. The one-dimensional chemical kinetics program has indicated

that the separation bubble in the first stage is in the order of 30 to 40 per-

cent of the duct area, while in the second stage 3 only 15 percent of flow

area is blocked. This points to a low level of turbulence, and poor mixing in

the second stage. General Electric's Report_ Reference I-I_ stated: "The

constant-area section provides maximum pressure disturbances for given fuel

injection and burning; a necessary situation if high-Mach efficiency is to be

9ood". Since the quoted statement was based on experiments 3 no detailed

explanation was given in that report. The static pressure distributions fromthis test are reproduced in Figure 8.2-1 for reference. The implication was

two-fold. First because the "high-Mach" referred to was Mach 9.53 where burner

inlet static pressure and temperature were approximately 4.8 PSIA and 2500°F

respectively_ the chemical kinetic problem was absent. The calculated ignitionI dA

delay time was at most 50 _sec; The divergence parameter _- _ was 0.0139-I

am at the initial point. Second_ because of the high static temperature_the static pressure rise due to combustion is lower; this results in less flow

separationj less turbulence and poorer mixing. The latter is considered tobe the basic problem in future high-Mach number flight conditions.

In view of the above discussion_ the future research program should be

directed toward the following:

(a) To correlate turbulence produced by external sources with mixing 3

such as the effects of boundary layer thickness_ shock strength_

size of separation bubble 3 combustor 9eometry_ pressure gradient and

combustion. Particular emphasis should be placed on a confined

geometry with favorable pressure gradients.

_ AIRESEARCM MANUFACTURING COMPANYLM/mllll_ CalkFarnm


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(b) To develop a turbulence generation method. Swithenbank argued that

the distance to generate turbulence in a swirling jet is about I/3

the distance required by a nonswirllng jet. Furthermore 3 the intensity

of the turbulence in the developed region is higher in a swirling

jet 3 because for a given axial velocity of the jet there is an

additional tangential velocity representing an increase in the jet

kinetic energy.

(c) One of the difficulties in experimental work on turbulent mixing is

the accurate measurement of the mixing process. The measured quan-

tities are averages of the instantaneous values because the turbulence is a

random 3 fluctuating flow and the flow is three-dimensional. The mixing is not

as complete as that indicated by the time-averaged measurements taken over a

period of time using a gas-sampling probe. The sampling probe mixes rich and

lean regions to indicate an average composition. This may explain the low

combustor efficiencies in the two-dimensional combustor tests 3 in which gas-

sampling measurements indicated uniform mixed flow at the exit. This phenom-

enon was also reported in Reference 8-3 and requires further exploration.

8.2.3 Methods to Improve Mixing

A sudden rearward-facing step in a combustor will promote mixing, how-

ever 3 it would result in lower pressure forces on the combustor wall. In

other words_ the rearward-facing step will produce higher chemical efficiency3

but lower total pressure. The tradeoff between these two should be closelyexamined.

At high-flight Mach numbers where thermal choking is not likely to occur_a converging burner which would enhance flow separation cannot be ruled out asa potential solution.

The effects of surface roughness were clearly demonstrated in the Phase

I boilerplate engine. In the paper presented at the 3rd AIAA Propulsion

Specialist Meeting_ it was stated that "The Hastelloy-X-coated engine demon-

strated quite different characteristics from the pure nickel-coated engine."

The high pressure at the fuel injection station indicated spontaneous combus-

tion 3 the flow was nearly chokedj the ignition temperature was lowered about

300°F and the slope of the pressure curve was much steeper. This phenomenon

may be due to a combination of the effects of (I) the higher surface tempera-

ture_ (2) the increased thickness of Hastelloy X coatingj which reduces the

flow area and increases the static pressure and temperature, (3) the greater

area contact with the airstream of the Hastelloy X, which contains 50 percent

nickel 3 and (4) turbulence produced by the rough surface coating. In order to

further examine these effects 3 the surface was smoothed from the throat to a

distance approximately 12 to 14 in. downstream of the throat. The test results

indicated that there was no significant difference between the rough- and the

smooth-surfaced engines. The smoothed surface was later verified by laboratory

check as having an average roughness of 300 microinches.

Examination of the methods discussed above indicates the surface coating

to be most adaptable to the AIM engine.

