PERFORMANCE ENHANCEMENTS ON A PULSED DETONATION … · PERFORMANCE ENHANCEMENTS ON A PULSED DETONATION ROCKET Publication No. Jason Matthew Meyers, M.S. The University of Texas at

PERFORMANCE ENHANCEMENTS ON A PULSED

DETONATION ROCKET

The members of the Committee approve the mastersthesis of Jason Matthew Meyers

Donald R. WilsonSupervising Professor

Frank K. Lu

Dale A. Anderson

To Grandma and Grandpa


DETONATION ROCKET

by

JASON MATTHEW MEYERS

Presented to the Faculty of the Graduate School of

The University of Texas at Arlington in Partial Ful¯llment

of the Requirements

for the Degree of

MASTER OF SCIENCE IN AEROSPACE ENGINEERING

THE UNIVERSITY OF TEXAS AT ARLINGTON

December 2002

ACKNOWLEDGMENTS

First and foremost I would like to thank my advisor Dr. Don Wilson and Dr.

Frank Lu for giving me the opportunity to work at the Aerodynamics Research Center.

Their guidance and direction has introduced me to a world of academia that I never

could have reached on my own. I would also like to thank Jim Holland and Scott

Stuessy whose technical help assured this projects progress. Last but not least, I would

like to thank my friends Joji Matsumoto and Chris Roseberry for sharing their advice

and council when times were tough.

This work was sponsored by the Texas Advanced Technology Program (ATP grant

#: 14761051) and the Civilian Research and Development Foundation (CRDF grant

#: 26-7501-07).

November, 2002

iv

ABSTRACT


DETONATION ROCKET

Publication No.

Jason Matthew Meyers, M.S.

The University of Texas at Arlington, 2002

Supervising Professor: Donald R. Wilson

A major problem applying detonations into aero-propulsive devices is the de°a-

gration to detonation transition, or DDT. The longer the DDT, the longer the physical

length of the engine must be to facilitate the propagation of the °ame as it transitions

into a detonation. However, lengthening of the detonation chamber can signi¯cantly

increase weight, rendering the reduction of DDT length of great importance. One of the

most common means of shortening DDT lengths is with the aid of a Shchelkin spiral.

A simple helical apparatus, it was used in early single-shot detonation investigations

to over-exaggerate wall roughness e®ects. It was through empirical investigations that

the reduced DDT phenomenon was observed. The present investigation explored the

possibility of applying such an apparatus into an intermittent pulsed detonation device.

Results show signi¯cant improvements in comparison to cases without the spiral. Tests

through a range of cycle frequencies up to 20Hz in oxygen-propane mixtures at 1atm

demonstrated the feasibility of the Shchelkin spiral in a pulsed mode.

v

TABLE OF CONTENTS

ACKNOWLEDGMENTS : : : : : : : : : : : : : : : : : : : : : : : : : : : : iv

ABSTRACT : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : v

LIST OF FIGURES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ix

LIST OF TABLES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : xiii

LIST OF ABBREVIATIONS : : : : : : : : : : : : : : : : : : : : : : : : : : xiv

1. INTRODUCTION : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1

1.1 De°agration and Detonation . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Detonation Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 Detonation Applications to Propulsion . . . . . . . . . . . . . . . . . . . 9

1.4 De°agration-to-Detonation Transition . . . . . . . . . . . . . . . . . . . . 11

2. EXPERIMENTAL SET-UP : : : : : : : : : : : : : : : : : : : : : : : : 15

2.1 Detonation Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Ignition System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3 Injection System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4 Data Acquisition System . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4.1 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4.2 Reduction Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.5 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

vi

3. RESULTS AND DISCUSSION : : : : : : : : : : : : : : : : : : : : : : 26

3.1 Mass Flow Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2 O®-Stoichiometric Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3 Varied Cycle Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4 Clean Con¯guration Results at Baseline Regulator Settings . . . . . . . . 32

3.5 Shchelkin Spiral Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.5.1 20 Hz Cycle Frequency . . . . . . . . . . . . . . . . . . . . . . . . 36

3.5.2 14.4Hz Cycle Frequency . . . . . . . . . . . . . . . . . . . . . . . 38

3.5.3 6.9 Hz Cycle Frequency . . . . . . . . . . . . . . . . . . . . . . . 41

3.5.4 4.4Hz Cycle Frequency . . . . . . . . . . . . . . . . . . . . . . . . 43

3.6 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.7 Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4. CONCLUSIONS AND RECOMMENDATIONS : : : : : : : : : : : : 56

4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

APPENDIX

A RAYLEIGH AND HUGONIOT RELATION DERIVATIONS : : : 58

B DATA REDUCTION CODE : : : : : : : : : : : : : : : : : : : : : : : : 62

C INJECTION AREA CALCULATIONS : : : : : : : : : : : : : : : : : 78

D IGNITION SYSTEM CIRCUIT DIAGRAMS : : : : : : : : : : : : : 84

E PLUMBING SCHEMATIC : : : : : : : : : : : : : : : : : : : : : : : : 88

F RUN LOG : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 91

vii

REFERENCES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 94

BIOGRAPHICAL STATEMENT : : : : : : : : : : : : : : : : : : : : : : : 96

viii

LIST OF FIGURES

Figure Page

1.1 Diagram of notation for stationary detonation . . . . . . . . . . . . . . . 3

1.2 Hugoniot Diagram with Rayleigh Line . . . . . . . . . . . . . . . . . . . 5

1.3 Rayleigh line-Hugoniot curve °ow solutions . . . . . . . . . . . . . . . . 6

1.4 ZND detonation wave model pro¯le propagating from a rigid wall . . . . 6

1.5 Brayton and Humphrey Cycle Diagrams . . . . . . . . . . . . . . . . . . 7

1.6 Detonation and de°agration e±ciency comparison . . . . . . . . . . . . 9

1.7 Ideal PDE cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.8 Detonation Transition [10] . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.9 Experimental setup; distances in mm [10] . . . . . . . . . . . . . . . . . 13

1.10 Wave diagram for ¯gure 1.8 . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1 Clean detonation chamber con¯guration . . . . . . . . . . . . . . . . . . 16

2.2 Detonation chamber with Shchelkin spiral installed . . . . . . . . . . . . 17

2.3 Ignition system schematic . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4 Ignition system picture . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5 Diagram of high-current arc-plug . . . . . . . . . . . . . . . . . . . . . . 18

2.6 Ignition system timing sequence . . . . . . . . . . . . . . . . . . . . . . 19

2.7 Arc discharge measurements . . . . . . . . . . . . . . . . . . . . . . . . 20

2.8 Discharge energy as a function of ignition system

operation frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.9 Critical °ow nozzle location and terminology schematic . . . . . . . . . . 21

ix

2.10 Single rotary injection valve . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.11 Injection assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1 Mass °ow sensitivity to temperature upstream of critical °ow nozzle . . 27

3.2 Stoichiometric oxygen and propane regulator settings . . . . . . . . . . . 28

3.3 CJ detonation velocity as a function of equivalence ratio for a 1 atm

C3H8=O2 pre-detonation mixture [11]. . . . . . . . . . . . . . . . . . . . 29

3.4 O® stoichiometric performance for 6.9 Hz cycle frequency . . . . . . . . 30

3.5 O® stoichiometric performance for 6 Hz cycle frequency . . . . . . . . . 31

3.6 Ignition and injection timing as a function of cycle frequency . . . . . . 32

3.7 Injection area as a function of time for varying cycle frequencies . . . . . 33

3.8 Clean con¯guration wave pro¯le with 6.9 Hz cycle frequency - 1 . . . . . 33

3.9 Wave diagram and average time of °ight for wave pro¯le in

¯gure 3.8 - 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33



¯gure 3.10 - 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34



¯gure 3.12 - 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.14 Chamber pressure history at 20 Hz . . . . . . . . . . . . . . . . . . . . . 37

3.15 Transducer mounting void . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.16 Typical wave pro¯le from 20 Hz test case . . . . . . . . . . . . . . . . . 38

3.17 Wave diagram for 20 Hz test in ¯gure 3.16 . . . . . . . . . . . . . . . . . 39

3.18 Average velocity plot for 20 Hz test in ¯gure 3.16 . . . . . . . . . . . . . 39

3.19 Chamber pressure history from 14 Hz test case . . . . . . . . . . . . . . 40

x

3.20 Typical wave pro¯le from 14.4 Hz test case . . . . . . . . . . . . . . . . 41

3.21 Wave diagram for 14.4 Hz test in ¯gure 3.20 . . . . . . . . . . . . . . . . 42

3.22 Average velocity plot for 14.4 Hz test in ¯gure 3.20 . . . . . . . . . . . . 42

3.23 Typical wave pro¯le from 6.9Hz test case . . . . . . . . . . . . . . . . . 43



3.26 Typical wave pro¯le from 4.4 Hz test case . . . . . . . . . . . . . . . . . 45



3.29 Clean and Shchelkin spiral con¯guration pressure pro¯le comparison

results at 6.9 Hz cycle frequency . . . . . . . . . . . . . . . . . . . . . . 51

3.30 Clean and Shchelkin spiral con¯guration velocity comparison at 6.9Hz

cycle frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.31 Single pulse propagation comparison at varied frequencies . . . . . . . . 52

3.32 Average velocity plot for Shchelkin spiral installed con¯guration with

C3H8=43 psig and O2=146 psig . . . . . . . . . . . . . . . . . . . . . . . 53

3.33 Machining uncertainty and notation . . . . . . . . . . . . . . . . . . . . 53

3.34 Actual pressure pro¯le with sampling times superimposed . . . . . . . . 54

3.35 Velocity error plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

C.1 Area of injection for a single injection valve port . . . . . . . . . . . . . 79

C.2 Wedge area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

C.3 Triangular area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

C.4 Notation for angular velocity and tangential velocity . . . . . . . . . . . 81

C.5 Time relation approximation to h . . . . . . . . . . . . . . . . . . . . . . 82

C.6 Injection area as a function of time for varying cycle frequencies . . . . . 83

xi

D.1 Ignition system circuit schematic . . . . . . . . . . . . . . . . . . . . . . 86

D.2 Mallory Ignition Control Circuit . . . . . . . . . . . . . . . . . . . . . . 87

D.3 Silicon controlled recti¯er control circuit . . . . . . . . . . . . . . . . . . 88

E.1 Plumbing schematic for gas delivery . . . . . . . . . . . . . . . . . . . . 91

xii

LIST OF TABLES

Table Page

1.1 General de°agration and detonation properties for a stationary shock

reference frame [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Detonation properties for various stoichiometric mixtures at 1 atm and

295 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1 Available Modules for DAQ System . . . . . . . . . . . . . . . . . . . . . 24

