December 2004

NASA/CR-2004-213508

Development of an Actuator for Flow Control

Utilizing Detonation

Patrick J. Lonneman and Andrew D. Cutler

The George Washington University

Joint Institute for Advancement of Flight Sciences

Langley Research Center, Hampton, Virginia
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December 2004

NASA/CR-2004-213508

Development of an Actuator for Flow Control

Utilizing Detonation

Patrick J. Lonneman and Andrew D. Cutler

The George Washington University

Joint Institute for Advancement of Flight Sciences

Langley Research Center, Hampton, Virginia
Available from:

NASA Center for AeroSpace Information (CASI) National Technical Information Service (NTIS)

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ABSTRACT 

The control of flow separation has been demonstrated using both passive and 

active methods in multiple computational and experimental studies. Active flow control 

devices including mass injection systems and zero-net-mass flux actuators (synthetic jets) 

have been employed to delay flow separation. These devices are capable of interacting 

with low-speed, subsonic flows, but situations exist where a stronger crossflow 

interaction is needed. Small actuators that utilize detonation of premixed fuel and 

oxidizer should be capable of producing supersonic exit jet velocities. An actuator 

producing exit velocities of this magnitude should provide a more significant interaction 

with transonic and supersonic crossflows. This concept would be applicable to airfoils on 

high-speed aircraft as well as inlet and diffuser flow control. 

The present work consists of the development of a detonation actuator capable of 

producing a detonation in a single shot (one cycle). Multiple actuator configurations, 

initial fill pressures, oxidizers, equivalence ratios, ignition energies, and the addition of a 

turbulence generating device were considered experimentally and computationally. 

It was found that increased initial fill pressures and the addition of a turbulence 

generator aided in the detonation process. The actuators successfully produced 

Chapman-Jouguet detonations and wave speeds on the order of 3000 m/s. 

iii
iv
TABLE OF CONTENTS 

Abstract 

List of Figures 

List of Tables 

List of Acronyms and Symbols 

Chapter 1 Introduction 

1.1 Detonation Actuator Overview 

1.2 Detonation Theory 

1.3 Acceleration of DDT 

1.4 Objectives of Research 

Chapter 2 Experimental Description 

2.1 Detonation Tube 

2.2 Detonation Actuators 

2.3 Injection System

2.4 Ignition System

2.5 Shchelkin Spiral 

2.6 Instrumentation and Data Acquisition 

2.7 Test Procedures 

2.8 Fuel-Oxidizer Mixing 

Chapter 3 Test Program

3.1 Initial Fill Pressure 

Page

iii 

viii 

xiv 

xv 

1 

2 

3 

6 

7 

9 

9 

10 

10 

11 

12 

13 

14 

15 

17 

17 

v
3.2 Equivalence Ratio 

3.3 Oxidizer Composition Fraction 

3.4 Geometric Configuration 

3.5 Ignition Energy 

3.6 Turbulence Generator 

Chapter 4 Experimental Data Analysis 

Chapter 5 Discussion of Experimental Results 

5.1 Constant Area Tube 

5.1.1 Variation of Initial Fill Pressure 

5.1.2 Variation of Equivalence Ratio 

5.1.3 Variation of Ignition Energy 

5.1.4 Variation of Oxidizer Composition Fraction 

5.1.5 Addition of a Turbulence Generator 

5.1.6 Summary of Detonation Tube Experiments 

5.2 Detonation Actuators 

5.2.1 Variation of Initial Fill Pressure 

5.2.2 Variation of Equivalence Ratio 

5.2.3 Addition of a Turbulence Generator 

5.2.4 Summary of Detonation Actuators 

5.3 Comparison of the Constant Area Tube and Actuators 

Chapter 6 Discussion of Numerical Results 

Chapter 7 Experimental Uncertainties 

Chapter 8 Conclusions and Recommendations 

17 

18 

18 

19 

19 

22 

24 

24 

24 

27 

29 

31 

32 

33 

35 

35 

40 

42 

46 

46 

49 

51 

53 

vi
References 

Figures 

Appendix A 

 

 

56 

59 

151 

vii
LIST OF FIGURES 

Figure 1 

Figure 2 

Figure 3 

Figure 4 

Figure 5 

Figure 6 

Figure 7 

Figure 8 

Figure 9 

Figure 10(a) 

Figure 10(b) 

Figure 11 

Figure 12 

Figure 13 

Figure 14 

Figure 15 

Figure 16 

Figure 17 

Figure 18 

Figure 19 

Simplified detonation actuator.............................................. 

The Hugoniot plot divided into five regions .............................. 

Characteristic detonation profile in a constant area tube [10]......... 

Detonation tube in initial and actuator configurations.................. 

Detonation tube with an actuator installed............................... 

Detonation actuators........................................................ 

Simplified schematics of detonation actuators.......................... 

Simplified schematic of the detonation tube facility setup............ 

Simplified schematic of the initial and high-energy ignition 

systems........................................................................ 

Shchelkin spirals used in the actuators.................................... 

Shchelkin spirals used in the constant area tube......................... 

Shchelkin spiral installed in a detonation actuator...................... 

Wave speeds for various mixing techniques.............................. 

Pressure histories in the tube for a 103 kPa (15 psia) fill pressure..... 

Pressure histories in the tube for a 207 kPa (30 psia) fill pressure..... 

Pressure histories in the tube for a 345 kPa (50 psia) fill pressure..... 

Pressure histories in the tube for a 483 kPa (70 psia) fill pressure..... 

Wave speeds in the tube for various fill pressures....................... 

Distance required for DDT versus fill pressure ........................... 

Time required for DDT versus fill pressure .............................. 

Page

59 

60 

61 

62 

63 

64 

65 

67 

68 

69 

70 

71 

72 

73 

74 

75 

76 

77 

78 

79 

viii
Figure 20 

Figure 21 

Figure 22 

Figure 23 

Figure 24 

Figure 25 

Figure 26 

Figure 27 

Figure 28 

Figure 29 

Figure 30 

Figure 31 

Figure 32 

Figure 33 

Figure 34 

Figure 35 

Figure 36 

Figure 37 

Figure 38 

Figure 39 

Figure 40 

Figure 41 

Pressure histories in the tube with an equivalence ratio of 0.3......... 

Pressure histories in the tube with an equivalence ratio of 0.5........ 

Pressure histories in the tube with an equivalence ratio of 0.7........ 

Pressure histories in the tube with an equivalence ratio of 0.9........ 

Pressure histories in the tube with an equivalence ratio of 1.1........ 

Pressure histories in the tube with an equivalence ratio of 1.3........ 

Wave speeds in the tube for various equivalence ratios ............... 

Time required for DDT versus equivalence ratio....................... 

Pressure histories in the tube with an ignition energy of 0.025J...... 

Pressure histories in the tube with an ignition energy of 0.25J........ 

Pressure histories in the tube with an ignition energy of 2.5J......... 

Pressure histories in the tube with an ignition energy of 5.0J......... 

Pressure histories in the tube with an ignition energy of 10.0J........ 

Pressure histories in the tube with an ignition energy of 15.0J........ 

Wave speeds in the tube for various ignition energies.................. 

Pressure histories in the tube with a composition fraction of 0.25.... 

Pressure histories in the tube with a composition fraction of 0.50.... 

Pressure histories in the tube with a composition fraction of 0.75.... 

Wave speeds in the tube for various composition fractions ........... 

Time required for DDT versus the composition fraction............... 

Distance required for DDT versus composition fraction............... 

Pressure histories in the tube at a 103 kPa (15 psia) fill pressure 

using a spiral.................................................................. 

80 

81 

82 

83 

84 

85 

86 

87 

88 

89 

90 

91 

92 

93 

94 

95 

96 

97 

98 

99 

100 

101 

ix
Figure 42 

Figure 43 

Figure 44 

Figure 45 

Figure 46 

Figure 47 

Figure 48 

Figure 49 

Figure 50 

Figure 51 

Figure 52 

Figure 53 

Figure 54 

Figure 55 

Figure 56 

Figure 57 

Figure 58 

Figure 59 

Figure 60 

Figure 61 

Figure 62 

Pressure histories in the tube at a 207 kPa (30 psia) fill pressure 

using a spiral.................................................................. 

Pressure histories in the tube at a 345 kPa (50 psia) fill pressure 

using a spiral.................................................................. 

Comparison of wave speeds in the tube with and without a spiral.... 

Pressure histories in actuator A with a 103 kPa (15 psia) fill pressure 

Pressure histories in actuator A with a 207 kPa (30 psia) fill pressure 

Pressure histories in actuator A with a 345 kPa (50 psia) fill pressure 

Pressure histories in actuator A with a 483 kPa (70 psia) fill pressure 

Wave speeds for each fill pressure case using actuator A.............. 

Pressure histories in actuator B with a 103 kPa (15 psia) fill pressure 

Pressure histories in actuator B with a 207 kPa (30 psia) fill pressure 

Pressure histories in actuator B with a 345 kPa (50 psia) fill pressure 

Pressure histories in actuator B with a 483 kPa (70 psia) fill pressure 

Wave speeds for each fill pressure case using actuator B.............. 

Pressure histories in actuator C with a 103 kPa (15 psia) fill pressure 

Pressure histories in actuator C with a 207 kPa (30 psia) fill pressure 

Pressure histories in actuator C with a 345 kPa (50 psia) fill pressure 

Pressure histories in actuator C with a 483 kPa (70 psia) fill pressure 

Wave speeds for each fill pressure case using actuator C................ 

Exit wave speeds for each actuator at various fill pressures............. 

Pressure histories in actuator A with an equivalence ratio=0.7......... 

Pressure histories in actuator A with an equivalence ratio=0.9......... 

102 

103 

104 

105 

106 

107 

108 

109 

110 

111 

112 

113 

114 

115 

116 

117 

118 

119 

120 

121 

122 

x
Figure 63 

Figure 64 

Figure 65 

Figure 66 

Figure 67 

Figure 68 

Figure 69 

Figure 70 

Figure 71 

Figure 72 

Figure 73 

Figure 74 

Figure 75 

Figure 76 

Figure 77 

Figure 78 

Figure 79 

Pressure histories in actuator A with an equivalence ratio=1.1........ 