_==

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9. CONCLUSION

The results of this study lead to a number of conclusions with regard to

chemical kinetics in a supersonic combustor. One broad conclusion obtained

is that chemical kinetics is very sensitive to the divergence of the combustor.

Basicaliy_ this is attributed to the low stream static temperature which

"freezes" the species in a manner very similar to that in nozzle flow.

The detailed chemical-kinetic simulation of the HRE two-dimensional com-

bustor test results indicated that low combustor efficiencies in the second

stage were due to mixing. In the extreme case of late but complete mixing 3 the

chemical efficiency approached 82 percent which indicated that the second-stage

flow was not overly kinetics-limited due to the decreasing temperature in thedivergent duct.

For the AIM engine at Mach 6 flight conditions_ with second-stage fuel

injected at,stations 2a and 2c; calculations indicated that combustion was

not chemical-kinetics limited. Assuming that the fuel was completely mixed

with air at the injection station3 the second-stage flow was choked.

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REFERENCES

I-I,

I -2o

2-1,

2-2,

3-1,

5-2.

5-/,

3-5,

3-6.

3-7

/-4-1.

5-1°

General Electric Co. Evendale_ Ohio_ Analytical and Experimental

Evaluation of the Supersonic Combustion Ramiet En_ine (U)_ TechnicalII

Report AF APL-TR-bS-I033 VoI. If2 Component Evaluation."

United Aircraft Research Laboratories 2 Mach 5 Test Results of Hydrogen-

Fueled Variable-Geometry Scramiet (U)_ Technical Report AFAPL-TR-b8-116.

Cookson3 R. A._ P. Flanagan3 and G. S. Penney3 A Study of Free-Jet and

Enclosed Supersonic Diffusion Flames_ Twelfth Symposium (International)

on Combustion3 The Combustion Instltute2 Pittsburgh3 Pennsylvania.

Frey 3 H. M._ J. R. Kliegelj G. R. Nickerson3 T. J. Tyson3 Shear Layer

Combustion Computer Proqram 3 Vol. 13 Dynamic Science 3 A Division ofMarshall Industries:

Zupnik_ T.j E. Nilsonj V. Sanlij Investigation of Nonequilibrium FlowEffects in High Expansion Ratio Nozzles _Contract NAS3-2572)3

NASCAR-5_O&23 United Aircraft Corp.

Schott 3 G. L. 3 and J. L. Kinsey 3 Kinetic Studies of Hydroxyl Radicals

in Shock Wave. II. Induction Time in the Hydrogen-Oxyqen Reaction_Jour. Chem. Phy. 3 Vol. 293 No. 53 Nov. 19583 pp. 1177-1182.

Nicholls_ J. A. 3 Stabilization of Gaseous Detonation Waves with Emphasison the Iqnition Zone_ Thesis for Ph.D.3 Univ. of Michigan 3 19603Ann Arbor3 Michigan.

Momtchiloff_ I. N._ E. D. Taback3 and R. F. Buswell3 An Analytical

Method of ComputinR Reaction Rates for HydroRen-Air Mixture_ Paper

presented at the Ninth International Meeting of the Combustion Institutej

CornelI Univ. 3 August 1962.

Lezberg_ E. A._ Ignition and Chemical Kinetics in Hypersonic RamJets3 (C)

on Hypersonic Aircraft Technoloqy_ AME Research Center3 May 16-18_ 1967.

Pergament 3 H. S._ A Theoretical Analysis of Non-Equilibrium Hydrogen-

Air Reaction in Flow Systems_ AF55(657)-7911.

Brokaw 3 R. S.x Analytical Solutions to the Ignition Kinetics of The

Hydro_en-Oxyqen Reaction_ NASA TN D-2542.

Just_ T. H. 3 F. Schmalz3 Measurement of Ignition Delays of H2-Air MixtureUnder Simulated Conditions of Supersonic Combustion Chambers_ Institute

Fuel Luftstrahlantriebe Forz-Wahn_ Germany_ July 1968.

Quau3 v. 3 J. E. Meide_ J. R. Kliegel 3 G. R. Muckerson_ and H. M. Frey_

Kinetic Performance of Barrier-Cooled Rocket Nozzles 3 of Spacecraft andRockets3 5j I0 October 1968_ pp. 1157-11/_2.