3.1 FlowDyne Corp. critical °ow nozzle calibration data. . . . . . . . . . . . 26

D.1 Clean Con¯guration Test Run Data Log . . . . . . . . . . . . . . . . . . 94

D.2 Shchelkin Spiral Con¯guration Test Run Data Log . . . . . . . . . . . . . 95

xiii

LIST OF ABBREVIATIONS

c sound speed

CD convergent-divergent

CJ Chapman-Jouguet

e speci¯c internal energy

h speci¯c enthalpy

M Mach number

P static pressure

q speci¯c heat added

u velocity

° speci¯c heat ratio

¹ wave speed factor

º speci¯c volume (1/½)

½ density

Acronyms

PDE pulse detonation engine

PDR pulse detonation rocket

DSP Digital Signal Processing

DAQ data acquisition

xiv

Subscripts

1 pre-detonated species

2 post-detonated species, transducer location 3 in.

downstream of 3

3 transducer location 3 in. downstream of 4




7 transducer location nearest the closed end of the

detonation chamber

xv

CHAPTER 1

INTRODUCTION

1.1 De°agration and Detonation

Two modes exist under which an exothermic and luminous reaction, or combustion,

can propagate. When the reaction propagates at a speed much less than that of the

local speed of sound, it is said to be in a de°agrating mode of combustion. This is the

common form of combustion and runs in practically every gas generative device; internal

combustion engines, jet engines, etc. All information of pressure is propagated at the

speed of sound and quite signi¯cantly outruns the °ame front which travels at speeds

around 1{2 m/s [1]. In an environment where the de°agration is allowed to propagate in

an unrestricted manner, the process is essentially a constant pressure phenomenon. A

di®erent combustion propagation regime also exists characterized by very large gradients

in local velocity and pressure. This phenomenon is known as a detonation where the

°ame front velocities can be on the order of 2{3 km/s. These high velocities generate

a coupled shock and °ame front that characterizes a detonation. The velocities of this

type of combustion process are so high that a constant volume combustion process is

assumed. Table 1.1 is a list of key parameters for comparisons between the two processes

with notation from ¯gure 1.1.

1.2 Detonation Physics

Detonation observances and experimentation are nothing new; in fact, they are over

a century old. Detonation phenomenon was ¯rst recognized in the late 19th century

through studies of °ame propagation. Shortly afterwards, at the end of the 19th and

1

2

Table 1.1. General de°agration and detonation properties for a stationary shock refer-ence frame [13].

Properties De°agration Detonation

u1/c1 0.0001-0.03 5-10u2/u1 4-6 (acceleration) 0.4-0.7 (deceleration)P2/P1 0.98 (slight expansion) 13-55 (compression)T2/T1 4-16 (heat addition) 8-21 (heat addition)

early part of the 20th centuries, the ¯rst simple one-dimensional theory was adapted to

describe the curious phenomenon by Chapman and Jouguet independently. However,

it was realized that detonation is not a simple one-dimensional problem and that it

has many properties such as a transverse wave. The complexities in modelling and

theory behind a non{one{dimensional wave are exhaustive. In the early 1940's, another,

more appropriate, one-dimensional model was derived, independently, by Zeldovich, von

Neumann, and Doering, known as the ZND model of a detonation. For the remainder

of this report, only this ZND one-dimensional analysis will be approached for explaining

detonation phenomenon. In this model, several explicit assumptions are made [13]:

1. The °ow is one-dimensional

2. The shock is a jump discontinuity (transport e®ects of heat conduction,

radiation, di®usion, viscosity are neglected)

3. The reaction is irreversible

4. All thermodynamic variables are in local equilibrium everywhere.

Assume a stationary shock with heat addition in a constant area duct [4], as shown

in ¯gure 1.1.

3

Figure 1.1. Diagram of notation for stationary detonation.

The equations of mass, momentum, and energy conservation for one-dimensional °ow

with heat addition are:

½1u1 = ½2u2 (1.1)

P1 + ½1u12 = P2 + ½2u2

2 (1.2)

h1 +u12

2+ q = h2 +

u22

2(1.3)

This one-dimensional °ow with heat addition is known as Rayleigh °ow [5]. For sim-

plicity of argument, de¯ne:

P =P2P1and º =

º2º1

The familiar Rayleigh-line equation:

P ¡ 1 = ¡¹ (º ¡ 1) (1.4)

can be found by combining the mass and momentum equations. A detailed derivation

is found in the Appendix A.

4

Equation 1.4 is the Rayleigh line relation in the P -v plane where the slope ¹ is the wave

speed factor.

Mach numbers and velocities are the most common means of quantifying the

nature of a shock wave. One can also view the wave as purely thermodynamic properties

through the Hugoniot equation. The Hugonoit relation is acquired by combining the

mass, momentum and energy equations. Detailed derivations are, again, documented

in the appendix. In enthalpy form, the Hugoniot relation is:

h1 ¡ h2 + q = 1

2[P1 (1¡ P )] [º1 (º + 1)] (1.5)

The Hugoniot equations give thermodynamic properties upstream and downstream of

the combustion. When plotted on a P-º plane, the Hugoniot presents a series of curves,

which vary with a non-dimensional heat of reaction:

® = q½1=P1

a variable containing information of initial conditions and combustion properties. No-

tice, from equation 1.4, that the Rayleigh line will always intersect the P=1, v=1

position. This is illustrated in ¯gure 1.2.

The Rayleigh line will always have a negative slope since the wave speed is always

positive and it will always intersect the point (1,1). This renders the non-shaded re-

gions in ¯gure 1.2 with no physical meaning. Now there remains two regions of physical

relevance, the left shaded region of detonation and the right shaded region of de°agra-

tion. It was determined, independently, by Chapman and Jouguet that there exists a

condition of minimum wave speed. This C-J condition is graphically interpreted as the

tangent point of the Rayleigh line with the Hugoniot curve for a given chemical species

as shown in ¯gure 1.3. From a physical point of view, there is a condition where a

5P

v

1

1deflagrationregion

detonationregion

a=0

Hugonoit Curve

Rayleigh LineIncreasing a

Figure 1.2. Hugoniot Diagram with Rayleigh Line.

detonation can be self-sustaining. Mutual support from the shock will heat the chem-

ical species to a temperature combustion and the energy release from the combustion

reaction will be signi¯cant enough to support the shock front. This is known as a C-J

detonation.

Now consider a pressure pro¯le of the detonation propagating from a rigid wall

of a constant area duct with one closed and one open end. Figure 1.4 is a diagram of

such a pro¯le. The gases at state 1 represent the pre-detonation species. A shock front,

represented by state s, compresses the gas and increases its temperature to the level

of combustion, occurring approximately 1 ¹s after the shock compression begins. The

strength of this compression can be simply modelled by the basic normal shock relation

of the pre-detonation °ow:.

PsP1= 1 +

2°1°1 + 1

³M1

2 ¡ 1´

(1.6)

6

Figure 1.3. Rayleigh line-Hugoniot curve °ow solutions.

Figure 1.4. ZND detonation wave model pro¯le propagating from a rigid wall.

State CJ on the diagram occurs right after all combusted species have been consumed.

This is the well-known CJ state of the detonation wave. The pressure ratio relation for

this condition becomes [5]:

P2P1= 1 +

1 + °1M12

1 + °2(1.7)

A region of rarefaction soon follows as the detonation propagates from the rigid wall

boundary, increasing the volume behind it.

7

Signi¯cant increases in pressure and temperature are not the only noteworthy

detonation characteristics. Major gains in thermal e±ciency exist as well. Consider

the T -s and P -v diagrams for both the de°agration and detonation processes in ¯g-

ure 1.5. The common Brayton cycle, 0-1-4-5-0, de¯nes the de°agration process while

P

v

1

2

3

4

50

T

s

1

2

3

4

5

0

Figure 1.5. Brayton and Humphrey Cycle Diagrams.

the Humphrey cycle, 0-1-2-3-0, represents the detonation process. Thermal e±ciency

for a de°agration combustion process is totally dependent on the isentropic compression

or expansion temperature ratios [4]:

´deflagration = 1¡ T0T1= 1¡ T4

T5(1.8)

For a detonation cycle, the e±ciency calculation is a bit more involved [4]:

´detonation = 1¡ CT0T1

(1.9)

where:

C = °

24(T2=T1)1=° ¡ 1T2=T1 ¡ 1

35 (1.10)

Equation 1.9 is exactly the same as equation 1.8 except for the addition of a correction

term C. This value is always less than one and because of that, the thermal e±ciency

8

of the detonation will always be greater than that of a de°agration combustion process.

Another representation of thermal e±ciency is de¯ned as the ratio of the work output to

the heat input to the system. On the P ¡ º cycle diagram represented in ¯gure 1.5, thearea enclosed in the curve accounts for the work output of the process. The pressure

P2 represented in the P ¡ º diagram for the detonation process is severely under-

scaled. Pressure levels at this point can easily be 20 times the value at state 1 of the

de°agration process. Thus, the area for the detonation process is greater than that

of the de°agration process which implies a larger work output from the detonation

process. Since the heat input is relatively comparable, the e±ciency of the detonation

process is much greater. Figure 1.6 is a plot of e±ciency for a given compression ratio for

detonation and de°agration processes. For a compression ratio (mechanical compression

for de°agration process and shock compression for detonation process) around 10, the

thermal e±ciency can improve by almost 60%.

Figure 1.6. Detonation and de°agration e±ciency comparison.

9

1.3 Detonation Applications to Propulsion

Almost all combustion driven engines burn their fuel and oxidizer in a de°agrative man-

ner. However, the application of detonation combustion phenomenon in aero-propulsion

studies has gathered considerable attention due to the potential of increased perfor-

mance over that of typical de°agration combustion processes. Early attempts by the

Germans in the late 1930's with the buzz bomb were not a success because the engine

could never achieve a detonation mode of combustion. Since then, many research groups

have been involved and generated so much attention that even major aero-propulsion

companies have ventured into the feasibility of a pulsed-detonation engine.

Figure 1.7 is a diagram of the familiar PDE cycle and how the detonation engine

concept works. Stage 1 of the cycle has the engine chamber at some initial condition, in

Figure 1.7. Ideal PDE cycle.

this case P0 and T0. The end plate on the left is then opened by some valve mechanism

and a combination of fuel and oxidizer is pumped into the chamber at a pressure P1

10

and T1, as seen in stage 2. Next, in stage 3, ignition at the now closed end occurs

creating, ideally, a direct detonation to propagate towards the open end with a pro¯le

similar to ¯gure 1.4. The ignition source can be anything with signi¯cant energy to

generate a direct detonation; an electrical arc, a laser source, a chemical pre-detonator,

or even a shock wave. The strength of the detonation can be measured by normalizing

the pressure immediately behind it, P2, with the pre-detonation propellant pressure P1.

This pressure ratio is large, as is for all detonation waves, and will therefore induce a

velocity much larger than the propellant expansion speed. The increase in propellant

volume with the aid of the shock combustion process creates rarefaction (expansion)

waves at the closed end to ensure a zero axial velocity condition at the end plate (Stage

4). Stage 5 shows the shock and the propellant reaching the open end at the same time.