Pressure histories in actuator A with an equivalence ratio=1.3........ 

Wave speeds for each equivalence ratio case using actuator A........ 

Pressure histories in actuator B with an equivalence ratio=0.7........ 

Pressure histories in actuator B with an equivalence ratio=1.3........ 

Wave speeds for each equivalence ratio case using actuator B........ 

Pressure histories in actuator C with an equivalence ratio=0.7........ 

Pressure histories in actuator C with an equivalence ratio=1.3........ 

Wave speeds for each equivalence ratio case using actuator C........ 

Pressure histories in actuator A with spiral added at 103 kPa (15 

psia)................................................................................................... 

Pressure histories in actuator A with spiral added at 207 kPa (30 

psia).................................................................................................... 

Pressure histories in actuator A with spiral added at 345 kPa (50 

psia)................................................................................................... 

Pressure histories in actuator A with spiral added at 483 kPa (70 

psia).................................................................................................... 

Wave speeds using actuator A with spiral added......................... 

Pressure histories in actuator B with spiral added at 103 kPa (15 

psia)................................................................................................... 

Pressure histories in actuator B with spiral added at 207 kPa (30 

psia)................................................................................................... 

Pressure histories in actuator B with spiral added at 345 kPa (50 

123 

124 

125 

126 

127 

128 

129 

130 

131 

132 

133 

134 

135 

136 

137 

138 

xi
Figure 80 

Figure 81 

Figure 82 

Figure 83 

Figure 84 

Figure 85 

Figure 86 

Figure 87 

Figure 88 

Figure 89 

Figure 90 

Figure A1 

Figure A2 

psia)................................................................................................... 

Pressure histories in actuator B with spiral added at 483 kPa (70 

psia)................................................................................................... 

Wave speeds using actuator B with spiral added........................ 

Pressure histories in actuator C with spiral added at 103 kPa (15 

psia)............................................................................ 

Pressure histories in actuator C with spiral added at 207 kPa (30 

psia)............................................................................ 

Pressure histories in actuator C with spiral added at 345 kPa (50 

psia)............................................................................ 

Pressure histories in actuator C with spiral added at 483 kPa (70 

psia)............................................................................ 

Wave speeds using actuator C with spiral added........................ 

Pressure histories in actuator B with a 4.8 mm (.1875 in) spiral 

installed at 103 kPa (15 psia).............................................. 

Pressure histories in actuator B with a 4.8 mm (.1875 in) spiral 

installed at 207 kPa (30 psia).............................................. 

Pressure histories in actuator B with a 4.8 mm (.1875 in) spiral 

installed at 345 kPa (50 psia).............................................. 

Wave speeds in actuator B with 4.8 mm (.1875 in) spiral 

installed........................................................................ 

Detailed engineering drawing of the detonation tube.................. 

Detailed engineering drawing of the modifications to the ignition end 

139 

140 

141 

142 

143 

144 

145 

146 

147 

148 

149 

150 

152 

xii
Figure A3 

Figure A4 

Figure A5 

blind flange................................................................... 

Detailed engineering drawing of the detonation facility injection 

system.......................................................................... 

Detail drawing of the electrodes and installation assembly............. 

Detailed drawing of the three–electrode ignition system............... 

153 

154 

155 

156 

xiii
LIST OF TABLES 

Table 1.1 

Table 3.1 

Table 5.1 

Table 5.2 

Table 5.3 

Table 5.4 

Qualitative differences between detonations and deflagrations in 

gases [9]...................................................................... 

Summary of completed experimental tests.............................. 

Speeds of sound and CJ detonation velocities for various initial fill 

pressures...................................................................... 

Speeds of sound and CJ detonation velocities for various 

equivalence ratios........................................................... 

Summary of ignition energy tests........................................ 

Speeds of sound and CJ detonation velocities for various fractions. 

Page

4 

20 

25 

28 

30 

31 

xiv
LIST OF ACRONYMS AND SYMBOLS 

AIAA 

CJ 

DDT 

psia 

psig 

c 

γ 

φ 

J 

u 

P 

q 

ρ 

T 

VD 

H2 

O2 

N2 

H2O

American Institute of Aeronautics and Astronautics 

Chapman-Jouguet 

Deflagration to Detonation Transition 

Pounds per square inch absolute 

Pounds per square inch gage 

Speed of sound. 

Gamma, Ratio of specific heats 

Phi, Equivalence Ratio 

Joules 

Velocity 

Pressure 

Heat added per unit mass 

Rho, Density 

Temperature 

Detonation Velocity 

Gaseous hydrogen 

Gaseous oxygen 

Gaseous nitrogen 

Water vapor

xv
xvi
CHAPTER 1 

INTRODUCTION 

Large performance gains can be achieved through the control of the flow 

associated with aircraft, automobiles, sea vehicles, turbomachines, and other flow 

systems. In most cases, these gains are achieved through the postponement of boundary 

layer separation which leads to reduced drag, delayed stall, enhanced lift, and improved 

pressure recovery. Future applications in thrust vectoring may even require the 

intentional separation of a boundary layer [1]. Separation control has been demonstrated 

through both passive and active methods. Passive methods such as micro-vortex 

generators give improvements in efficiency without the need for complex mechanical 

systems. However, in low angle of attack configurations, performance drops 

significantly. Active flow control devices include mechanical deflection actuators, mass 

injection systems, and zero-net-mass flux actuators (synthetic jets). Synthetic jets have 

shown promise in manipulating flow over airfoils and other bluff bodies [2]. These 

micro actuators use an oscillating diaphragm to add momentum to a flow without net 

mass transfer. Studies have shown exit jet velocities up to 50 m/s. Mass injection 

systems include steady blowing jets, pulsed jets [3], and combustion driven jet actuators 

[4]. The combustion driven jet actuators utilize low-speed or deflagration combustion to 

produce a pulsed exit jet. However, they have been shown to penetrate a crossflow only 

up to Mach 0.7. These types of actuators and the others listed above all suffer the same

limitations, namely the ability to manipulate a crossflow in the transonic and supersonic 

flow regime. The SparkJet, a solid state device which rapidly heats gas within a chamber 
by means of an electrical discharge to obtain a high velocity jet, has been proven capable 

of penetrating supersonic flows [5]. This paper will describe research on another device, 

which utilizes detonation combustion, and holds the promise of controlling high-speed 

flows. 

1.1 Detonation Actuator Overview

The detonation actuators are small convergent nozzles that utilize localized 

detonation combustion to produce a pulsed supersonic exit jet. A premixed fuel-oxidant 

(hydrogen-oxygen) mixture is injected into the combustion chamber before being ignited 

by a spark. Once ignited, a deflagration will propagate downstream, ideally transitioning 

to a strong detonation before exiting the nozzle. A simplified schematic of the detonation 

actuator is shown in Figure 1. 

Detonations are highly energetic combustion waves coupled with shock waves 

capable of flame speeds up to 3000 m/s in premixed hydrogen-oxygen mixtures. An 

actuator with exit velocities of this magnitude should be capable of extending the 

effectiveness of actuator jet interaction for separation control well into the supersonic 

flow regime [6]. This paper will present the results from experimental parametric studies 

completed to determine the capability of this device. Numerical calculations were also 

completed to help understand and validate the flow processes seen in the laboratory 

experiments. All results are for a single cycle (inject fuel, ignite mixture, purge 

products). Work is concurrently in progress to develop resonant detonation actuators that 

these results may guide [6]. 

Numerous applications besides active flow control have been envisioned for the 

actuators. Pulse Detonation Engines (PDEs) rely on detonation combustion for the 

2
pressures needed for thrust generation. A small actuator like the one researched for this 

thesis could be used to start the detonation process in a shorter distance or initiate a 

detonation in a less reactive fuel. High-speed military rockets could use them as thrusters 

for lateral control. A detonation actuator would improve the effectiveness by providing a 

more substantial crossflow interaction. 

1.2 Detonation Theory 

There are two types of combustion phenomena: deflagration and detonation. 

Deflagration combustion is characterized by subsonic flame speeds and negligible 

pressure rises. For this reason, deflagrations can be modeled as an isobaric (constant 

pressure) process. Detonations on the other hand are characterized by supersonic flame 

speeds and very high-pressure differentials [8]. A constant volume process is often used 

to model detonations because of the high flame speed. The differences in velocity, 

pressure, temperature, and density of deflagrations and detonations are shown in Table 

1.1. The subscripts u and b used in Table 1.1 stand for unburned and burned gases, 

respectively. 

It is helpful to look at a development of the different types of combustion through 

the use of the Hugoniot Curve. Starting with the integrated conservation equations and 

the state equations, the Hugoniot curve (Equation 1.1) is obtained after some

manipulation [9]. 

P P q

P P − − − + = − ) 1 1 ( )( 2

1 ( ) 1 1 2

2 1

1

1

2

2

γ ρ ρ ρ ρ

γ (1.1) 

The Hugoniot is essentially a plot of all the possible values of 2 (1/ ρ , P2) for a given 

value of ( 1 1/ ρ , P1) at the given heat added per unit mass, q. The regions of possible 

3
solutions are constructed by drawing tangents to the curve that go through [(1/ρ1), P1]. 

Since the form of the Hugoniot equation obtained is a hyperbola, there are two tangents 

to the curve through A as shown in Figure 2. The tangents and the horizontal and vertical 

lines through the initial condition A divide the Hugoniot into five regions, as specified by 

Roman numerals. 

Usual magnitude of ratio

Ratio Detonation Deflagration

uu/cu

a 5-10 0.0001-0.03

ub/uu 0.4-0.7 4-16

Pb/Pu 13-55 0.978-0.9776

Tb/Tu 8-21 4-16

ρb/ρu 1.4-2.6 0.06-0.25 a cu is the acoustic velocity in the 

unburned gases. uu/cu is the Mach number of 

the wave. 

Table 1.1. Qualitative differences between detonations and deflagrations in gases [9]. 