AIRE$FARCH MANUFACTURING COMPANY

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REFERENCES (Continued)

5-2

5-3

6-I

6-2

6-3

6-4

KIiege1_ J. R.3 G. R. Nickersonj H. M. Frey3 V. Q.uau2 and J. E. Melde3

"ICRPGj Two-Dimensional Kinetic Reference Program"3 Dynamic Science2

Irvine2 Calif. 2 July 1968.

Engineering Staff_ Hypersonic Research Engine Project-Phase IIA3

Combustor Pro.qram Second Interium Technical Data Report_ AiResearch

Report AP-67-25352 September 1967.

Bauich2 D. L. 2 D. D. Orysdale2 and A. C. Lloyd3 Critical Evaluation ofRate Data for Homogeneous s Gas Phase Reactions of Interest in High-Temperature Systems2 Vol. 3 3 School of Chemistry2 The University3Leeds_ England.

Tyson_ T. 2 and J. R, KIiege13 "An Implicit Integration Procedure for

Chemical Kinetics"_ AIAA 6th Aerospace Science Meeting2 Paper No. 68-1803

January 1958.

Baulch2 D. L. 3 O. D. Drysdale2 and A. C. Lloyd_ "Critical Evaluation ofRate Data for Homogeneous Gas-Phase Reactions of Interest in High-Temperature Systems" 2 VoI. 2t Schoo] of Chemistry 3 The University 3Leedsj England.

Tyson_ T. and J. Kliege12 "An Implicit Integration Procedure for

Chemical Kinetics2" AIAA 6th Aerospace Sciences Meeting2 Paper No.

68-1803 January 1968.

6-5

6-6

Cherry_ S.S. 2 "Phase II Final Report Screening of Reaction Rarest" TRW

Report No. 08832-6002_ I0002 TRW Systems Group_ Redondo Beach 2 Calif. j6 Dec 1967.

Frey_ H.M. 2 Dynamic Science 2 Irvine 2 Calif. -private communication.

8-1

8-2

8-3.

Fifth Oral Review Technical Presentation (U)j Hypersonic Research Engine

Project2 Phase II by AiResearch Manufacturing Co. 3 Los Angeles_ Calif._Report No. AP-69-5696 (CONFIDENTIAL)

Swithenbankj J._ and N. A. Chigier2 "Vortex Mixing for Supersonic Com-

bustions" Dept. of Fuel Technology and Chemical Engineering2 The

University of Sheffield 2 England. Twelfth Symposium (International)on Combustion.

Hawthorne 2 W. S. 2 D. S. Weddell 3 and H. C. Hattel 2 "Mising and Combus-tion in Turbulent Gas Jet". Third Symposium on Combustion Flame andExplosion Phenomena.

_ AIRESEARCH MANUFACTURING COMPANYL_ _'nllm'L C,ik_mfa

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APPENDIX A

/

RESULTS FROM CHEMICAL KINETIC SIMULATION

OF RUN 258_ TIME - 520.30 SECONDS.

STOICHIOHETRIC FUEL-AIR RATIO ,, 0.052568

AIRESEARCHMANUFACTURING COMPANY

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First Stage Combustor - Run 238

Mixing Model 23 50 percent mixing at eachStation 12.

2A(in. ) m(lb m/sec)