This is important for optimal engine operation. When the detonation drags behind, the

propellant is expelled out the back end before it can be consumed by the detonation

and is essentially wasted. If the detonation consumes the propellant before the open

end, then the detonation could lose its driving energy and die out before it is expelled

out the back. Finally, Stage 6 represents the blow-down process where all the gases are

expelled out the back end. After rapidly quenching to initial conditions by purging air,

oxygen, or some other inert gas, the cycle can now be repeated. This cycle is repeated

as often as necessary in a pulsating manner, thus a pulsed detonation engine.

A shock is a compression ratio process. Table 1.2 is a list of detonation properties

for some common combustible mixtures. A stoichiometric C3H8-O2 mixture generates

a CJ compression ratio is about 30. Basically, a sea-level pre-detonation CJ pressure of

1 atm would yield a post-detonation CJ pressure of about 30 atm.

Since a detonation wave is supersonic, a shock of considerable strength precedes

any combustion. This shock front is closely coupled (1 ¹s delay) with the combustion re-

11

Table 1.2. Detonation properties for various stoichiometric mixtures at 1 atm and 295K

Fuel=Oxidizer VCJ@1atm Vsonic PCJ=P1

m=s (ft=s) m=s (ft=s)

H2/O2 2800 (9200) 550 (1800) 20

H2/Air 1950 (6400) 410 (1300) 25

C3H8/O2 2400 (7750) 300 (1000) 30

CH4/O2 2700 (8700) 400 (1200) ?

action region. The shock actually precompresses the propellants before the combustion

front, negating the need for any mechanical precompression. Compressor and turbine

assemblies are by far the most expensive components of standard gas generative devices

in terms of design, fabrication and maintenance, and weight. The propagating shock

wave of the detonation process acts as a compressor by increasing the pressure and

temperature and eliminates the need for these high cost and high mass components,

making a PDE/R a prime choice. PDE/R's may still require small turbo pumps for

the fuel and oxidizer delivery, but the overall weight and cost can be signi¯cantly low.

This combined with the considerable increase in thermal e±ciency of the detonation

combustion process make the PDE/R concept even more desirable.

1.4 De°agration-to-Detonation Transition

The ideal PDE/R cycle represented in ¯gure 1.7 relies on a direct detonation initiation

which may prove a di±cult task. Most detonation investigations rely on the transition

of a non-detonation combustion process into a full blown detonation. However, these

lengths can be quite signi¯cant with low energy ignition sources, being on the order

of 1 to 2 meters. This phenomenon is known as de°agration-to-detonation transition,

or DDT. The following ¯gure is an illustration from a plot investigating the e®ect of

12

di®erent injection nozzles on DDT lengths. The four pulses represent the four locations

Figure 1.8. Detonation Transition [10] .

of instrumentation ports for pressure transducers and photo-detectors as illustrated in

¯gure 1.9.

Notice the weak shock front (SW) and severely decoupled °ame front (FF) in

traces represented by station 1. Obviously, this is not a detonation. As the shock and

°ame fronts propagate downstream, the °ame front accelerates at a greater rate than

the compression front. Eventually, the °ame front catches up to the shock front and

merge to form a detonation, clearly evident at station 4. A retonation wave, another

indicator of detonation formation, is created during this coalescing of the shock and

°ame front and propagates upstream. Figure 1.10 is an x¡ t diagram of the transition

process of ¯gure 1.8. The shock and °ame front acceleration are clearly evident as well

13

Figure 1.9. Experimental setup; distances in mm [10] .

Figure 1.10. Wave diagram for ¯gure 1.8 .

as the retonation propagation. Extrapolating by eye, one might consider detonation

formation at about 340 ¹s.

Reduction of the DDT length is essential for propulsion applications. With a

reduced DDT length, a shorter, lighter, and cheaper propulsion mechanism can be de-

veloped. A common means of achieving this is with the aid of a Shchelkin spiral. A sim-

ple helical apparatus, it was used in early detonation investigations to over-exaggerate

wall roughness e®ects. For a smooth pipe, the losses due to friction and heat loss are

relatively small compared to the overall energy level of the detonation and only very

14

slightly a®ect its velocity. A method of investigating these losses with extremely large-

scale roughness was done by Shchelkin in the early 1900's [2]. Coils of wire of various

thicknesses were inserted into a single-shot experimental apparatus. It was through

empirical investigations that the reduced DDT phenomenon was observed. A common

belief is that large-scale turbulence promotes the °ame acceleration creating shock and

°ame coupling more promptly than in a clean chamber. This investigation explored the

possibility of applying such a device into the UTA pulsed detonation rocket.

CHAPTER 2

EXPERIMENTAL SET-UP

The experiments in this report were carried out on the University of Texas at Ar-

lington's high frequency PDR/E facility. In operation since 1994, it utilizes a mechanical

rotary valve injection system for three gas species (fuel, oxidizer, and purge). The pro-

pellants are directly detonated with the use of a high current, electric arc discharge.

Near stoichiometric ratios were calibrated with the aid of two critical °ow nozzles; one

for fuel and one for oxidizer.

2.1 Detonation Chamber

The detonation engine is constructed of steel tubing with an inside diameter of 3 inches

and outside diameter of 6 inches. Various lengths of 3, 6, and 12 inch were available.

Flanges were then welded to the ends of each tube for assembly with rubber o-ring

seals. Each segment was also prepared for proper instrumentation, such as pressure

transducers, thermocouples, heat °ux gauges, or photo-detectors. The 30.48 cm (12 in)

sections allow for four equally spaced instrumentation ports along the tube. Sections of

15.24 cm (6 in) allow two ports, and 7.62 cm (3 in) sections allow one port. Another

7.62 cm (3 in) section was used to support the mounting of the arc-plug igniter.

Figure 2.1 is a schematic of the detonation chamber for clean con¯guration ex-

periments. Sections were assembled to the injection end-plate to yield a total chamber

length of 53.34 cm [21 in]. The ¯rst 7.62 cm [3 in] section was used to mount the igniter

3.81 cm [1.5 in] downstream of the injection wall. The following 30.48 cm [12 in] and

then 15.24 cm [6 in] sections housed four ports and two ports, respectively, used for

15

16

transducer mounting. The ¯rst instrumentation port is located 7.62 cm [3 in] down-

stream of the igniter with each of the ¯ve successive transducer ports at 7.62 cm [3 in]

intervals.

Figure 2.1. Clean detonation chamber con¯guration.

The Shchelkin spiral experimental setup is shown in ¯gure 2.2. The same deto-

nation chamber sections were incorporated with a short spiral with a length of 20.32cm

(8 in) mounted across from the ignition source. The spiral had a pitch of 15 degrees

and wire diameter of 9.53 mm (3/8 in). Blockage ratio, the area of the obstruction to

the area of the clean cross-section, for the spiral was about 0.21, relatively small when

compared to other DDT experimental studies [8].

2.2 Ignition System

A proper ignition system is one of the most crucial components for successful multi-

cycle detonation experimentation. An ignition system for pulsed detonation engines

was developed under a NASA grant as a supplement to UTA's Hypersonic Research

Center in 1995. While various detonation initiation methods were considered; shock-

induced detonation, explosives, lasers, electrical spark/arc, etc., it was the concept of a

17

Figure 2.2. Detonation chamber with Shchelkin spiral installed.

high current, electrical discharge that became the practical choice. The UTA ignition

system consists of a series of two capacitor banks and a specialized arc-plug consisting

of three electrodes similar to a common triggered spark gap device. A schematic of the

ignition system is shown in ¯gure 2.3 followed by a picture in ¯gure 2.4. More detailed

ignition system circuit diagrams are located in Appendix D.

Figure 2.3. Ignition system schematic.

Household electricity is transformed and recti¯ed up to 2200 VDC, which is used

to charge the ¯rst series of capacitor banks. This potential charges the second bank as

18

Figure 2.4. Ignition system picture.

soon as the silicon-controlled recti¯er (SCR) is triggered by the low current circuitry.

Once the second discharge capacitor bank is charged, there is a potential of up to 2200

VDC between the pair of large electrodes, shown in ¯gure 2.5. The gap between the

Figure 2.5. Diagram of high-current arc-plug.

larger electrodes is too great for the second capacitor banks potential to discharge across

them. However, when an automotive ignition spark is triggered, a low energy spark is

discharged from the smaller electrode to the ground electrode. When this occurs, the

path between the high-current anode and ground electrode becomes ionized to the level

where potential breakdown of the discharge capacitor bank is imminent. Figure 2.6 is

a timing sequence diagram for the ignition system.

Signal 1 represents the TTL pulse from the magnetic pick-up on the mechanical

19

Figure 2.6. Ignition system timing sequence.

rotary valve sent to the low current trigger circuitry. The signal represented by 2 in

¯gure 2.6 is a conditioned 2.5 ms square waveform sent to the automotive ignition circuit

from the low current trigger circuitry. The third signal is the same 2.5 ms long square

wave as depicted in signal 2 but with a 2.5 ms delay. This signal is also generated in

the low current trigger circuitry but is sent to the high current trigger circuitry instead.

The ¯nal signal represented in ¯gure 2.6 is a square waveform with a duration just over

2.5 ms and sent to the SCR to trigger the ¯rst capacitor bank to recharge the second

discharge capacitor bank. The entire timing sequence takes just over 5ms, which implies

an operating frequency up to 200Hz. Single-shot discharge measurements of a 1700 VDC

capacitor potential are plotted in ¯gure 2.7. Measurements of voltage and current were

used to back out levels of energy and power through the following equations:

E =1

2CV 2 (2.1)

P = iV (2.2)

The discharge levels, however, are strongly dependent on the ignition system operation

frequency. Figure 2.8 shows the discharge energy as a function of operation frequency

for a 2200 VDC capacitor potential level.

20

Figure 2.7. Arc discharge measurements.

2.3 Injection System

Tackling the problem of injecting stoichiometric gas species into an intermittent deto-

nation device is a bit more involved than the partial pressure method used when charging

up a single shot detonation experiment. Two FlowDyne Corp. critical °ow nozzles were

used in metering both oxygen and fuel °ow rates. Upstream values of pressure and

temperature were obtained from transducers. From that information, along with the

area ratio of the CD nozzle, a relationship of the following form can be made for both

fuel and oxidizer gases:

_m = K(A=A¤; P1)P1pT1

(2.3)

Readings of steady values of P1 and T1 are taken upstream of the °ow nozzles as illus-

trated in ¯gure 2.9.

Calibration was carried out using cold °ows. Choking of the nozzle is crucial for

proper measurements. A steady pressure trace should be recorded even as the injection

system pulses °ow into the chamber. If oscillations occur at the cycle frequency, then

the °ow nozzles are not choked. After the cold °ow calibration is complete, mass

21

Figure 2.8. Discharge energy as a function of ignition system operation frequency.

Figure 2.9. Critical °ow nozzle location and terminology schematic.