In regions I and II solutions give compression waves, high velocities, and are 

regions of detonations. Solutions in regions III and IV give expansion waves, which are 

low velocity subsonic waves already classified as deflagrations. Solutions in regions II, 

IV, and V are said to not exist since the solutions are physically unrealizable. The only 

experimentally possible results along the Hugoniot curve are the point J and region III. It 

can be shown that the velocity of sound in the burned gases is greater than the velocity of 

the detonation wave relative to the burned gases. Consequently, if a rarefaction wave due 

to any reason whatsoever starts behind the wave, it will catch up with the detonation 

front. The rarefaction will then reduce the pressure and cause the final value of P2 and 

1/ρ2 to drop and move down the curve toward J. Thus points above J are not stable and 

are referred to as overdriven detonations. Heat losses, turbulence, friction, etc., can start 

the rarefaction. At point J, the velocity of the detonation wave is equal to the velocity of 

4
sound in the burned gases plus the mass velocity of the gases, so that the rarefaction will 

not overtake it. The point and conditions at J are referred to as the Chapman-Jouguet 

results. Therefore, solutions in region I are possible, however they are transient and the 

solution will converge on the point J. For a more thorough development see Glassman 

[9]. 

Glassman offers an explanation to how a deflagration can be transitioned into a 

detonation, known as deflagration to detonation transition (DDT) [9]. If a mixture is 

ignited at the closed end of a long horizontal tube, a combustion wave is formed. The 

burned gas products of this wave have a specific volume of the order of 5-15 times the 

unburned mixture and act as a piston. This piston generates compression waves that 

impart a velocity down the tube to the unburned gases ahead of the flame. Each 

compression wave tends to heat the unburned gas mixture somewhat, causing the sound 

velocity to increase and the succeeding waves to catch up with the initial one. The 

preheating tends to increase the flame speed, which then accelerates the unburned gas 

mixture further to a point where turbulence is developed in the unburned gas. Then, a 

greater flame velocity is obtained, accelerating the unburned gases, and creating 

compression waves. Therefore, a shock strong enough to ignite the gas mixture is 

formed. The reaction zone behind this shock sends forward a continuous compression 

wave that keeps the shock front from decaying and a stable detonation is obtained. 

The characteristic pressure distribution of a detonation wave propagating 

downstream that has been initiated at the closed end of a tube is shown in Figure 3 [10]. 

The detonation wave can be modeled as a 1-D strong shock, which triggers combustion, 

and a thin flame front in which heat addition occurs just behind the shock. The shock 

5
front moves at the detonation velocity, VD, relative to the gas and increases the pressure 

and temperature of the gas from its previous values of P1 and T1. 

Just behind the shock front is an area of high pressure known as the von Neumann 

pressure spike. This area consists of the ignition delay and its thickness is governed by 

chemical kinetics. The duration of the spike is on the order of one microsecond. Once 

the chemical kinetics are initiated, heat addition occurs, and consequently the pressure is 

lowered and the temperature increases. The thickness of this region is determined by the 

time required for the combustion processes to complete. Finally, in a tube where the 

detonation is initiated at the closed end, an expansion region is developed to ensure that 

zero velocity is realized at State 3. 

1.3 Acceleration of DDT 

The transition of a deflagration to a detonation requires a certain distance 

downstream of the ignition point. The detonation actuators are less than 0.125 m (5 in) 

long and accelerating the DDT process is of the utmost importance. DDT acceleration 

methods such as varying the initial fill pressure and equivalence ratio will be discussed in 

this paper along with results from the addition of a turbulence generating device. These 

devices include orifice plates, centerbodies, concentric rings, and Shchelkin spirals in 

addition to the use of additives. The use of these devices has been shown to help promote 

the transition to a detonation [11,12,13,14]. Of these methods, the one most commonly 

used is the Shchelkin spiral [15], which is a wire coil of certain diameter and pitch. 

The success of the Shchelkin spiral over other methods may be due to an 

important feature of the transition process as visualized by Urtiew and Oppenheim [16]. 

They observed a phenomenon known as an ‘explosion-in-the-explosion’ in smooth tubes 

6
that produces a bow-shaped shock which reflects off the side walls and intensifies the 

flame-shock interaction. Unlike axisymmetric obstacles, the Shchelkin spiral can support 

additional helical modes that can propagate upstream as they grow and interact with the 

side walls. This increases the probability of coupling between the shock structure and 

turbulent flame propagation, thereby increasing the likelihood of DDT [14]. For this 

reason, the Shchelkin spirals were utilized in this experimental study. A detailed 

discussion of the dimensions and installation of the spiral will be presented in the next 

chapter. 

1.4 Objectives of Research 

As stated above, the need exists for an actuator with a strong exit jet capable of 

interacting with transonic and supersonic crossflows. Research was undertaken to extend 

the effectiveness of flow control actuators to meet this need. This thesis describes the 

work completed on a single shot actuator installed in a detonation tube. The 

experimental study was broken into two parts. The first consists of understanding the 

detonation process and how to obtain a CJ detonation experimentally in a constant area 

tube. Second, actuator concepts were tested experimentally applying the lessons learned 

from the constant area tube studies. In addition, the actuators were studied 

computationally to help validate and understand the experimental results. 

In both cases a number of parameters were studied to determine their significance 

to the detonation phenomena. Since the detonation tube was airtight, various initial fill 

pressures above atmospheric were studied. In addition, the effect of fuel-oxidizer ratios 

was studied to determine if certain values accelerate the detonation process. Other 

factors evaluated included varying the oxidizer from pure oxygen to air and varying the 

7
ignition energy released by the spark. Finally, the effect of adding turbulence was tested 

by installing a spiral of wire inside the actuators. It was the purpose of this thesis to 

understand the detonation process and apply that knowledge to the development of a 

better flow control actuator. 

8
CHAPTER 2 

EXPERIMENTAL DESCRIPTION 

The experiment consisted of four main components: the detonation tube, injection 

system, ignition system, and the instrumentation. The majority of the components were 

located in the test cell of NASA Langley’s Direct Connect Supersonic Combustion Test 

Facility, a 4.8 by 4.8 by 15.8 m (16 by 16 by 52 ft) test cell with 0.61m (2 ft) steelreinforced concrete walls. The room was equipped with a forced air ventilation system

that yielded a ventilation rate of 225 room exchanges of air per hour. These features 

guarded against any potential problems associated with a hydrogen gas leak. The control 

software and data acquisition equipment was located outside the test cell allowing the 

operator to start the tests from a remote location. 

2.1 Detonation Tube 

The detonation tube and its components were designed to allow tests with fill 

pressures up to 689 kPa (100 psia). As shown in Figure 4, the 316 stainless steel schedule 

XXS pipe was 1.22 m (48 in) long with a 11.1 kN (2500 lb) 316 stainless steel flange 

welded to the ignition end and a 6.67 kN (1500 lb) flange welded to the opposite end. It 

had a 0.051 m (2.0 in) outer diameter and a 0.038 m (1.5 in) inner diameter. The blind 

flanges enclosing it on either end, together with a gasket, formed an airtight seal. The 

flange on the ignition end had three holes for tungsten electrodes. Seven ports are tapped 

at 0.152 m (6 in) intervals along the tube for the PCB pressure transducers (see Section 

2.6). Fuel and oxidizer were injected into the tube through a valve rated at 69000 kPa 

(10000 psia). The tube was vented directly into the test cell through another valve rated at 

the same pressure located at the opposite end. A picture of the tube with an actuator 

9
installed is shown in Figure 5. A detailed engineering drawing of the tube is given in 

Figure A1 in Appendix A. A detailed drawing of the modifications to the blind flange on 

the ignition end for the electrode installation is given in Figure A2. 

2.2 Detonation Actuators 

Three actuators were fabricated for the study that differ in the size and type of the 

throat. The actuators were convergent-divergent nozzles with one version having a 

constant area throat extension. A picture of the actuators is shown in Figure 6. The first 

nozzle, actuator A, diagrammed in Figure 7(a), had an inlet to throat area ratio of 25. 

Figure 7(b) shows the second nozzle, actuator B, which had a throat radius of 0.25 cm

(0.098 in) and an inlet to throat area ratio of 100. Finally, in Figure 7(c), the third nozzle, 

actuator C, had the same throat radius, however, it had a constant area throat extension of 

1 cm (0.394 in). It was designed with this feature to help sustain and possibly strengthen 

a detonation formed in the convergent section of the nozzle. From this point on the 

actuators will be referenced based on their letter, as designated by Figure 7. 

The actuators were installed between the end flange and the tube on the ignition 

end. The setup is shown in Figure 4. In this setup, the detonation tube was used as a 

dump tank for the actuators. 

2.3 Injection System

The system was designed to supply a combination of gaseous hydrogen, oxygen, 

and air to the detonation tube. A schematic of the injection system is supplied in 

Appendix A in Figure A3. A simplified schematic of the injection system is shown in 

Figure 8. A series of piping and valves connected the fuel and oxidizer bottles to the 

detonation tube components. The hydrogen, oxygen, and nitrogen gas is located in k10
bottles outside of the test cell. The air was supplied from 689 kPa (100 psig) service air. 

Flow of these gases was regulated with needle valves and a Mensor digital pressure 

gauge for accurate injection into the tube. The Mensor gauge was accurate to 68.9 Pa 

(0.01 psia) and could measure pressures from 0-1030 kPa (0-150 psia). Because of this 

pressure limitation, a series of valves isolated it from the tube during tests. The tube was 

evacuated before fuel and oxidizer injection by use of a Cenco Hyvac vacuum pump. The 

pump was capable of evacuating the tube down to approximately 6.89 Pa (0.001 psia), 

which allowed for very near stoichiometric mixtures in the tube for tests. During the fill 

process and after a test nitrogen was used to purge the supply lines and the tube of any 

reactive gases. 

2.4 Ignition System 

The ignition system consisted of a high-voltage power supply, flash lamp power 

supply, 5 μF capacitor and two or three tungsten electrodes, depending on the energy 

required. A detailed drawing of the electrodes is included in Figure A4 in Appendix A. 