2.45O I .7810

2.518 I .7881

2.483 I .7881

2.483 I .7941

2.434

2.344

2.32O

2.324

2.390

2.432

2.491

2.907

3.398

3.794

3.970

4.112

4. 207

4.305

4.536

4.781

5.067

5.303

5.308

5.253

5.1385. 032

4.992 I .7941

Station

7.3000

7.5212

7.8112

8.5162

9.0012

10. 0462

10.8462

11.091 2

I I .4887

I .5887

I .6887

2. 0337

2. 5337

3.0212

3.5737

4.0287

14.5112

15.0062

15.5562

16.0562

16.5562

17. 0500

I 7. 5500

17• 9950

I8.4950

18.9950

19.1950

injector, I00 percent mixing at

(mixed)_H2 "m

0 0

O. 003551 0.50

0.003551 0.50

O. 006561 O. 50

0.006830 0.52

0.009121 0.70

0.011693 0.89

0.01 2234 0.93

0.01 2839 0.98

0.01 2958 0.99

0.013015 0.99

0.013119 I .00

0.013119 I .00

"c _H2 + _Hz2

0

0.0071 0.007078

O.0083 O. 007078

0.0000 0.0131 22

O.0002

O.004 I

O. 0443

O.0937

O. 2856

O.5668

O.536 I

0.7912

0.9306

0.9552

0 o966 0

0.9713

O. 9750

0.9779

O. 9997

O. 9998

0.9998

O. 9998

O. 9998

O. 9998

O.9998 _O. 9998

0.9998 0.013122

¢

0

O. 1220

O. 1220

O. 2262

O.2262

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26O0

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2000-

1900,

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X_ IN.

2O

Figure A.I-I. Temperature vs Axial Distance

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t

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Figure A.I-2. Area Ratio vs Axial Distance

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I00_ MIXING AT STATION

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Figure A.I-3. Concentration of H20 vs Axial Distance


Page A. I-5

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120

Figure A.I-4. Concentration of H2O vs Axial Distance

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Figure A.I-5. Concentration of OH vs Axial Distance

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Figure A.I-6. Concentration of 02 vs Axial Distance


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Figure A.I-8. Concentrations of H vs Axial Distance

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Los A_ Co_4om_UNCLASSIFIED

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2. Second Stage Combustor - Run 238

Mixing Model 2, 50 percent local mixing

mixing at Station 28.62.

at each

(mixed)Station A(in. 2) m(Ib m/sec) mH2 _m

19. 1950 4.990 I .7941 0.013119 1,00

i9.8550 5,300 1.8068 0.0i9491 0.755

20.6000 5.326 I .8068 0.022315 0.755

20.8100 5.757 I .8176 0.024931 0.680

21.4150 6.192 0.025068 0.684

22.0150 6.605 0.025461 0.695

22.5600 6.943 0.026041 0.711

23. 1600 7.270 0,026928 0.735

23.5600 7.484 0.027662 0.755

24.1600 7.818 0.028977 0.791

24.5600 8.056 0.02998 0.819

25. 1050 8,399 0.03150 0,860

25.5050 8.631 0.032516 0.887

26. 0750 8 • 985 O. 033765 O. 922

26.4750 9. 286 O. 034509 O. 942

27.0750 9.755 0.035420 0.967

27.4750 10.079 1 0.035891 0.98028.0300 10,547 0.036363 0.992

28.6200 11.065 1.8176 0.036635 1.00

injector 3

O. 9998

0.6917

0.8612

O. 7209

O. 8774

0.9150

O. 9257

O. 9284

0.9272

0.9230

0.9 91

0.9 42

0.9 32

0.9 35

0.9 42

O.9 59

0.9 75

O. 9203

O. 9244

I00 percent

_H2 "+ mHz2 ¢

0.013122 0,2262

0.025815 0,4443

0.025815 0.4443

0.036640 0.6317

JO. 036640 0,63 i 7

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23.5062 6.541 0.019981 0.55

24.1062 6.794 0.020392 0.56

24.5062 6.965 0.020640 0.56

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27.5887 8.358 0.021840 0.596

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RESULTS FROM CHEMICAL KINETIC SIMULATION

OF RUN 242_ TIME = 682.55 SECONDS.

STOICHIOHETRIC FUEL-AIR RATIO - 0.034746

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Station

Star;on A(ln. 2)

7.3 3. 126

7.51 25 3. 203

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8.5925 2.934

9.1925 2. 765

9.5925 2.684

I O. 1000 2. 796

I 0.5000 3. 083

I .0450 3.318

I .4450 3. 190

I • 9525 3. 255

2.5525 3.569

3. 0900 3. 885

3.4900 4.006

4.0375 4.181

4.6275 4. 259

5. 1975 4.342

5.5975 4.408

6.1975 4.512

6.5975 4.584

7. 1425 4.787

7.54 25 5.07 I

8. 0800 5.150

8.6800 4. 990

9.0800 4.893

9.6000 4.776

9.7925 2.679

I I .6450 3. 139

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m(lb m/sec)

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I. 545

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0.97 0.9155

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