°ows were measured during hot °ow or engine-on conditions. When these mass °ows

were calculated and con¯rmed with that of the cold °ow tests, then the two pressure

transducers and two thermocouples may be removed to free memory for higher resolution

or longer duration data sampling.

Caution must be taken when using the measured mass °ows because they are

metered about 1.5 m upstream of the injection valves. Due to compressibility e®ects in

the remaining tubing downstream of the °ow nozzles, the calculated equivalence ratio

of the injected species may not be at a stoichiometric value. These mass °ows remain

22

estimates. Minor trimming of the regulator pressures from the estimated stoichiometric

values can be done until maximum engine performance is obtained.

The fuel and oxygen sources were kept at a reasonable distance from each other

as well as the PDR for safety reasons. Flash arrestors were also installed about 15m

upstream of the mass-°ow meters to further ensure safety. The reactants were delivered

to the detonation chamber via a mechanical rotary valve injection system. This valve

was designed and fabricated at UTA for fuel injection, oxygen injection, and purging

purposes. Gases were injected from the side opposite the drive gear and then distributed

from three ports, see ¯gure 2.10, in a radial fashion from the internal rotating shaft.

Figure 2.10. Single rotary injection valve.

The three valves are mounted to the engine via a trapezoid shaped mounting

block as seen in ¯gure 2.11. This block directed the propellant and purge °ows into

the engine from the end wall. The gases are then forced into a swirling motion by an

injection disk mounted on the end wall inside the detonation tube to enhance mixing.

Due to the present drive gear radius and friction of the rotating system, the 0.5 hp

electric motor was only capable of driving the system up to a cycle frequency of 20 Hz.

23

Figure 2.11. Injection assembly.

2.4 Data Acquisition System

2.4.1 Hardware

Data samples were taken through a DSP Technology, Inc. model 9200 12-bit data ac-

quisition unit. This system has seperate rack-mountable modules for digitzing, ampli-

¯cation, and storage. Table 2.1 lists the modules used for this report.

Three main con¯gurations were incorporated. The 100 kHz digitizers, at the

maximum 10 ¹s sampling resolution, along with the 512 ksample memory modules

were used for initial mass °ow calibrations where lower sampling resolution as well as

smaller storage space were adequate for simpler data reduction. Another con¯guration

was used for relatively long multi-cycle demonstrations. Again, the 100 kHz digitizers

and 512 ksample memory modules were used, but this time the digitizers sampled at

50 ¹s. The ¯nal con¯guration was set up purely for detailed detonation wave analysis.

Both of the 4-channel digitizers, set to 1 ¹s were included. To ensure adequate records,

the 2.048 Msample memory module had to be used. This limited the sampling window

to 250 ms, but due to the enormous ¯le sizes generated, it never was fully reduced.

24

Table 2.1. Available Modules for DAQ System

Description Model No. No. of Units Channels

100kHz 8-channel digitizer 2812 6 48

(up to 10¹s sampling res)

1 MHz 4-channel digitizer 2860 2 8

(up to 1¹s sampling res)

8-channel ampli¯er 1008 6 48

512k sample memory module 5204 1 48

2048k sample memory module 5005 1 8

Only the portions of interest in about 10 ms windows were reduced.

2.4.2 Reduction Code

The DAQ system uses \counts" as its values for data interpretation. These counts must

be reduced into an engineering unit base that can be quanti¯ed. The reduction code

transforms the count units into recognizable engineering units. For the 12-bit DSP

system, there are 212 = 4096 counts. This is the resolution level of all transducer data

for this system. A count of 0 is about ¡4:998 ( 5) volts, a count of 2048 is about 0volts, and a count of 4096 is about +4:998 ( 5) volts.

Before reduction can begin, physical calibration parameters must be known about

every transducer used in the experiment. A detailed account for all transducers used for

this report is located in section 2.5. Input examples for the setup ¯le, \SETUPFM.DAT",

with 48-channel low-frequency sampling resolution and 8-channel high-frequency sam-

pling are give in Appendix B. Once these ¯les are adequately entered, a batch ¯le will be

con¯gured based on the number of channels, number of ¯les, number of data windows,

25

and size of each data window. This is done through the \PDBATFMS.FOR" code lo-

cated in Appendix B. Data reduction begins when the created batch ¯le \DETONFM.BAT"

is run. The main reduction program was written by W.S. Stuessy with the aid of S.

Stanley. Preliminary code to combine the raw data into a single ¯le was done by I.M.

Kalkhoran with modi¯cations by W.S. Stuessy. Modi¯cations for reduction of the 8-

channel case made by the author is located in Appendix B as \PDMNFMMS.FOR".

2.5 Instrumentation

The detonation chamber pressure traces were recorded with six PCB model 111A24

dynamic pressure transducers. Physical characteristics of these transducers include an

impulse pressure magnitude of 1000 psi with a signal rise time of 1 ¹s. Each pressure

transducer was equipped with a water cooling jacket (PCB model 64A) to not only

ensure transducer survivability but also to limit the e®ects of signal rise to the heating

characteristics of the transducer during multi-cycle tests.

Fuel and oxygen pressures for the critical °ow nozzles were taken with Sensotec

model A205/0281-07G transducers capable of a 200 psig pressure range. Fuel and oxy-

gen temperatures for the critical °ow nozzles were taken with OMEGATJ36-CXSS-18E-

6 auto-clave probe style type E thermocouples with an exposed junction. Temperature

reference was taken from a DSP Technology Universal Temperature Reference RTD

model E475.

CHAPTER 3

RESULTS AND DISCUSSION

3.1 Mass Flow Calibration

Stoichiometric calibrations of the mass °ow nozzles were done before detonation tests

could begin. Measurements of °ow nozzle pressure and temperature (¯gure 2.9) were

reduced for both propane and oxygen through a range of regulator settings. Mass °ow

equations as a function of regulator pressure were then determined for both gas species

over the entire regulator range using the calibration data supplied by the FlowDyne

Corp (table 3.1).

Table 3.1. FlowDyne Corp. critical °ow nozzle calibration data.

Gas A=A¤ K a b c

O2 34.9 a+bP1+c/(P1)0:5 0.005270450 2:302107£ 10¡7 ¡1:636309£ 10¡4

C3H8 73.1 a+b(P1)1:5+c/(P1)

2 0.002750032 1:089844£ 10¡7 ¡6:093723£ 10¡3

Combining table 3.1 and equation 2.3 with the reduced calibration data yielded the

following relations for regulator pressure and mass °ows of C3H8 and O2 gas species:

_mC3H8=(1:1091£ 10¡4)PC3H8+2:207£ 10¡3

_mO2=(1:731£ 10¡4)PO2+2:527£ 10¡3

where the mass °ux is in lb/s and the pressure is in psig.

26

27

Temperature °uctuations were minor from test to test during both cold °ow and

engine-on °ow calibration. Gas temperatures were always within a few degrees of 60±F

and so the temperature was considered constant at 60±F for the calibration plots. This

posed no signi¯cant problem since the mass °ows will be trimmed to a desired level.

Figure 3.1 shows the minor mass °ow sensitivity with gas temperature just upstream

of the °ow nozzle.

Figure 3.1. Mass °ow sensitivity to temperature upstream of critical °ow nozzle.

Stoichiometric fuel-to-oxidizer ratio for C3H8=O2 was taken from the following

reaction:

C3H8+5O2!4H2O+3CO2

The molecular weight for propane and diatomic oxygen are 44 and 32 respectively.

Therefore, the stoichiometric fuel to oxidizer ratio, fstoich, can be determined from the

above reaction as 1 mole of propane reacting per 5 moles of diatomic oxygen, or:

fstoich =44

5(32)=44

160=11

40

Using this result along with the mass °ux equations for oxygen and propane while

assuming steady °ow yields

28

_mC3H8

_mO2

=1:109£ 10¡4PC3H8 + 2:207£ 10¡31:731£ 10¡4PO2 + 2:527£ 10¡3

=11

40

Rearranging the above equation yields a relationship between the oxygen regulator

pressure and the propane regulator pressure:

PO2=(2:5627)PC3H8+36.401

A plot for stoichiometric regulator settings for propane and oxygen is shown in ¯g-

ure 3.2 (Á = 1). Lines of constant o®-stoichiometric settings are also illustrated in

¯gure 3.2 with Á varying from 0.80 to 1.20. Figure 3.2 also includes test points for o®-

Figure 3.2. Stoichiometric oxygen and propane regulator settings.

stoichiometric settings. This was done by varying the oxygen regulator pressure and/or

the propane regulator pressure.

29

3.2 O®-Stoichiometric Tests

As stated earlier, the calculated stoichiometric mixture from the °ow-nozzle calibration

data is an estimate. The regulator settings should be trimmed around this pseudo-

stoichiometric level to obtain maximum performance or at least a setting suitable enough

to proceed with experiments.

Figure 3.3 is a data plot [11] of CJ detonation velocity vs. fuel-oxidizer equivalence

ratio for propane and oxygen mixtures at initial conditions of 1 atm and 295 K with a

3rd order polynomial ¯t. Peak velocity level is located in the slightly fuel-rich regime,

Figure 3.3. CJ detonation velocity as a function of equivalence ratio for a 1 atm C3H8=O2pre-detonation mixture [11].

an equivalence ratio around 1.9. Regulator settings of the o®-stoichiometric test runs

with the clean con¯guration detonation chamber to determine an optimal setting are

shown in ¯gure 3.2.

Average time-of-°ight plots of these tests for 6.9 and 6 Hz cycle frequencies are

shown in ¯gures 3.4 and 3.5 respectively. The Á = 0:91 plots represents results from two

30

separate test runs. Notice the increase in open end average velocity for the presumed

Figure 3.4. O® stoichiometric performance for 6.9 Hz cycle frequency.

leaner fuel mixtures. This is contradictory to the illustration of ¯gure 3.3 which indicates

that for a slightly richer propellant mixture, Á greater than 1.0, would result in a higher

CJ velocity level. Figures 3.4 and 3.5 fail to show this trend. A possible scenario

to explain what may be occurring is as follows. Suppose the calculated stoichiometric

settings from the mass °ux calibration resulted in a setting that was actually in the fuel-

rich regime beyond the level of the maximum CJ velocity condition. A leaner mixture

from this point would lead to a higher CJ velocity state generating trends similar to

¯gures 3.4 and 3.5. Regardless, none of the wave fronts ever reach a sustained detonation

state let alone a CJ velocity level of 7750 ft/s within the length of the detonation

chamber. This made it di±cult to choose an optimal baseline fuel/oxidizer setting.

Because of this complication, the calculated stoichiometric setting (see ¯gure 3.2) was

chosen as the baseline for the remaining experiments.

31

Figure 3.5. O® stoichiometric performance for 6 Hz cycle frequency.

3.3 Varied Cycle Frequency

Section 2.3 describes the mechanical injection system as being highly dependent on

the drive motor rotation rate. Two main areas of concern due to this coupling are the

timing between ignition, injection, and purge processes and the duration of injection

and purge cycles.