Initially, only two electrodes were used to form a spark gap. They were connected to the 

Spectralite 919 flash lamp power supply, which housed a bank of capacitors and was 

capable of discharging up to 2.5J into the gap. A simplified schematic showing this 

system is shown in Figure 9(a). It was later determined that more energy was needed to 

obtain CJ detonations within the actuators. A third electrode, 5 μF capacitor, high-voltage 

power supply, and required circuitry were added to boost the maximum energy to 15J. 

The gas between the electrodes was ionized by a high-voltage pulse from the flash lamp

power supply and upon creation of the plasma in the gap, the capacitor connected to the 

third electrode discharged in the same gap creating a spark of the stated energy. A 

11
simplified schematic of the circuit is shown in Figure 9(b). A detailed schematic of this 

ignition system is given in Figure A5 in Appendix A. 

Due to the large currents and voltages imposed by the ignition system, shielding 

was required to keep the noise created by electrical interference at a minimum. The 

cables running from the electrodes to the capacitors were kept as short as possible and 

were shielded with an aluminum mesh. Gaps between the cables and the electrodes were 

filled with putty and wrapped in aluminum foil so that the entire component was 

shielded. A filtering technique was used to remove the remainder of the noise and will be 

discussed in Chapter 4. 

2.5 Shchelkin Spiral 

As discussed in Chapter 1, a turbulence generator known as a Shchelkin spiral 

was installed in the actuators and tube for evaluation. Two spirals made from copper 

wire that had approximately five turns and were 0.076 m (3 in) long were tested in the 

actuators and are shown in Figure 10(a). The two spirals differed in the diameter of the 

copper wire: one was 1.6 mm (0.0625 in) and the other was 4.8 mm (0.1875 in) The 

smaller diameter spiral reduced the entrance area of the actuator by ~12% and the larger 

spiral by ~35%. This constriction was greater as the spiral approached the throat. The 

spiral with the diameter of 1.6 mm (0.0625 in) was used in the majority of the testing and 

the 4.8 mm (0.1875 in) version was evaluated as a comparison. Since these spirals were 

conical, a constant area version was made for testing in the straight tube, shown in Figure 

10(b). It was made from the 1.6 mm (0.0625 in) diameter copper wire and was 0.076 m

(3 in) long with approximately 5 turns. 

12
The dimensions of the spirals were based loosely on the references given in 

Chapter 1. Schauer, et al [13] placed a 0.305 m (12 in) spiral made from wire with a 4.8 

mm (.1875 in) diameter in a tube with an inner diameter of 0.051 m (2 in). Meyer, et al 

[14] also used two 4.8 mm (0.1875 in) wire diameter spirals which were 0.457 m (18 in) 

and 1.37 m (54 in) long. The spirals used in the current study were only 0.076 m (3 in) 

long so that the throat of the actuators was not blocked. The spiral used in the tube was 

made the same length for comparison purposes. 

The spirals were installed immediately downstream of the ignition end wall and 

were secured with aluminum tape. The tape was used so that the spirals were flush with 

the side walls and so that they could be removed with ease during the various tests of the 

tube and actuators. A picture of the smaller spiral installed in an actuator is shown in 

Figure 11. 

2.6 Instrumentation and Data Acquisition 

The instrumentation consisted primarily of six piezoresistive pressure transducers, 

manufactured by PCB Piezotronics, Inc. Four of the PCB transducers were model 

113A22 with a full-scale range of 0-34500 kPa (0-5000 psi), rise time of 1.0 μsec, and a 

resonant frequency of 500 kHz. The other two PCB transducers were model 113A21 and 

had a full-scale range of 0-6900 kPa (0-1000 psi), rise time of 1.0 μsec, and a resonant 

frequency of 500kHz. These two probes were placed in strategic locations to help see the 

DDT process while the four model 113A22 transducers were used to capture the higher 

pressures of the detonation waves. The PCB transducers could withstand a maximum

flash temperature of 1922 °K (3000 °F ). Since detonation waves typically have 

temperatures greater than this value, the faceplates of the PCB transducers were coated 

13
with approximately 0.36 mm (0.014 in) of high temperature silicon RTV compound, as 

recommended by PCB. 

The PCB pressure transducers were connected to a PCB Amplifier model 

4B3803. LeCroy model 9314 and 9314A oscilloscopes acquired the data from the 

transducers. Model 9314 had a 300 MHz bandwidth and four channels each with 10 Kpts 

of acquisition memory. Model 9314A had a 400 MHz bandwidth and four channels each 

with 50 Kpts of acquisition memory. Both models were capable of 100 MHz 

simultaneous sampling rate on all channels. A LabVIEW program was written to setup 

and calibrate the oscilloscopes and PCB transducers and ignite the mixture. Since the 

PCB transducers were dynamic probes, and not capable of measuring mean pressures, the 

Mensor model 2101 digital pressure probe was used to monitor the filling and evacuation 

of the tube. 

2.7 Test Procedures 

The first step in running the experiments was to determine the configuration that 

was to be tested. This was recorded in the log book and the tube was setup accordingly. 

The next step was to shutdown the AC power inside the test cell and turn on the 

explosion proof lights and ventilation fan. Once this was complete the fuel and oxidizer 

bottles, located outside of the test cell, were opened. The service air was then turned on 

by opening the valve located in the test cell and all the test equipment located in the test 

cell was then turned on. Next, the tube was purged using inert nitrogen gas to ensure no 

reactive chemicals remained. Once this was complete, the tube was evacuated using the 

vacuum pump. When the pressure in the tube was at or below 68.8 Pa (0.01 psia), the 

vacuum pump was turned off and the oxidizer was injected into the tube. To prevent a 

14
premature ignition caused by the transient start-up voltages and currents of the ignition 

system components, they were turned on and set to the correct voltages before the 

injection of the fuel. Once they were powered up the fuel was injected and allowed to 

mix with the oxidizer. When the tube was filled to the desired pressure it was sealed off

and the injection system piping was then purged using nitrogen. This was done to prevent 

damage to equipment from an explosion traveling back through the injection system. All 

test personnel were then evacuated and the test cell was sealed off. 

While waiting for the fuel and oxidizer to properly mix, the oscilloscopes and 

computer were powered up. Next, the LabVIEW program was setup with the proper 

values for the LeCroy scopes and PCB transducers. When the mixing time, discussed in 

Section 2.8, was complete, the 5 μF capacitor was charged and the contents in the 

detonation tube were then immediately ignited. Once the combustion was complete and 

the data was saved, the ignition system was turned off and the tube was purged of any 

product and unreacted fuel mixture. Additional tests were completed by evacuating the 

detonation tube. If the last run of the day had been completed the fuel and oxidizer bottles 

were closed and all the test equipment was powered off. 

2.8 Fuel-Oxidizer Mixing 

The fuel and oxidizer were not premixed before they were injected into the 

detonation tube. To understand and compare various tests it was important to have 

consistent, repeatable results. Therefore, time was devoted to understanding the mixing 

process and its effect on deflagration to detonation transition. Two methods were 

evaluated on their ability to produce repeatable results. These tests were completed using 

actuator C. The number of transducers and their spacing in this actuator will be discussed 

15
in Chapter 5. One method used to mix the fuel and oxidizer was to inject them in layers. 

For example, the fills would be layered by putting fuel, oxidant, fuel, oxidant, etc. into 

the tube. A mixture of 103 kPa (15 psia) H2/O2 with four layers would be obtained by 

injecting 17.2 kPa (2.5 psia) of O2, 34.5 kPa (5 psia) of H2, 17.2 kPa (2.5 psia) of O2, and 

34.5 kPa (5 psia) of H2. Tests using 2, 4, and 5 layers were studied to understand the 

methods effect on mixing. Approximately thirty seconds passed while the injection 

piping was purged and the test cell was secured before the mixture was ignited. The 

wave speeds for each run are shown in Figure 12. The method for calculating the wave 

speed will be discussed in Chapter 4. The wave speeds compare nicely at the first three 

locations, however, at the fourth location large variations exist. The next method simply 

allowed the fuel and oxidizer to mix over increasing longer periods. For these cases, the 

oxidizer was injected before the fuel with no layering. As the mixing wait time 

increased, the fuel and oxidizer should approach a premixed mixture. Three mix times 

were tested: 5, 10, and 20 minutes. The wave speeds for these runs are also shown in 

Figure 12. As the data in the figure shows, all three cases compare very well at each of 

the transducer locations. Since the 5 minute data agrees well with the 10 and 20 minute 

cases, it was decided that all subsequent tests would be completed with this mix time. It 

should be noted that the data points shown in Figure 12 are the average wave speeds from

multiple tests at each test condition. 

16
CHAPTER 3 

TEST PROGRAM 

The research undertaken consisted of experimental parametric studies. The 

parameters that were investigated can be put into three different categories. The first 

consists of parameters associated with the fuel and oxidizer mixtures. Variables studied 

included initial fill pressure, equivalence ratio, and different oxidizers. The second 

category contains the geometric parameters such as tube or actuator and the subsequent 

variations on the actuator dimensions. Thirdly, methods to initiate a detonation were 

evaluated. The ignition energy was varied and a spiral of wire was added to develop 

turbulence and enhance mixing. A summary of all the tests discussed in this thesis is 

shown in Table 3.1. 

3.1 Initial Fill Pressure 

As mentioned before, the detonation tube was designed to handle conditions from

a vacuum to the pressure associated with detonations without leaking significant reactants 

or products to the test cell. The leak rates are discussed in Chapter 7. Therefore, tests 

were completed with fill pressures ranging from 103 kPa (15 psia) to 483 kPa (70 psia). 

From these results, the effect of higher fill pressures could be determined. This effect was 

studied in the constant area tube and all the actuator configurations. 

3.2 Equivalence Ratio 

Mixtures of varying equivalence ratio were studied to determine the effect of 

added fuel or oxidizer to the initiation of a detonation. Fuel-lean mixtures down to an 

equivalence ratio of 0.3 were investigated in addition to fuel-rich mixtures up to a ratio of 

1.3. It was important to understand the effect of equivalence ratio because of its impact 

17
on fuel consumption. If the actuators could perform well at a lean mixture, less fuel 

would be needed on board the vehicle. 

3.3 Oxidizer Composition Fraction 

The composition of the oxidant was varied to discover how changing the oxidizer 

from pure oxygen to air affected the performance. The composition fraction was defined 

as follows 

a b

a Composition Fraction

+ = (3.1) 

where a and b are coefficients in the following chemical reaction 

2 2 2 2 2 2 H + aO + b(0.21O + 0.79N ) = H O + 0.79bN (3.2) 

The coefficients can be solved once the value of the composition fraction is chosen since 

there are two equations and two unknowns. A composition fraction of one corresponded 

to all oxygen, while a fraction of zero meant the oxidizer was air. Between these limits, 

fractions of 0.25, 0.50 and 0.75 were studied. A vehicle that used an actuator using only 

air as an oxidizer would require no onboard oxygen storage. 

3.4 Geometric Configuration 

To get an understanding of how detonations are initiated and the properties of 

their propagation, tests were completed using the constant area detonation tube. Once 

this understanding was obtained the various actuator concepts were evaluated. The 

actuators were developed as convergent-divergent nozzles in an attempt to create high 

pressures through compression to help the DDT process. Numerical calculations done 

prior to this study showed that the actuators were capable of accelerating the DDT 

process. The three configurations vary in the value of their throat diameter. As shown 

before, two had a throat diameter of 0.25 cm (0.098 in) and one had a diameter of 0.50 

18
cm (0.197 in). In addition, one of the smaller diameter nozzles had a constant area throat 

extension of 1 cm (0.394 in) before the small diffuser. 

3.5 Ignition Energy 

CJ detonations can be initiated directly or through a deflagration to detonation 

transition. To obtain direct initiation large amounts of energy must be deposited into the 

combustible mixture to immediately create the shock-coupled combustion wave. Using 

the Spectralite 919 power supply and a 5 μF capacitor at 3kV, energies from 0.025 Joules 

up to 15 Joules were tested in an attempt to directly initiate a CJ detonation. The 

advantage of direct initiation is that smaller actuators can be designed, however, at the 

disadvantage of higher electrical power consumption and higher weight. 

3.6 Turbulence Generator 

Finally, in an attempt to develop a detonation in the convergent section of the 

actuators, coils of wire were added to create turbulence in the flow. The motivation 

behind the spirals and a physical description is given in Chapters 1 and 2, respectively. 

As previously discussed, two different spirals were tested. The spirals were tested at 

various initial fill pressures in both the tube and the actuators to determine their effect on 

the detonation process. 

19
Configuration

Initial Fill Pressure, 

kPa (psia) Test Description Figure 

# 

Tube 103 (15) Varied fill pressure 13 

Tube 207 (30) Varied fill pressure 14 

Tube 345 (50) Varied fill pressure 15 

Tube 483 (70) Varied fill pressure 16 

Tube 103 (15) Equivalence Ratio = 0.3 20 

Tube 103 (15) Equivalence Ratio = 0.5 21 

Tube 103 (15) Equivalence Ratio = 0.7 22 

Tube 103 (15) Equivalence Ratio = 0.9 23 

Tube 103 (15) Equivalence Ratio = 1.1 24 

Tube 103 (15) Equivalence Ratio = 1.3 25 

Tube 103 (15) Ignition Energy = 0.025 J 28 

Tube 103 (15) Ignition Energy = 0.25 J 29 

Tube 103 (15) Ignition Energy = 2.50 J 30 

Tube 103 (15) Ignition Energy = 5.00 J 31 

Tube 103 (15) Ignition Energy = 10.0 J 32 

Tube 103 (15) Ignition Energy = 15.0 J 33 

Tube 345 (50) Composition Fraction = 0.25 35 

Tube 345 (50) Composition Fraction = 0.50 36 

Tube 345 (50) Composition Fraction = 0.75 37 

Tube 103 (15) Shchelkin Spiral 41 

Tube 207 (30) Shchelkin Spiral 42 

Tube 345 (50) Shchelkin Spiral 43 

A 103 (15) Varied fill pressure 45 

A 207 (30) Varied fill pressure 46 

A 345 (50) Varied fill pressure 47 

A 483 (70) Varied fill pressure 48 

B 103 (15) Varied fill pressure 50 

B 207 (30) Varied fill pressure 51 

B 345 (50) Varied fill pressure 52 

B 483 (70) Varied fill pressure 53 

C 103 (15) Varied fill pressure 55 

C 207 (30) Varied fill pressure 56 

C 345 (50) Varied fill pressure 57 

C 483 (70) Varied fill pressure 58 

Table 3.1. Summary of completed experimental tests. 

20
Configuration

Initial Fill Pressure, 

kPa (psia) Test Description Figure 

# 

A 103 (15) Equivalence Ratio = 0.7 61 

A 103 (15) Equivalence Ratio = 0.9 62 

A 103 (15) Equivalence Ratio = 1.1 63 

A 103 (15) Equivalence Ratio = 1.3 64 

B 103 (15) Equivalence Ratio = 0.7 66 

B 103 (15) Equivalence Ratio = 1.3 67 

C 103 (15) Equivalence Ratio = 0.7 69 

C 103 (15) Equivalence Ratio = 1.3 70 

A 103 (15) Shchelkin Spiral 72 

A 207 (30) Shchelkin Spiral 73 

A 345 (50) Shchelkin Spiral 74 

A 483 (70) Shchelkin Spiral 75 

B 103 (15) Shchelkin Spiral 77 

B 207 (30) Shchelkin Spiral 78 

B 345 (50) Shchelkin Spiral 79 

B 483 (70) Shchelkin Spiral 80 

C 103 (15) Shchelkin Spiral 82 

C 207 (30) Shchelkin Spiral 83 

C 345 (50) Shchelkin Spiral 84 

C 483 (70) Shchelkin Spiral 85 

B 103 (15) 3/16" Shchelkin Spiral 87 

B 207 (30) 3/16" Shchelkin Spiral 88 

B 345 (50) 3/16" Shchelkin Spiral 89 

Table 3.1. Summary of completed experimental tests, cont. 

21
CHAPTER 4 

EXPERIMENTAL DATA ANALYSIS 

Pressure signals acquired from PCB transducers were transferred from the LeCroy 

oscilloscopes and stored on a PC by means of a LabVIEW control program. This data 

could then be analyzed without the need for any additional manipulation. However, 

because of the rapid nature of the detonation combustion process, much of the data from

the probes carried noise. This noise was created when the shock wave passed the 

transducer, causing it to resonate. To combat this problem, the data was sent through a 

program written in MathWork’s® MATLAB software which filtered the data, removing 

the majority of the high frequency noise. The program implemented a Butterworth lowpass filter, allowing only frequencies below 300kHz to pass through. The resonant 

frequency of the probes was 500kHz; however, this lower cutoff frequency was 

determined by achieving a balance between the level of noise reduction and amplitude 

attenuation. Once the data was filtered, it was output into a text file for analysis in a 

plotting software package. 

Since the only measurement obtainable from the experiments was pressure, then 

analysis must be from it alone. If the pressure is plotted versus time, the profiles that 

arise show the pressure history for each individual probe throughout the combustion 

process. From these plots, wavespeed can be calculated in addition to location of DDT 

and the time required for it to occur. The wavespeed, V, was calculated from a simple 

time of flight equation, 

Time of travel of combustion wave

Length between transducers V = (4.1) 

22
Values obtained from this equation could be compared to the theoretical values obtained 

from the Gordon and McBride CEA© code [17]. The CEA© code calculates the 

theoretical detonation wavespeed for any reaction at any initial condition (temperature, 

pressure, equivalence ratio, etc...). The CEA© code was also used to find the speeds of 

sound of the unburned mixtures for the various initial conditions above. This value was 

helpful in determining whether the wave could be considered a weak detonation or 

deflagration. 

Much can be learned from studying the pressure histories. When a detonation is 

fully formed, it consists of a shockwave coupled to a combustion zone. Because the 

shockwave is moving at or above sonic speeds, no information about its arrival is 

propagated downstream. Therefore, a fully formed CJ detonation should appear in the 

pressure plots as a sharp pressure rise followed by an expansion wave of decreasing 

pressure. Because of this property, the time required for DDT to occur and the distance 

needed can be found from the pressure history plots. This information allows for the 

detonability of mixtures to be determined. 

Experimental and theoretical pressure ratios associated with the detonation 

process for a number of mixtures have been calculated. However, the magnitudes of the 

pressure rises were not trusted due to the filtering of the data. For this reason, only 

wavespeed and pressure histories were used to determine whether a detonation had 

formed. 

23
CHAPTER 5 

DISCUSSION OF EXPERIMENTAL RESULTS 

As mentioned previously, parametric studies of selected initial conditions were 

conducted using two different configurations. A 1.22 m (48 in) long constant area tube 

was used to observe the detonation process and understand how certain variables affect it. 

Next, three actuator concepts were tested using the ideas learned from the constant-area 

tube studies with the primary objective of obtaining a Chapman-Jouguet (CJ) detonation. 

Table 3.1 summarizes all the experimental tests to be discussed. 

5.1 Constant-Area Tube 

Parametric studies using the constant area tube are presented first. Using gaseous 

hydrogen as the fuel, both oxygen and air were used as potential oxidizers. Attempts 

were made using the hydrogen/air mixture; however, CJ detonation never occurred before 

the combustion wave reflected from end of the tube. Fill pressures up to 689 kPa (100 

psia) were attempted with no success. Therefore, hydrogen/oxygen mixtures will be the 

focus of the following results. It is a much more reactive mixture and, as the results will 

show, proved excellent at developing CJ detonations. 

5.1.1 Variation of Initial Fill Pressure 

The first variable evaluated was the initial fill pressure, using stoichiometric 

mixtures ranging from 103 (15) to 483 kPa (70 psia). The pressure plots for the 103 (15), 

207 (30), 345 (50), and 483 kPa (70 psia) cases are shown in Figures 13-16, respectively. 