Triggering of the ignition system was done through a magnetic pick-up near the

fuel injection rotary valve. A metal screw head used to trigger the magnetic pick-up was

located about 120± after the fuel/oxidizer injection. Purging of the high temperature

combusted species occurred 180± after the injection of the propellants. Due to the

coupling of these processes, the engine cycle frequency greatly in°uences the timing

of each cycle as illustrated by calculated values in ¯gure 3.6. To interpret the ¯gure

assume a cycle frequency. For 10 Hz the injection process begins at 0 ms and then

ends less than 10 ms later. Ignition will take place about 30 ms after the injection

process began. The purging phase begins at 50 ms with the same 10 ms duration as the

injection process. Finally, the cycle ends when the injection valve begins to open again

32

100 ms after the cycle started.

Figure 3.6. Ignition and injection timing as a function of cycle frequency.

Propellant injection duration is also highly dependent on the cycle frequency. The

higher the operation frequency, the shorter the time that the injection valve will stay

open, thus causing less fuel and oxidizer to be introduced into the detonation chamber.

Figure 3.7 plots the relation of calculated injection period and injection area for various

operation frequencies with detailed calculations located in the appendix.

3.4 Clean Con¯guration Results at Baseline Regulator Settings

Clean con¯guration results are from baseline regulator settings at a cycle frequency

of 6.9 Hz. Data acquisition was con¯gured for a 1 MHz/channel sampling frequency

but because of the large amounts of data produced only a 3 ms window of the wave

pro¯le was reduced. The following three series of plots typify the clean con¯guration

performance. Low velocity wave fronts with a re°ected shock front accelerating from

behind.

In every case a weak compression front is initialized (stage P7) shortly after ig-

33

Figure 3.7. Injection area as a function of time for varying cycle frequencies.

Figure 3.8. Clean con¯guration wave pro¯le with 6.9 Hz cycle frequency - 1.

Figure 3.9. Wave diagram and average time of °ight for wave pro¯le in ¯gure 3.8 - 1.

34


Figure 3.11. Wave diagram and average time of °ight for wave pro¯le in ¯gure 3.10 - 2


35

Figure 3.13. Wave diagram and average time of °ight for wave pro¯le in ¯gure 3.12 - 3

nition. An overpressure level is generated from the re°ection o® the end-wall. Recall

that the ignition source is mounted 1.5 inches downstream from the closed end of the

detonation chamber. This re°ected shock tends to lose strength as it accelerates to-

wards the leading compression front. By the time the shock front reaches station P4

13.5 inches downstream, it is completely unnoticeable after coalescing with the leading

compression front.

The wave diagrams for each wave pro¯le dissection show this wave acceleration and

coalescence from another perspective. The leading wave velocity is represented by the

solid line discretized between the pressure sensor and ignition locations. The dashed line

denotes the assumed path that the re°ected wave would take while accelerating towards

the initial front. However, one test case shows a point outside of the dashed trend line

(¯gure 3.11). This location of a shock on an x-t diagram is usually due to the presence

of a retonation wave (¯gure 1.10). But no signi¯cant detonation front is recognizable in

any of the three wave pro¯les that would form a retonation. An explanation into this

event remains unresolved.

Time-of-°ight plots are as signi¯cant in determining detonation performance as

are the pressure wave pro¯les. No signi¯cant velocity levels were measured supporting

the evidence of poor performance visible through the wave pressure pro¯les. Each time-

of-°ight plot represents the leading compression front only. Every case shows initial

36

average velocity just over the sonic velocity for a 1 atm stoichiometric C3H8/O2 pre-

detonation mixture. Even though wave acceleration is clearly evident, velocity levels

barely reach 30% of the CJ state by the end of the 21 inch detonation chamber.

3.5 Shchelkin Spiral Results

The following results pertain to the con¯guration illustrated in ¯gure 2.2. Propane and

oxygen regulators remain at the calculated stoichiometric baseline setting of PC3H8 =

43psig and PO2 = 146psig. The only varying parameter is the cycle frequency, which

greatly a®ects the performance of the engine. A range of four cycle frequency settings

was chosen from the maximum 20 Hz to a relatively low setting of 4.4 Hz.

3.5.1 20 Hz Cycle Frequency

For the 20 Hz cycle frequency test case the sampling frequency was at 100 kHz/channel

due to memory constraints. This was adequate for a cycle-to-cycle repeatability exper-

iment of relative long sampling duration. Cycle-to-cycle repeatability shows signi¯cant

overpressure levels of around 200 psia on average, albeit lower than the CJ level. The

way that the pressure transducer hardware was mounted to the experimental set-up

(see ¯gure 3.15) left a small volume between the sensing surface of the transducer and

the detonation chamber. This small volume damped out the pressure signal and never

allowed the dynamic transducers to register the full shocked level. One way to remedy

this problem is to mount the transducer °ush to the detonation chamber inside wall.

Past experiments using this method exhibited a stronger overpressure pro¯le than that

of the water jacket mounted case [7]. However, those tests were done in a single shot

mode of operation. For relatively high operation frequencies, it is imperative that water

jackets be used for protecting the pressure transducers.

A more in-depth performance evaluation can be done by zooming into an indi-

37

Figure 3.14. Chamber pressure history at 20 Hz.

Figure 3.15. Transducer mounting void.

38

vidual wave pro¯le. In the region of the Shchelkin spiral's in°uence, the wave shows

signi¯cant transition towards a detonation front in overpressure levels as well as average

velocities. However, the wave tends to weaken considerably as it propagates towards

the open end. Although each of the forty to ¯fty individual wave pro¯les shows poor

performance (¯gure 3.16), the consistent intermittent overpressure history (¯gure 3.14)

encourages support for the use of the Shchelkin spiral in higher frequency modes of

operation.

Figure 3.16. Typical wave pro¯le from 20 Hz test case.

3.5.2 14.4 Hz Cycle Frequency

The next test example is from a 14.4 Hz cycle frequency test case. Sample frequency

was also set at 100 kHz for the purpose of adequate memory for long sampling dura-

tions. Cycle to cycle repeatability is illustrated in 3.19. Again, signi¯cant cycle-to-cycle

overpressure levels are demonstrated. Average peak pressure is slightly higher than that

of the 20 Hz case. Upon zooming in (see ¯gure 3.20) the same early transition trend can

be seen in the region of the spiral. However, after the end of the spiral, P3 the pro¯le

39

Figure 3.17. Wave diagram for 20 Hz test in ¯gure 3.16.

Figure 3.18. Average velocity plot for 20 Hz test in ¯gure 3.16.

40

Figure 3.19. Chamber pressure history from 14 Hz test case.

41

shows a higher pressure peak than in the 20 Hz case, as evident in ¯gure 3.20 as well

as ¯gure 3.22.

Figure 3.20. Typical wave pro¯le from 14.4 Hz test case.


The DAQ hardware con¯guration was changed to allow a 1 MHz sampling resolution

with a purpose to signi¯cantly resolve the wave pro¯le. Sample times were around

250 ms and created massive data ¯les. Only 3 ms windows around the wave pro¯les of

interest were reduced to simplify the post-processing of the data. No macroscopic cycle-

to-cycle demonstration was available for any case with the 1 MHz sampling resolution

because of the modi¯cation. Figure 3.23 is the pro¯le from the 6.9 Hz test case. Two

peaks are clearly visible, a leading overpressure followed closely by a re°ected front.

Both are mapped in the Wave diagram of ¯gure 3.24

A signi¯cant trend is now beginning to develop. Not only is there rapid transition

into a detonation pro¯le in the Shchelkin spiral region, but there is also considerable

sustentation after the wave passes the obstacle. Peak average velocities even reach the

42

Figure 3.21. Wave diagram for 14.4 Hz test in ¯gure 3.20.

Figure 3.22. Average velocity plot for 14.4 Hz test in ¯gure 3.20.

43

Figure 3.23. Typical wave pro¯le from 6.9Hz test case.

CJ level in the region of the spiral, a characteristic obviously absent in higher frequency

cases.


Again, with the DAQ sample resolution at 1 MHz, only the resolved individual wave

pro¯les are available for the 4.4 Hz cycle frequency tests. This is the lowest cycle fre-

quency test case recorded and shows the best performance of all the frequency settings.

Not only did the Shchelkin spiral demonstrate a detonation wave being generated in a

relatively short distance (between 4.5 and 7.5 inches), but it also shows that the wave

can sustain itself to the end of the 21 in chamber with only minor velocity level decline.

3.6 Discussions

Signi¯cant lack of performance was observed with the clean con¯guration at a modest

cycle frequency of 6.9 Hz. Not a single detonation was achieved and velocity lev-

els barely peaked at 30% of the CJ level. Several reasons may be the cause of this

problem. One is that the calculated stoichiometric level could have been severely o®

from the true stoichiometric value as previously discussed. Another possibility is that

44



45

Figure 3.26. Typical wave pro¯le from 4.4 Hz test case.


46


the length of tubing between the mass °ow meters and the injection valving created

non-stoichiometric levels upon injection into the detonation chamber. In addition, the

problem of adequate mixing was not tackled. Figure 3.6 shows that at 6.9 Hz, only

about a 40 ms window (the time after the injection valve closed to the time of ignition)

would be available for mixing. The swirling disc used to enhance mixing may not be

creating the desired level of turbulence to completely mix the C3H8/O2 gases in such a

short period.

The clean con¯guration pro¯le shows poor performance early in comparison to the

wave pro¯le of the Shchelkin spiral case with identical run conditions at 6.9 Hz. To the

untrained eye, it is very di±cult to see any improvement in wave pro¯le beyond that.

But, upon looking closer at the pro¯les from P6, P5, and P4 for the Shchelkin spiral case

(see ¯gure`3.23, there is a considerably distinct pressure spike which is characteristic

of shocked °ow. At every location for the clean con¯guration case, an obvious pre-

47

compression is evident before the large overpressure level.

Improved performance in the Shchelkin spiral con¯guration is even more obvious

in the time-of-°ight plot of ¯gure 3.30. The wave consistently reaches a CJ level in a

short distance near the end of the Shchelkin spiral. This velocity lasts only for a short

distance before the lack of ¯ll in the chamber begins to take e®ect.

Fill time due to cycle frequency did posed an egregious problem in the ability to

sustain a detonation through the length of the chamber. Figure 3.31 combines pro¯le

plots from the 20, 14.4, 6.9, and 4.4 Hz cycle frequency test cases with the Shchelkin

spiral installed. The characteristic shocked °ow pro¯le becomes much more visible

toward the open end of the tube as the cycle frequency is reduced, with a corresponding

increase in injection and mixing times. This varied frequency e®ect is just as evident

in the time-of-°ight plot of ¯gure 3.32. Cases of ¯ve di®erent cycle frequencies are

superimposed on the same plot illustrating the di±culty of achieving high velocities at

high frequencies. Signi¯cant average velocities above or near the CJ level occur in the

lower frequency cases. Higher cycle frequency velocities fall short of that plateau and

tend to ebb o® much more sharply.