A comparison of these four cases shows that varying the pressure had a significant effect 

on the detonation process. Figure 13 shows the pressure histories from a run using a 103 

kPa (15 psia) fill pressure. A phenomena known as precompression is apparent in the 

24
first two plots. Since the flame speed is lower than the Chapman-Jouguet (CJ) velocity, 

the flame accelerates in areas where the combustion rate increases such as the boundary 

layer caused by the shockwave [18]. This acceleration in the boundary layer causes the 

shock front to take on a concave “bowl-like” shape. As the flame front continues to 

accelerate the shock front takes on a 1-D planar shape and the precompression mentioned 

before diminishes. No precompression exists in the third plot of Figure 13 and a strong 

detonation is assumed to have formed. A wave speed plot is given in Figure 17 that 

shows the time of flight velocities between the transducers located in the tube. The 103 

kPa (15 psia) curve shows that the wave accelerates to near CJ velocity. However, it is 

not possible to determine if this velocity is maintained since no measurements exist 

beyond this point. Table 5.1 shows the speed of sound and theoretical CJ velocities for 

the four initial fill pressure cases to be discussed. 

Initial Fill Pressure, 

kPa (psia) 

Speed of Sound, 

m/s

Theoretical Wave 

Speed, m/s 

103 (15) 537.9 2837.5 

207 (30) 537.9 2875.0 

345 (50) 537.9 2902.5 

483 (70) 537.9 2920.5 

Table 5.1. Speeds of sound and CJ detonation velocities for various initial fill pressures. 

The 207 kPa (30 psia) case is shown in Figure 14. Comparisons with the 103 kPa 

(15 psia) histories show that the DDT process occurs much faster in the higher fill 

pressure case. A detonation has formed by the third transducer located 0.457 m (18 in) 

downstream of the ignition end wall. The third plot in Figure 14 was created from data 

collected using one of the pressure transducers with a maximum range of 3447 kPa (500 

psia). As mentioned earlier, wave speed and DDT location and time could still be found 

25
if the exact pressure was not known. Therefore, saturated probe data were often 

accepted. 

Figure 15 shows the pressure histories from a 345 kPa (50 psia) case. The 

increase in fill pressure allows a detonation to form between the first and second 

transducers. The wave speed plot shows a velocity of 4200 m/s at the second transducer. 

The theoretical wave speed was calculated as 2902.5 m/s from the CEA code, confirming 

that an overdriven CJ detonation had formed in the tube. This situation was described 

earlier as a transient state with conditions that will converge on the stable ChapmanJouguet point. Figure 17 shows that the wave speed has lowered to the CJ velocity by the 

second transducer and oscillates slightly as the wave propagates downstream. Nettleton 

[19] describes this oscillating velocity as a “galloping-front” and that the peak velocities 

of the leading front can exceed the CJ velocity. This occurs in mixtures that are too close 

to the limits of detonability and are not capable of supporting a continuous detonation 

front [19]. 

Pressure histories from a 483 kPa (70 psia) case are shown in Figure 16. 

Although the data is saturated in the first two plots, a detonation can be assumed to have 

formed by the first transducer due to the shape of the curve. The wave speeds were 

calculated as slightly higher than the CJ velocity throughout the tube. The pressure peak 

that occurs after the shock wave passes the transducer in the third plot of Figure 16 is 

most likely due to instabilities in the pressure transducer caused by the large accelerations 

from the detonation wave passing. Subsequent pressure rises downstream are from the 

wave reflecting off the end walls of the tube. 

26
The location of DDT versus the fill pressure is shown in Figure 18. This location 

is the average of the location of the pressure transducer that first shows a CJ detonation 

profile and the one immediately upstream. Error bars are plotted to show that the CJ 

detonation could have been developed anywhere between these two transducers. It 

should be noted that the fill pressure plays an important role in the DDT process. As the 

fill pressure increases, the distance required for a CJ detonation to develop decreases. 

The time required for a CJ detonation to develop versus the initial fill pressure is 

shown in Figure 19. Similar to Figure 18, the points plotted show the average between 

the time of arrival of the CJ detonation wave at the transducer first indicating a 

detonation and the time that the wave passes the transducer immediately upstream. The 

error bars for the 448 (65) and 483 kPa (70 psia) cases are much wider due to the fact that 

a detonation has setup by the first transducer. Therefore, a CJ detonation could have 

formed instantly or just before it passed the first transducer. Similar to the DDT distance 

trend, increasing the initial fill pressure decreases the time required to develop a CJ 

detonation. 

5.1.2 Variation of Equivalence Ratio 

The equivalence ratio was the second variable studied using the detonation tube. 

For the fill pressure tests, all mixtures were stoichiometric with an equivalence ratio of

one. To understand the effect that fuel-lean and fuel-rich mixtures have on the 

combustion process, the equivalence ratio was varied between 0.3 and 1.3. Values less 

than unity denote a fuel-lean mixture, while values greater are fuel-rich. The tests were 

completed using 103 kPa (15 psia) H2/O2 mixture. Plotted in Figures 20-25 are the 

pressure plots for equivalence ratios of 0.3, 0.5, 0.7, 0.9, 1.1, and 1.3, respectively. Wave 

27
speeds for each case plotted against distance from the ignition end wall are shown in 

Figure 26. The speeds of sound and CJ detonation velocities are shown below in Table 

5.2. 

Equivalence 

Ratio, φ

Speed of 

Sound, m/s 

CJ Detonation 

Velocity, m/s 

0.3 408.7 2023.0

0.5 451.7 2319.4

0.7 489.2 2554.2

0.9 522.5 2750.8

1.1 552.5 2917.0

1.3 579.7 3057.6

Table 5.2. Speeds of sound and CJ detonation velocities for various equivalence ratios. 

Figure 20 shows the pressure histories from a run with an equivalence ratio of 0.3. 

DDT does not occur before the combustion wave reflects from the end wall. Pressure 

data from the first three transducers are plotted, showing a weakening combustion wave 

that is decelerating as it propagates down the tube. The wave speed plot shows that the 

velocity is slightly below the speed of sound. When the mixture is increased to an 

equivalence ratio of 0.5, shown in Figure 21, DDT occurs by 1.4 ms. The peak pressure 

in this case is around 3447 kPa (500 psia), similar to the peak pressure of the 

stoichiometric case discussed earlier. The wave speed plot shows that the velocity over 

shoots the CJ detonation speed before decelerating toward it. Figure 22 shows that a 

mixture with an equivalence ratio of 0.7 develops a CJ detonation by 1.2 ms at the same

location in the tube. The velocity of the main front also overshoots the CJ value for this 

case. It appears to be converging on the CJ speed as it continues to propagate down the 

tube. 

 As the equivalence ratio nears unity, the time for a CJ detonation to develop 

increases. Figure 23 shows that a mixture with an equivalence ratio of 0.9 becomes CJ in 

28
nature around 1.4 ms. The wave speed plot for this case looks very similar to the φ = 0.7 

case. It overshoots the CJ value and then converges back to it as it continues to 

propagate. Figure 24 shows that no CJ detonation develops by the last transducer in the 

tube, however, the wave speed plot for this case shows that the velocity is above the CJ 

value, indicating an overdriven detonation. If the wave behaved similar to the previous 

cases it would have tried to converge on the CJ velocity as it attempted to become more 

stable. The φ = 1.3 case shows that no CJ detonation occurred by the last transducer. 

The time required for the DDT process is shown in Figure 27. In order to show 

the spread of the data, included in this plot are results from all the tests completed. As 

was shown above, a mixture with an equivalence ratio of 0.7 gave the minimum time 

required to obtain a detonation, around 1.2 ms. Error bars are included to show that the 

detonation could have been formed earlier except the pressure probes are only located in 

a few discrete locations, every 0.152 m (6 in). This result is good in that fuel-lean 

mixtures can be used to obtain a detonation, thus lowering fuel and weight requirements. 

5.1.3 Variation of Ignition Energy 

The ignition energy could be varied from 0.025J to 15J, allowing its effect on 

detonation initiation to be evaluated. The fill pressure was held constant at 103 kPa (15 

psia) using stoichiometric H2/O2 throughout all the tests. Pressure transducers were 

installed in the first six locations leaving the seventh empty. The pressure plots are 

shown in Figures 28-33, for ignition energies of 0.025, 0.25, 2.5, 5, 10, and 15J, 

respectively. The pressure histories from the first probe in addition to the last three are 

plotted. This was done to show how varying the energy changed the time at which the 

combustion wave passed the first transducer as well as changes in the DDT process. 

29
The wave speeds for each ignition energy case are shown in Figure 34. The wave 

speeds are all initially right above the speed of sound and increase as the wave propagates 

downstream in tube. At the second transducer, the wave speeds are higher for increasing 

ignition energy; however, this trend is not held as the wave propagates downstream. The 

velocity of the wave at the final transducer has no dependence on the energy and the 

results behave randomly. The lack of dependence on energy could be due to the fact the 

ignition energy is possibly below a threshold where varying its value has no effect. The 

randomness could then be associated with experimental uncertainties discussed in 

Chapter 7. 

Some important results from the plots are shown below in Table 5.3. The case 

that used 10J of energy was the only case in which DDT occurred by the last transducer. 

Therefore, the only difference that the ignition energy had was to decrease the amount of 

time before the combustion wave passed the first transducer, essentially decreasing the 

amount of time before the start of combustion. This was not a significant enough result 

to justify using higher energies. As described in a previous section, more equipment was 

required to create a higher energy spark. Hence, a decrease in the amount of energy 

required will lower the cost and weight requirements of the system. 

E, J Time to first 

transducer, ms

DDT? 

0.025 6.1 No

0.25 5.4 No

2.5 5.2 No

5 4.7 No

10 4.8 Yes

15 4.5 No

Table 5.3. Summary of ignition energy tests. 

30
5.1.4 Variation of Oxidizer Composition Fraction 

The next variable that was studied using the tube configuration was the oxidizer 

composition fraction, which is the volume fraction of oxygen in a mixture of oxygen and 

air. One represents pure oxygen while zero denotes air. The fractions tested were 

completed using a more energetic 345 kPa (50 psia) fill pressure instead of 103 kPa (15 

psia) since moving toward air as an oxidizer will increase the amount of time and 

distance required for a detonation to develop. It was shown in Section 5.1.1 that 

increasing pressure decreases the time and distance to detonation. The pressure plots are 

shown in Figures 35-37 for composition fractions of 0.25, 0.50, and 0.75, respectively. 

Figure 15 shows the results from the 345 kPa (50 psia) fill pressure case using pure 

oxygen as the oxidizer. The wave speeds for each case are shown in Figure 38 and the 

speeds of sound and CJ detonation velocities from the CEA code are shown below in 

Table 5.4. 

Fraction, % Speed of Sound, 

m/s

CJ Detonation 

Velocity, m/s 

0 406.7 1965.5

25 455.5 2264.5

50 479.7 2484.1

75 510.3 2669.5

Table 5.4. Speeds of sound and CJ detonation velocities for various fractions. 

Figure 35 shows the pressure plots from the case with a fraction of 0.25. No CJ 

detonation is developed before the wave reaches the end wall of the tube. A weak 

detonation appears to have developed since the wave speeds are above the speed of 

sound, however, they are still below the CJ value for this case. The results for the 0.50 

case are shown in Figure 36. The pressure histories show that a strong detonation has 

developed by the transducer located 0.610 m (24 in) downstream of the ignition end wall. 

31
Based on the wave speed plot, the detonation enters an overdriven state before it 

converges to the CJ velocity around 2500 m/s. Finally, the pressure histories for the 

fraction of 0.75 are shown in Figure 37, which show CJ profiles by the second transducer. 

Similar to the previous case, the detonation is overdriven and decelerates to the CJ 

velocity as it propagates downstream. As a comparison, the wave speed data from a 345 

kPa (50 psia) case with a fraction of 1.0 is given in Figure 38. The CJ velocity and speed 

of sound are higher in this case, apparent from the greater wave speeds through out the 

tube. 

From Figures 35-37, it can be noted that decreasing the fraction toward zero will 

lessen the likelihood that a detonation will develop. The time that is required for a 

detonation to develop is shown in Figure 39. A trend that should be noted is that as the 

fraction tends toward one the time for a CJ detonation to develop decreases. This is also 

apparent from the pressure plots above. A similar trend can be noted from Figure 40, 

which shows the distance required for a detonation to occur for varying composition 

fraction. A mixture with a fraction of 0.75 is still capable of developing a CJ detonation 

in approximately the same time and distance, but at lower velocities than the pure oxygen 

case. 

5.1.5 Addition of a Turbulence Generator 

A turbulence generator device as described in Section 2, in the form of a wire 

spiral, was installed in the tube immediately downstream of the ignition end wall. The 

goal of the spiral was to accelerate the transition to a CJ detonation as compared to the 

tube with no device added. Tests were completed using three initial fill pressures: 103 

(15), 207 (30), and 345 kPa (50 psia). The 483 kPa (70 psia) case was not attempted 

32
since a CJ detonation was initiated by the first transducer downstream of the ignition end 

wall without a spiral. The pressure time histories are shown in Figures 41-43. A 

comparison of the wave speeds with those measured with no spiral is shown in Figure 44. 

In the 103 kPa (15 psia) fill pressure case, the wave speeds measured after the 

first transducer are greater than the no spiral case. A comparison of the pressure histories 

in Figures 13 and 41 show that DDT distance is shortened when the spiral is installed. 

The wave transitions 0.152 m (6 in) upstream compared to the case with no spiral. The 

results from the 207 kPa (30 psia) case show an even greater improvement. The case 

without the spiral reaches CJ velocities 0.914 m (36 in) downstream of the ignition end 

wall. The addition of the spiral accelerates this transition to just 0.457 m (18 in) 

downstream. Figure 43 shows the pressure histories from the 345 kPa (50 psia) case. 

Comparing this to the case with no spiral, shown in Figure 15, shows that both transition 

0.305 m (12 in) from the ignition end wall. The only difference is in the wave speed plot, 

where the no spiral case shows overdriven velocities before it converges to the CJ speed. 

5.1.6 Summary of Detonation Tube Experiments. 

Results from the 483 kPa (70 psia) initial fill pressure case showed the fastest 

transition to a CJ detonation. Detonations were formed by the first transducer, which is 

located 0.152 m (6 in) from the ignition end of the tube. The second variable studied was 

the equivalence ratio, which showed the time to develop a detonation could be minimized 

by using a fuel-lean mixture of φ=0.7. Ignition energy was then varied and it was learned 

that no significant gains came from increasing the energy to 15J. The flame front passed 

the first transducer quicker; however, the DDT did not occur at an earlier location as 

compared to lower ignition energies. The final variable evaluated was the composition 

33
fraction. As expected, the detonation process was delayed or did not occur at all as the 

fraction tended toward zero. Mixtures with fractions of 0.75 and 0.50 developed CJ 

detonations at a location further downstream of the ignition end wall as compared with 

O2 as an oxidizer. A spiral was added in an attempt to accelerate the transition to a CJ 

detonation. The addition of the spiral shortened the distance for DDT, except at 345 kPa 

(50 psia) where in both cases transition occurred very close to the ignition end wall. 

. 

34
5.2 Detonation Actuators 

Three different configurations of the detonation actuators were installed in the 

detonation tube and tested at various initial conditions. Figure 4 shows an actuator 

installed between the flange and the tube on the ignition end. Parametric studies were 

again carried out toward the goal of developing a CJ detonation in the convergent section 

of the actuator. The initial conditions evaluated included varying the initial fill pressure, 

equivalence ratio, and the addition of a Shchelkin spiral turbulence generator. Ignition 

energy and composition fraction were not studied since they did not accelerate the DDT 

process in the constant area tube tests. 

5.2.1 Variation of Initial Fill Pressure

The fill pressure was again varied between 103 (15) and 483 kPa (70 psia) for 

each actuator concept. Actuator A was the first evaluated, which had a 1 cm (0.394 in) 

throat diameter. The pressure histories for 103 (15), 207 (30), 345 (50), and 483 kPa (70 

psia) initial fill pressure cases are shown in Figures 45-48, respectively. A plot of the 

wave speeds through the actuator for all four cases is shown in Figure 49. This actuator 

had five pressure taps available, however, only the last four were utilized since the first 

one was directly above the ignition point and was subject to a large amount of electrical 

noise from the spark. 

For the 103 kPa (15 psia) case, shown in Figure 45, the first pressure rise occurs 

in 3.6 ms, 0.034 m (1.34 in) downstream of the ignition end wall. It has a peak pressure 

of around 1380 kPa (200 psia) and does not exhibit the sharp rise that is common for 

detonation waves [20]. An increase in pressure occurs by the second transducer with a 

wave speed of 1000 m/s. This is above the sonic velocity of the unburned gas, indicating 

35
that a weak detonation had formed, although not of CJ strength. By the third and fourth 

transducers, the detonation could not be sustained as indicated by the subsonic wave 

speed, shown in Figure 49. The next case used a 207 kPa (30 psia) mixture. As shown in 

Figure 46, the pressure rises to a maximum of 11000 kPa (1600 psia) at the third 

transducer. The wave accelerates to a maximum wave speed of 700 m/s with the pressure 

increasing suddenly after a gradual rise, indicating that the shock is becoming more 

planar. Similar to the case above, the detonation can not be sustained as the wave speed 

decreases to 450 m/s and the pressure drops to about 6900 kPa (1000 psia) by the last 

transducer. 

The increased initial pressure of 345 kPa (50 psia) in Figure 47 leads to higher 

pressure rises, with the maximum of 13800 kPa (2000 psia) occurring at the third 

transducer. This peak pressure is maintained through the fourth transducer and the wave 

speed remains supersonic after a slight deceleration from an initial value calculated at 

1200 m/s. This decrease in wavespeed indicates that the detonation is weakening as it 

approaches the throat of the actuator, similar to the previous two cases. The final fill 

pressure attempted in this actuator was 483 kPa (70 psia), shown in Figure 48. As the 

pressure plots show the pressure increases and the spacing between the rises decreases as 

the wave propagates through the actuator. This is also apparent from the velocity plot, 

where the wave speed continues to increase to a maximum of 2350 m/s by the last 

transducer. This value is still below the 2920 m/s CJ velocity. However, it is interesting 

to note the strengthening of the wave in this case, as compared to the previous three 

results. 

36
Actuator B, with a throat diameter of 0.5 cm (0.197 in), was installed in the 

detonation tube next. The pressure histories are shown in Figures 50-53 for each fill 

pressure case. The pressure transducers were located in the same locations as the previous 

actuator. A plot of the wave speeds is shown in Figure 54. 

The pressure rises in the 103 kPa (15 psia) case appear to increase in amplitude, 

up to a maximum of around 4800 kPa (700 psia) by the third transducer. The fourth 

transducer records a peak pressure of only 2800 kPa (400 psia), indicating a weakening 

of the wave. From the velocity plot it should be noted that the wave speed is subsonic 

throughout the actuator and only deflagration combustion is present. The same can be 

said of the combustion process in the 207 kPa (30 psia) case, except a higher maximum

pressure of 8300 kPa (1200 psia) is recorded. The wave speed decreases from a value 

close to the speed of sound and then increases again as the wave propagates through the 

throat, although never going above the sonic line. It should be noted in Figures 50-53 

that the pressure readings are less than zero at the beginning of the run. This is from the 

oscillations that occurred when the ignition system was not shielded properly. It was 

determined that this did not affect the readings adversely since the pressure rises back to 

a normal value by 0.2 ms. 

 A 345 kPa (50 psia) initial fill pressure was attempted next and the results are 

shown in Figure 52. A peak pressure of almost 17240 kPa (2500 psia) was recorded by 

the third transducer and it appears as though the wave is strengthening. However, the 

velocity plot shows that this is not the case as the wave speed decreases from a 

supersonic to subsonic velocity by the last transducer. Results of the 483 kPa (70 psia) 

initial pressure case are shown in Figure 53. The pressure rises to 24800 kPa (3600 psia), 

37
but the wave speed never rises above the sonic line. The sharp pressure rise at 0.0039 sec 

is due to a loose cable connecting the transducer to the signal conditioner and is not flow 

related. The problem was identified and fixed in later tests. 