3.7 Uncertainty Analysis

Average velocity calculations were made with the relation shown in equation 3.1

Vtof =¢x

¢t(3.1)

The change in x, ¢x, represents the distance between successive transducer locations

and the change in t, ¢t, represents the time between pressure signals from the successive

transducer locations. Uncertainty in x is due machining tolerance alone. For simplicity,

de¯ne the pressure transducer locations for P7 as 7, P6 as 6, P5 as 5, etc.

48

Transducers are only located in sections 2 and 3 of ¯gure 3.33. Past reports state ma-

chining errors of 0.01 in. [13], however, this applies to each individual section. Every

instrument port was measured from one edge. For the ¯rst three average velocity cal-

culations, ¢x will have the same uncertainty:

¢x7¡6 = (4:5§ 0:01)¡ (1:5§ 0:01) = 3:0§ 0:02 in.¢x6¡5 = (7:5§ 0:01)¡ (4:5§ 0:01) = 3:0§ 0:02 in.¢x5¡4 = (10:5§ 0:01)¡ (7:5§ 0:01) = 3:0§ 0:02 in.

Between locations 4 and 3, mating one °ange to another must also be considered in the

error analysis:

¢x4¡3 = (12:0§ 0:01)¡ (10:5§ 0:01) + (1:5§ 0:01) = 3:0§ 0:03 in.

The ¯nal ¢x uncertainty is given by:

¢x3¡2 = (4:5§ 0:01)¡ (1:5§ 0:01) = 3:0§ 0:02 in.

Two main areas of concern in°uences the measurement of ¢t. One is the sampling

drift of the DAQ hardware. The DSP digitizers have a drift of §100 ns. Another factoris the sampling frequency of the DAQ system.

Figure 3.34 is an illustration of what sampling discretization can do to a true

detonation pro¯le. Represented is a pressure wave schematic propagating between two

successive transducer ports, A and B. The lighter vertical lines denote time intervals

between data sampling, or the inverse of the sampling frequency. Time tA is the tagged

49

location where, from the discretized sampling, the wave appears to reach the pressure

transducer. The previous and succeeding data sample are designated as tA¡ and tA+,

respectively. Having only discrete approximation of the actual pressure pro¯le, we can

say that the wave never could have passed between time locations tA and tA¡. The

initial rise of the wave could only have been sampled between times tA and tA+ . Thus,

the tagged location of when the wave arrives at the transducer sensing face is assumed

to be the midpoint of tA and tA+ and would have an uncertainty of §0:5=fsampling. Thesame would hold for the next tagged location, B. Coupling the two together to calculate

¢t for average velocity purposes yields:

¢t =1

2

³tB ¡ tB+

´§ 12

1

fsampling¡ 12

³tA ¡ tA+

´§ 12

1

fsampling(3.2)

or:

¢t =1

2

³tB ¡ tB+

´¡ 12

³tA ¡ tA+

´§ 1

fsampling(3.3)

Time-of-°ight calculation uncertainty was taken from [12]:

!R =

24Ã ±R±x1

!1

!2+

Ã±R

±x2!2

!2+ ¢ ¢ ¢+

Ã±R

±xn!n

!235 12

(3.4)

Where the result R = f(x1, x2,... , xn). De¯ning the result R as the time of °ight

velocity measurement, Vtof = f(x, t):

!Vtof =

24Ã±V±x!x

!2+

Ã±V

±t!t

!235 12

(3.5)

From equation 3.1:

±V

±x=1

¢t(3.6)

50

±V

±t= ¡¢x

¢t2(3.7)

Plugging in these relations back into equation 3.8:

!Vtof =

"µ1

¢t!x

¶2+µ¡¢x¢t2

!t

¶2# 12(3.8)

The values of !t depend on the sampling frequency of the DAQ system. For 100

kHz and 1 MHz sampling rates, !t=10 ¹s and 1 ¹s respectively. Values of !x depend

on the location of average velocity calculation. For locations 7-6, 6-5, 5-4, and 3-2,

!x=0.02 in. For the region where sections 2 and 3 were mated together, location 4-3,

!x=0.03 in.

Change uncertainty in transducer location due to the mating of di®erent sections

contributed little to the overall uncertainty. Figure 3.35 represents error for the !x=0.02

in. case. If the !x=0.03 in. were used in the velocity error plot, only a 0.01 to 0.15%

change in uncertainty would be visible. The following simple relation was used to

calculate velocity:

Vtof =3in:

¢t

where 3 in. is the distance between successive transducer locations. Now for example,

if a ¢t value of 0.05 msec were measured between two successive overpressure peaks

a nominal velocity of about 5000 ft/sec would be calculated. For 1 MHz sampling

frequency the actual velocity would be between 4900 and 5100 ft/sec. If the sampling

frequency were at 100 kHz as in the 20 and 14.4 Hz cycle frequency test cases, the

velocity could be anywhere between 4000 and 6000 ft/sec. This analysis shows the

importance of sampling at higher frequencies.

51

Figure 3.29. Clean and Shchelkin spiral con¯guration pressure pro¯le comparison resultsat 6.9 Hz cycle frequency

52

Figure 3.30. Clean and Shchelkin spiral con¯guration velocity comparison at 6.9Hzcycle frequency

Figure 3.31. Single pulse propagation comparison at varied frequencies.

53

Figure 3.32. Average velocity plot for Shchelkin spiral installed con¯guration withC3H8=43 psig and O2=146 psig

Figure 3.33. Machining uncertainty and notation .

54

Figure 3.34. Actual pressure pro¯le with sampling times superimposed .

55

Figure 3.35. Velocity error plot .

CHAPTER 4

CONCLUSIONS AND RECOMMENDATIONS

4.1 Conclusions

Detonations are readily obtained in a very short distance (8 to 10 in) for modest cycle

frequencies of 4.4 and 6.9 Hz with the Shchelkin spiral installed. This is apparent

through the time-of- °ight plots that show high velocity levels near or above the CJ

level for the standard atmosphere pre-detonation condition. Although the pressure

pro¯le plots show pressure spikes lower than that of CJ level (due to the method of

installing the pressure transducers as shown in ¯gure 3.15), they do show sharp shocked

pro¯les with hardly a sign of pre-compression except in early stages of transition.

At higher frequencies, 14.4 and 20 Hz, only strong intermittent overpressures are

observed. Each pressure pro¯le yielded weak pre-compressions followed closely with a

relatively strong overpressure peak that quickly deteriorated after passing the Shchelkin

spiral. Average velocity plots are consistent with this diminishing of the wave front as

velocity falls o® towards the end of the chamber, never reaching the CJ level. This is

possibly due to improper ¯lling of the detonation chamber from cycle to cycle which is

a major argument for the improved performance at lower frequencies.

The con¯guration of the PDR for this report showed poor performance at high

frequencies. However, cycle-to-cycle repeatability was shown in the Shchelkin spiral

con¯guration with better results than that of the clean con¯guration. A method of

injection must be redesigned to allow more mass of gases for each cycle regardless of

operating frequency.

56

57

4.2 Recommendations

The largest obstacle of this experiment was the injection system. At high frequencies,

only small slugs of gases could be injected each cycle. This was due to the coupling of

the rotary valves and drive motor which dictated cycle frequency. Two main recom-

mendations could remedy this problem.

The volume of the chamber may be unnecessarily large. Money constraints limited

purchasing and upgrade options so the old 140 in3 chamber was used. This chamber

has an inside diameter of 3 in which is excessively larger than the cell size of a propane-

oxygen detonation which is under 0.5 cm at a standard atmosphere pre-detonation

condition. Decreasing the chamber volume to a tube of 1in diameter (still signi¯cantly

larger than the detonation cell size) with the same length of 21 in would reduce cycle

to cycle propellant mass requirements by a factor of 9.

Another ¯x would be to eradicate the rotary valve system and develop a solenoid

valve one instead. Digitally controlling the injection duration would alleviate the cou-

pling of injection and cycle frequency. Consideration has been given to this improve-

ment, but ¯nding solenoid valves that can deliver enough mass at the high frequencies

desired has been challenging.

APPENDIX A

RAYLEIGH AND HUGONIOT RELATION DERIVATIONS

58

59

A.1 Rayleigh-Line Equation

Manipulate the momentum equation 1.2 to the following form:

½2³½1P1 + ½1

2u12´= ½1

³½2P2 + ½2

2u22´

From the mass continuity equation 1.1:

(½1u1)2 = (½2u2)

2 = B2

Combining the two:

½2³½1P1 +B

2´= ½1

³½2P2 +B

2´

½2½1P1 + ½2B2 = ½1½2P2 + ½1B

2

½1½2 (P1 ¡ P2) = B2 (½1 ¡ ½2)

P1 ¡ P2 = B2 (½1 ¡ ½2)½1½2

=B2

½1½2

Ã1

½2¡ 1

½1

!=B2

½1½2(º2 ¡ º1)

P1 ¡ P2º2 ¡ º1 =

B2

½1½2= ¹

P2=P1 ¡ 1º2=º1 ¡ 1 = ¡¹

P2P1¡ 1 = ¡¹

µº2º1¡ 1

¶

60

A.2 Hugoniot Equation

The continuity equation:

½1u1 = ½2u2

u2 = u1½1½2

Substituting into the momentum equation:

P1 + ½1u12 = P2 + ½2u2

2

P1 + ½1u12 = P2 + ½2

Ã½1½2u1

!2

u12 =

P2 ¡ P1½2 ¡ ½1

Ã½2½1

!

Again from the continuity equation:

½1u1 = ½2u2

u1 = u1½2½1

Substituting into the momentum equation:

P1 + ½1u12 = P2 + ½2u2

2

P1 + ½1

Ã½2½1u2

!2= P2 + ½2u2

2

u22 =

P2 ¡ P1½2 ¡ ½1

Ã½1½2

!

61

Substituting u21 and u22 into the energy equation:

h1 +u12

2+ q = h2 +

u22

2

h1 +1

2

ÃP2 ¡ P1½2 ¡ ½1

!Ã½2½1

!+ q = h2 +

1

2

ÃP2 ¡ P1½2 ¡ ½1

!Ã½1½2

!

h1 ¡ h2 + q = 1

2

ÃP2 ¡ P1½2 ¡ ½1

!Ã½1½2¡ ½2½1

!

h1 ¡ h2 + q = 1

2

0BBB@P2 ¡ P11

º2¡ 1

º1

1CCCAµº2º1¡ º1º2

¶

h1 ¡ h2 + q = 1

2

0BBB@P2 ¡ P1º1 ¡ º2º1º2

1CCCAÃº22 ¡ º12º1º2

!

h1 ¡ h2 + q = 1

2(P2 ¡ P1)

Ãº22 ¡ º12º1 ¡ º2

!

h1 ¡ h2 + q = ¡12(P2 ¡ P1) (º2 + º1)

h1 ¡ h2 + q = 1

2(P1 ¡ P2) (º2 + º1)

h1 ¡ h2 + q = 1

2

∙P1

µ1¡ P2

P1

¶¸ ∙º1

µº2º1+ 1

¶¸

APPENDIX B

DATA REDUCTION CODE

62

63

B.1 Setup ¯le for 48-channel reduction

SETUPFM.DAT data ¯le format for 48 channels used for sampling:

NP TC PTF HF

ITI IBARCH IRTDCH IVEXCT

PRSCH TCCH PTFCH HFCH

GBAR GRTD GVEXCT

IFCP IFCT

SNFN AAAF BBBF CCCF

IOCP IOCT

SNON AAAO BBBO CCCO

P2SN P2S P2Y P2G

P3SN P3S P3Y P3G

P4SN P4S P4Y P4G

P5SN P5S P5Y P5G

P6SN P6S P6Y P6G

PFSN PFS PFY PFG

POSN POS POY POG

TCFSN TCFS TCFY TCFG

TCOSN TCOS TCOY TCOG

P7SN P7S P7Y P7G

TC1SN TC1S TC1Y TC1G




64



PTF1SN PTF1S PTF1Y PTF1G






HF1SN HF1S HF1y HF1G






NP { # of pressure transducer channels (does not include Baratron transducer)

TC { # of thermocouple channels

PTF { # of platinum thin ¯lm heat °ux gage channels (not used)

HF { # of heat °ux channels (not used)

ITI { sampling resolution in ¹s

IBARCH { channel # of Baratron transducer

IRTDCH { channel # RTD

IVEXCT { channel # of Wheatstone bridge excitation (not used)

PRSCH { ¯rst pressure transducer channel after Baratron transducer

TCCH { channel # of ¯rst thermocouple

65

PTFCH { channel # of ¯rst platinum thin ¯lm heat °ux gage (not used)

HFCH { channel # of ¯rst heat °ux gage (not used)

GBAR { gain of Baratron transducer

GRTD { gain of RTD

GVEXCT - gain of wheatstone bridge excitation (not used)

IFCP { channel # of fuel pressure

IFCT { channel # of fuel temperature

SNFN { serial # of fuel °ow nozzle

AAAF { \a" coe±cient for fuel °ow calibration

BBBF { "b" coe±cient for fuel °ow calibration

CCCF { "c" coe±cient for fuel °ow calibration

IOCP { channel # of oxygen pressure

IOCT { channel # of oxygen temperature

SNON { serial # of oxygen °ow nozzle

AAAO { "a" coe±cient for oxygen °ow calibration

BBBO { "b" coe±cient for oxygen °ow calibration

CCCO { "c" coe±cient for oxygen °ow calibration

NOTE: for any of "not used" cases above , enter "-1"

P2SN { serial # of pressure transducer 2

...


P2S { slope of pressure transducer 2

66

...


P2Y { y-intercept of pressure transducer 2

...


P2G { gain of pressure transducer 2

...


PFSN { serial # of fuel °ow pressure transducer

PFS { slope of fuel °ow pressure transducer

PFY { y-intercept of fuel °ow pressure transducer

PFG { gain of fuel °ow pressure transducer

POSN { serial # of oxygen °ow pressure transducer

POS { slope of oxygen °ow pressure transducer

POY { y-intercept of oxygen °ow pressure transducer

POG { gain of oxygen °ow pressure transducer

TCFSN { serial # of fuel °ow thermocouple

TCFS { slope of fuel °ow thermocouple

TCFY { y-intercept of fuel °ow thermocouple

TCFG { gain of fuel °ow thermocouple

TCOSN { serial # of oxygen °ow thermocouple

TCOS { slope of oxygen °ow thermocouple

67

TCOY { y-intercept of oxygen °ow thermocouple

TCOG { gain of oxygen °ow thermocouple

P7SN { extra pressure transducer channel serial number (not used)

P7S { extra pressure transducer channel slope (not used)

P7Y { extra pressure transducer channel y-intercept (not used)

P7G { extra pressure transducer channel gain (not used)

TC1SN { serial # of thermocouple 1

...

TC6SN { serial # of thermocouple 6

TC1S { slope of thermocouple 1

...

TC6S { slope of thermocouple 6

TC1Y { y-intercept of thermocouple 1

...

TC6Y { y-intercept of thermocouple 6

TC1G { gain of thermocouple 1

...

TC6G { gain of thermocouple 6

PTF1SN { serial # of platinum thin ¯lm heat °ux gage 1

...

68

PTF6SN { serial # of platinum thin ¯lm heat °ux gage 6

PTF1S { slope of platinum thin ¯lm heat °ux gage 1

...

PTF6S { slope of platinum thin ¯lm heat °ux gage 6

PTF1Y { y-intercept of platinum thin ¯lm heat °ux gage 1

...

PTF6Y { y-intercept of platinum thin ¯lm heat °ux gage 6

PTF1G { gain of platinum thin ¯lm heat °ux gage 1

...

PTF6G { gain of platinum thin ¯lm heat °ux gage 6

HF1SN { serial # of heat °ux gage 1

...

HF6SN { serial # of heat °ux gage 6

HF1S { slope of heat °ux gage 1

...

HF6S { slope of heat °ux gage 6

HF1Y { y-intercept of heat °ux gage 1

...

HF6Y { y-intercept of heat °ux gage 6

69

HF1G { gain of heat °ux gage 1

...

HF6G { gain of heat °ux gage 6

B.2 Setup ¯le for 8 channel reduction

SETUPFM.DAT data ¯le format for 8-channel used for 1 ¹s sampling:

NP ITI IBARCH PRSCH

GBAR IP

P2SN P2S P2Y P2G

P3SN P3S P3Y P3G

P4SN P4S P4Y P4G

P5SN P5S P5Y P5G

P6SN P6S P6Y P6G

P7SN P7S P7Y P7G

P8SN P8S P8Y P8G

NP { # of pressure transducer cahnnels (does not include Baratron transducer)

ITI { sampling resolution in ¹s

IBARCH { channel # of Baratron transducer

PRSCH { ¯rst pressure transducer channel after Baratron

GBAR { gain of Baratron transducer

IP { # of total channels reducing

70


:



:



:



:


B.3 Reduction Code for 8 channel reduction

C SNP(#) - Pressure Transducer Serial Number of Transducer #

C MP(#) - Slope of Pressure Tranducer # Calibration Curve

C YP(#) - Y-Intercept of Pressure Tranducer # Calibration Curve

C GP(#) - Gain of Pressure Transducer #

C BARCH - Channel Number of Baratron Transducer

C PRSCH - Channel Number of First Pressure Transducer

C NP - Number of Pressure Transducers

71

C IP - Total Number of Data Channels

$NOFLOATCALLS

C PROGRAM PDMNFMMS.FOR

REAL RSP(48),EP(48),SCOTT(2,9),PRS0(16),MP(16),YP(16)

INTEGER BARCH,RTDCH,PRSCH,GP(7),SNP(16),GBAR

CHARACTER A(80),TITLE(8),TITO(12),TOUT(12)

CHARACTER*12 NAME,NAMEFL(48),NMOUT

EQUIVALENCE (NAME,TITO),(NMOUT,TOUT)

DATA TITO/12*' '/

CONV=2.441406250

C TORR X .019337 = PSI

C BARATRON OUTPUT IS MILLIVOLTS = TORR

C MULTIPLY READING BY 19.337 TO GET PSI

C WRITE(*,*)'IP ',IP

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

OPEN(98,FILE='SAMPLE',STATUS='OLD')

READ(98,593) ISAMPS,TMINV,START

CLOSE (98)


72

OPEN(26,FILE='SETUPFM.DAT',STATUS='OLD')

READ(26,551)NP,ITI,IBARCH,PRSCH

WRITE(*,*)'SETUP LINE 1'

READ(26,552)GBAR

WRITE(*,*)'SETUP LINE 2'

551 FORMAT(4(I4,5X))

552 FORMAT(1(I4,5X))

TI = FLOAT(ITI)

TI = TMINV

DO 131 JJ=1,NP

READ(26,555)SNP(JJ),MP(JJ),YP(JJ),GP(JJ)

555 FORMAT(I6,5X,E15.8,5X,E15.8,5X,I4)

131 CONTINUE

WRITE(*,*)'SETUP PRESSURE'

CLOSE(26)

CCCCCC[ Process Raw Data]CCCCCCCCCCCCCCCCCCCCCCCC

C READ IN NAME OF RAW DATA FILE PREFIX

OPEN(11,FILE='DTNAME',STATUS='OLD')

READ(11,503) (TITLE(I),I=1,8)

CLOSE(11)

73

C REMOVE SPACES FROM RAW DATA FILE IF LESS THAN 8 CHARACTERS

DO 31 J=1,8

IF (TITLE(J) .NE. ' ') THEN

TITO(J)=TITLE(J)

TOUT(J)=TITLE(J)

LLL=J

ENDIF

31 CONTINUE

C ADD POSTFIX TO RAW DATA FILES

TITO(LLL+1) = '.'

TITO(LLL+2) = 'D'

TITO(LLL+3) = 'A'

TITO(LLL+4) = 'T'

WRITE(*,511) NAME

TOUT(LLL+1) = '.'

TOUT(LLL+2) = 'O'

TOUT(LLL+3) = 'U'

TOUT(LLL+4) = 'T'

WRITE(*,511) NMOUT

C

OPEN(8,FILE=NAME,STATUS='OLD')

C SKIP FIRST FEW DATA POINTS

74

DO 101 J=1,24

READ(8,507,END=890) (RSP(K),K=1,IP)

101 CONTINUE

C AVERAGE 48 POINTS FOR INITIAL PRESSURE AND REFERENCE TEMPER-

ATURE

BARPRS=0.0

RTD=0.0

VEXCT=5.0

DO 121 I=1,6

PRS0(I)=0.0

121 CONTINUE

DO 103 J=1,48

READ(8,507,END=890) (RSP(K),K=1,IP)

BARPRS=BARPRS+RSP(IBARCH)-2048.

DO 104 I=PRSCH,PRSCH+NP-1

PRS0(I-PRSCH+1)=PRS0(I-PRSCH+1)+RSP(I)-2048.

104 CONTINUE

103 CONTINUE

BARPRS=BARPRS*.019337*CONV/(48.*GBAR)

WRITE(*,*)'BARPRS',BARPRS

75

DO 108 I=1,NP

PRS0(I)=PRS0(I)*CONV/(48.*GP(I))

108 CONTINUE

REWIND(8)

C

CCCCCCC[ Output Data ]CCCCCCCCCCCCCCCCCCCCCCCCCCC

OPEN(29,FILE=NMOUT,STATUS='NEW')

WRITE(29,561)'TIME','BARATRON','PRESSURE'

WRITE(29,563)(SNP(LI),LI=1,NP)

561 FORMAT(A4,4X,A8,6X,A8)

563 FORMAT(23X,9(I6,6X))

VEXCT=5.0

TIME = 0

KKK = -1

808 READ(8,507,END=890) (RSP(K),K=1,IP)

KKK = KKK + 1

TIME = TI * KKK + START


DO 171 I=1,IP

CCCCCC[ I = Baratron Chan # ]

76

IF(I .EQ. IBARCH) THEN

EP(I)=(RSP(I)-2048.)*.019337*CONV/GBAR

GOTO 171

ENDIF

C[ I>=1st Press Trans and I=<1st Press Trans+# Press Trans-1]

IF(I .GE. PRSCH .AND. I .LE. (PRSCH+NP-1)) THEN

EP(I)=(((RSP(I)-2048.)*CONV/GP(I+1-PRSCH))-PRS0(I-PRSCH+1))

X /MP(I+1-PRSCH)+YP(I+1-PRSCH)+BARPRS

GOTO 171

ENDIF

171 CONTINUE


GOTO 808

890 CLOSE(8)

CLOSE(29)

C

C

503 FORMAT(8A1)

505 FORMAT(32(I1,1X),/,16(I1,1X),I2)

77

506 FORMAT(16(2X,F6.1))

507 FORMAT(48(2X,F6.1))

511 FORMAT(5X,A25)

591 FORMAT(F9.3,50(E12.6))

593 FORMAT(I8,1X,E13.6,1X,E13.6)

C

STOP

END

APPENDIX C

INJECTION AREA CALCULATIONS

78

79

The following presents an approximation of the injection area for fuel and oxidizer

species on the 3 rotary valve PDR/E mechanical injection system. This will apply to all

three valves since the geometries of each are identical. First, the area as a function of

the gap of the opening, h, must be determined as illustrated by ¯gure C.1. The shaded

region represents the opening for the e²ux of gases.

h

Rotating Shaft

A 1/2h

Figure C.1. Area of injection for a single injection valve port.

Now calculate the half injection area A. Consider the wedge with angle 2Á and radius

r from ¯gure C.2.

Aw

��r

Figure C.2. Wedge area.

The area can be represented by a simple geometric relation:

80

r

(r-h)

At�

x

Figure C.3. Triangular area.

Aw = Ár2

The triangular region represented in ¯gure C.3 can be determined from:

At = 2

"1

2x

Ãr ¡ h

2

!#= x

Ãr ¡ h

2

!

x = r sin (Á)

At = r

Ãr ¡ h

2

!sin (Á)

The area of concern, A, is nothing more than the subtraction of At from Aw:

A = Aw ¡At = Ár2 ¡ rÃr ¡ h

2

!sin (Á)

Now ¯nd a relation for Á:

r cos (Á) = r ¡ h2

or:

Á = cos¡1Ãr ¡ h=2r

!

81

The opened area as a function of h must now be determined.

A = r2 cos¡1Ãr ¡ h=2r

!¡ r

Ãr ¡ h

2

!sin

Ãcos¡1

Ãr ¡ h=2r

!!

This only represents the half area of one injection port, but there are 3 ports for each

valve. Thus the area is actually:

A = 6

"r2 cos¡1

Ãr ¡ h=2r

!¡ r

Ãr ¡ h

2

!sin

Ãcos¡1

Ãr ¡ h=2r

!!#(C.1)

Area as a function of h has now been determined but must be represented as a

function of time. Assuming an operating frequency of f the rotation rate of the shaft

is:

Figure C.4. Notation for angular velocity and tangential velocity.

! = 2¼f

V = !R = 2¼Rf

82

The time from when the valve just begins to open until the time when the valve just

closes will be denoted by tf . This is found from the relation between the tangential

velocity and 2r, the approximate distance the rotary valve travels from initial opening

to closing.

tf =2r

V=

2r

2¼Rf=

r

¼Rf

At the halfway point, 1=2tf , the valve becomes fully opened. This is graphically repre-

sented in ¯gure C.5.

Figure C.5. Time relation approximation to h.

A model of h as a function of time is represented as a piece-wise function. The ¯rst

portion is generated from time t = 0 until time t = 1=2tf :

h = m1t

with the second half coming from the remaining time segment t = 1=2tf to t = tf :

h = 2r +m2t

Slopes m1 and m2 are:

83

m1 =2r

1=2tf= 4¼Rf

m2 = ¡m1 = ¡4¼Rf

A relation of h as a function of time is now found to be:

h(t) =

8>>>><>>>>:4¼Rft for 0 < t <

r

2¼Rf

2r ¡ 4¼Rft forr

2¼Rf< t <

r

¼Rf

With r and R known a plot for a relation between injection area and time of various

engine cycle frequencies is obtained by plugging in the recently derived function of h

with equation C.1.

Figure C.6. Injection area as a function of time for varying cycle frequencies.

APPENDIX D

IGNITION SYSTEM CIRCUIT DIAGRAMS

84

85

Figure D.1. Ignition system circuit schematic.

86

Figure D.2. Mallory Ignition Control Circuit.

87

Figure D.3. Silicon controlled recti¯er control circuit.

APPENDIX E

PLUMBING SCHEMATIC

88

89

The following diagram is a schematic of the plumbing for gas delivery. Fuel and

oxygen sources were kept at a reasonable distance from the detonation chamber and

isolated with separate °ash arrestors. To further ensure safety, all pneumatic valves were

controlled with solenoid valves charged with high pressure air to prevent any electrical

spark from coming in contact with potential combustible gases. High pressure air was

delivered from a 175psi compressor.

90

Figure E.1. Plumbing schematic for gas delivery.

APPENDIX F

RUN LOG

91

92

Table F.1. Clean Con¯guration Test Run Data Log

Run C3H8 [psig] O2 [psig] f [Hz] Resolution [¹s] Sample Time [ms]

01D18JUN 40 139 11.1 1 256

02D18JUN 40 139 8.8 1 256

03D18JUN 40 139 7.1 1 256

04D18JUN 40 139 4 1 256

05D18JUN 40 139 5 1 256

06D18JUN 40 139 6 1 256

07D18JUN 40 139 6 1 256

08D18JUN 43 130 6 1 256

09D18JUN 43 130 6 1 256

10D18JUN 43 125 6 1 256

11D18JUN 43 125 6 1 256

12D18JUN 43 115 6 1 256

01D21JUN 43 125 7 1 256

02D21JUN 43 130 7 1 256

03D21JUN 43 130 7 1 256

04D21JUN 43 135 7 1 256

01D27JUN 43 146 7 1 256

02D27JUN 43 146 7 1 256

01D01JUL 43 146 7 1 256

02D01JUL 43 153 7 1 256

93

Table F.2. Shchelkin Spiral Con¯guration Test Run Data Log

Run C3H8 [psig] O2 [psig] f [Hz] Resolution [¹s] Sample Time [ms]

01D02JUL 40 146 7 1 256

02D02JUL 40 146 7 1 256

03D02JUL 40 146 7 1 256

04D02JUL 40 146 7 1 256

05D02JUL 40 146 7 1 256

06D02JUL 40 146 7 10 2560

07D02JUL 40 146 14.4 10 2560

08D02JUL 43 146 14.4 10 2560

09D02JUL 43 146 20 10 2560

REFERENCES

[1] Fickett, Wildon, Davis, William C., \Detonation Theory and Experiment," Dover

Publications, Inc., Mineola, New York, 1979.

[2] Zeldovich, I. B., Kompaneets, A. S., \Theory of Detonation," Academic Press, New

York, 1960.

[3] Johnson, Robert G., \Design, Characterization, and Performance of a Valveless

Pulse Detonation Engine," Master of Science in Astronautical Engineering Thesis,

Naval Post Graduate School, Monterey, California 2000.

[4] Bussing, T. and Pappas, G., \Pulse Detonation Engine Theory and Concepts,"

Developments in High-Speed-Vehicle Propulsion Systems, edited by Murthy, S.

and Curran, E., Vol. 165, Progress in Astronautics and Aeronautics, AIAA, Reston,

Virginia, 1997.

[5] Anderson, John D., \Modern Compressible Flow with Historical Perspective,"

McGraw-Hill Publishing Company, New York, 1990.

[6] Stuessy, W. S., Taylor, David W., and Wilson, D. R., \Ignition System Develop-

ment for Pulsed Detonation Engines ," NASA Grant NAGW-3714, Final Report-

Supplement No.3, February 14th, 1996 No. 11, 1966, pp. 2136{2149.

[7] Stanley, S., Stuessy, W., S. and Wilson, D. R., \Experimental Investigation of

Pulse Detonation Wave Phenomenon," AIAA Paper 95{2197, 1995.

94

95

[8] S.-Y. Lee, C. Conrad, et. al, \De°agration to Detonation Transition Study Us-

ing Simultaneous Schlieren and OH PLIF Images," AIAA Paper 2000-3217, 36th

AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA, Huntsville, Al-

abama, 2000.

[9] Figliola, R. S. and Beasley, D. E., "Theory and Design for Mechanical Measure-

ments," 2nd ed., John Wiley & Sons, Inc., New York, 1995.

[10] V.V.Golub, F.K. Lu, et. al., The in°uence of shear layer control on DDT, Inter-

national Colloquium on Advances in Con¯ned Detonations, Moscow, Russia, July

2-5, 2002.

[11] E. Schultz, J.E. Shepherd, Validation of detailed reaction mechanisms for deto-

nation simulation, Graduate Aeronautical Laboratories of the California Institute

of Technology, Technical Report FM99-5, 1999

[12] Holman, J. P., "Experimental Methods for Engineers," 7th ed., McGraw Hill, New

York, NY, 2001.

[13] Lo, P. P., \Design and Testing of a Detonation Combustion Chamber with Multi-

Port Side Wall Injection," Master of Science in Aerospace Engineering Thesis,

University of Texas at Arlington, Arlington, Texas, 1997.

BIOGRAPHICAL STATEMENT

Jason Meyers was born in Lakewood California on November 27th, 1976. The

west coast was home for his ¯rst 13 years. He then moved on with family to Dallas

Texas where he began his high school education. Upon graduating high school in May

1994, he enrolled into the College of Engineering at the University of Texas at Arlington

(UTA). In December of 1999 he obtained his BS degree in Aerospace Engineering and

then joined the research group of F.K. Lu and D.R. Wilson the following January at the

Aerodynamics Research Center (ARC) to pursue interests in high speed gas dynamics

and propulsion. This paper is a detailed account of his work done for the Master of

Science degree requirement presented in May, 2002. He is a 5 year member of the

American Institute of Aeronautics and Astronautics.

96

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PERFORMANCE ENHANCEMENTS ON A PULSED DETONATION … · PERFORMANCE ENHANCEMENTS ON A PULSED DETONATION ROCKET Publication No. Jason Matthew Meyers, M.S. The University of Texas at