Every initial pressure attempted using actuator B produced only deflagrations at 

the throat. The wave speed and pressure for each case decreases by the last transducer. It 

is a possibility that the smaller throat diameter is constricting the flow to a large degree, 

creating unfavorable conditions for a transition to a detonation. 

 The next actuator, actuator C, had the same throat diameter, but had a 1 cm

(0.394 in) throat extension. It was designed in this manner with the hope of sustaining or 

strengthening a detonation in the constant-area section. Pressure histories are shown in 

Figures 55-58. A plot of the wave speed at each location in the actuator is provided in 

Figure 59. Actuator C also had one extra pressure port located in the throat extension. 

This is now the final transducer before the exit of the actuator located 0.108 m (4.25 in) 

downstream of the ignition end wall. 

The 103 kPa (15 psia) case, shown in Figure 55, has relatively low pressure rises 

with a maximum of around 4150 kPa (600 psia) in the constant area section. The 

pressure increases and decreases before reaching the throat. Velocity behaves in an 

opposite fashion by decreasing then increasing as the wave passes through the throat and 

constant area extension. The wave speed remains subsonic throughout the actuator. 

When the pressure and velocity plots are compared to those of the previous actuator, it 

should be noted that the constant area section helps to increase both velocity and 

pressure. It is also interesting to note that the pressure history in the throat extension 

exhibits a sudden rise typical of a CJ detonation. However, since only one transducer is 

38
located in the section it is impossible to tell whether the wave speed and the pressure 

increase by the exit, possibly producing a detonation. 

The pressure histories in Figure 56 look very similar to those in the 103 kPa (15 

psia) case. However, the maximum pressure obtained is approximately 12400 kPa (1800 

psia) at the third transducer. The pressure drops slightly by the constant area section, 

however, the wave speed increases to almost the speed of sound. This indicates that 

deflagration combustion is the driving process in the actuator. 

It should be noted that only four transducers are used for the 345 kPa (50 psia) 

and 483 kPa (70 psia) runs due to a malfunction in the first transducer. The maximum

peak pressure obtained in the 345 kPa (50 psia) case was around 12400 kPa (1800 psia). 

Similar to the previous two runs, the wave speed decreases to well below the sonic line 

before an increase caused by the deflagration propagating through the constant area 

section of the actuator. 

An initial pressure of 483 kPa (70 psia) was the final variation used to study the 

effect on fill pressure in the three actuator configurations. Besides a maximum pressure 

of 20000 kPa (2900 psia) occurring at the second transducer, the actuator performed the 

same as in the other cases. The wave speed was subsonic throughout, decreasing until a 

slight acceleration when the wave propagated through the constant area section. 

In summary, only the actuator with the largest throat diameter gave results that 

showed waves approaching CJ strength. Figure 60 shows the exit wave speeds for each 

nozzle at the various fill pressures. Only actuator A showed supersonic wave speeds at 

the throat. The 483 kPa (70 psia) case showed a strong acceleration up to a wave speed 

of 2350 m/s before the exit. Actuators B and C both constricted the flow to a point where 

39
detonations could not be sustained or were not initiated at all. The constant area throat 

extension helped to increase both the pressure and the velocity of the wave propagating 

through it. However, it was impossible to determine if a detonation had developed due to 

only one pressure port in this location. 

5.2.2 Variation of Equivalence Ratio 

When fuel-lean mixtures were used in the constant area tube configuration, the 

detonations transitioned into CJ detonations over a shorter distance. For this reason, the 

same tests will be carried out using the detonation actuators. Four equivalence ratios 

were used: 0.7, 0.9, 1.1, and 1.3 at a 103 kPa (15 psia) initial fill pressure. Actuator A 

was tested first and its pressure histories for the four cases are shown in Figures 61-64, 

respectively. A plot of the wave speeds is included in Figure 65 showing the change in 

velocity as the wave propagates downstream from the ignition source. In addition, 

included in Figure 65 are curves indicating the speed of sound in the unburned mixture 

for each of the equivalence ratios. The speed of sound is a function of equivalence ratio 

causing it to change for each value. 

A fuel-lean mixture with φ = 0.7 was tested first in the actuator. Similar to the 

stoichiometric runs above, the pressure increases as the wave propagates passed the first 

three transducers and then decreases by the throat. A maximum of 4150 kPa (600 psia) 

was recorded by the third transducer. From the wave speed plot, the velocity decreases 

from supersonic to subsonic as the wave propagates through the actuator. The weak 

detonation that was formed by the second transducer was not sustained and a deflagration 

exited the actuator throat. 

40
Similar results are obtained for the runs that used equivalence ratios of 0.9, 1.1, 

and 1.3, shown in Figures 62-64, respectively. Mixtures with φ =0.9 and 1.1 were 

initially supersonic, but weakened to subsonic deflagration by the throat. The φ =1.3 case 

is subsonic throughout. The equivalence ratio benefit seen in the constant area tube 

results was not enough to overcome the much shorter lengths used in the actuators. 

Actuator B was tested next and based on the results from the previous actuator, 

only the more extreme equivalence ratios were tested. The pressure plots are shown in 

Figure 66 and 67 and the wave speed plot is given in Figure 68. Similar pressure rises 

are seen in Figure 66 as compared with the same case using the previous actuator. It may 

be seen that the wave speeds have dropped below the previous values plotted in Figure 

65. However there is one difference in that they reach a minimum at the third transducer 

and then increase by the throat transducer. This value is still below the value obtained 

from the previous configuration. 

The most significant difference in the results for the φ = 1.3 case is the slightly 

higher wave speeds, as seen in Figure 68. This is due to the difference in the speed of 

sound between two mixtures. The fuel-rich case has a higher hydrogen content which has 

a lower molecular weight. This lowers the density and increases the speed of sound. The 

pressure histories are almost identical in both amplitude and profile. 

The actuator with the constant area throat extension was installed in the 

detonation tube and tested with mixtures of φ = 0.7 and 1.3. The pressure histories are 

shown in Figures 69 and 70 and the wave speeds plotted against x location in the actuator 

are shown in 71. As stated before, actuator C had a pressure tap located in the constant 

area section of the throat, making a total of five transducers. Looking at the φ = 0.7 case 

41
shows that the first four pressure transducers record very similar pressure curves as 

compared to actuator B. The additional transducer in the throat recorded a pressure of 

around 3447 kPa (500 psia), slightly lower than the peak pressure recorded at the second 

transducer. 

The velocities of the wave are shown in the wave speeds plot shown in Figure 71. 

The first three wave speeds compare well against their counterparts in the previous 

actuator run. The velocity decreases at the third transducer and then increases slightly as 

the wave propagates toward the fourth probe. Then, similar to the fill pressure cases 

discussed earlier, the wave accelerates as it passes through the constant area section. 

The fuel-rich case, φ = 1.3, has very similar pressure curves when compared to the 

fuel-lean case. However, the pressure rise associated with the propagating wave occurs 

earlier and the overall wave speeds are slightly higher. Both of these changes are due to 

the increase in speed of sound. The constant area section manages to increase the velocity 

again, however, both waves remain below the speed of sound and no detonation is 

developed. 

In summary, the variation of the equivalence ratio fails to assist in developing a 

strong CJ detonation in the actuators. In all cases, the wave is only a deflagration or 

possibly a very weak detonation. Actuators B and C showed promise by accelerating the 

wave as it approached the exit, contrary to the deceleration that occurred in actuator A. 

5.2.3 Addition of a Turbulence Generator 

The spiral made from the 1.6 mm (0.0625 in) diameter wire was installed in each 

actuator and tested with varying initial pressure. The actuators were evaluated using 103 

(15), 207 (30), 345 (50), and 483 kPa (70 psia) mixtures. The results of the actuator A 

42
tests are shown in Figures 72-75. A velocity plot is shown in Figure 76 with wave speeds 

plotted against location for this actuator. The first test completed used a mixture with a 

fill pressure of 103 kPa (15 psia). The results in Figure 72 show pressures similar to the 

case without the spiral, however the pressure rises appear to be spaced closer. Figure 76 

shows that the velocity of the wave propagating from the first to the second transducer 

was around 1750 m/s, which is well above the sonic velocity. Even though the pressure 

rise increases by the third transducer the velocity drops below the speed of sound and a 

detonation can not be sustained. The initial pressure was then increased to 207 kPa (30 

psia), shown in Figure 73. These plots show tightly spaced, sudden rises of pressure with 

little precompression. This type of profile is indicative of strong CJ detonations and the 

wave speed plot shows that the velocity increases from an initial value of about 1500 m/s 

to around 2600 m/s. This value is much closer to the CJ wave speed of 2875 m/s. It is not 

a CJ detonation, but it is an improvement over the runs with no added turbulence device. 

The 345 kPa (50 psia) initial pressure case is shown next in Figure 74. Peak 

pressure is around 8300 kPa (1200 psia) with the precompression diminishing as the 

wave propagates toward the throat. The wave speed plot in Figure 76 shows a velocity of 

3850 m/s, higher than the CJ detonation wave speed. The velocity drops to around 

2400m/s and then increases to the CJ velocity by the fourth transducer. This “gallopingfront” phenomena was described earlier and was attributed to regions where the 

detonation front could not be sustained, such as in area where the fuel-oxidizer mixing 

was poor. In addition, the combustion front accelerates in regions of greater turbulence. 

As the wave passes over the localized regions of enhanced mixing created by the spiral, 

an acceleration of the combustion wave occurs. The “galloping-front” can also be seen in 

43
the 483 kPa (70 psia) fill pressure case. Figure 76 shows a wave speed of almost 4500 

m/s at the third transducer before a deceleration brings the velocity of the wave to 3650 

m/s at the actuator throat. These results show that overdriven and CJ detonations can be 

created in the actuators by the addition of a turbulence generator. 

The results from the testing of the spiral in the actuator B are discussed next. 

Plots for initial pressures of 103 (15), 207 (30), 345 (50), and 483 kPa (70 psia) are 

shown in Figures 77-80, respectively. The wave speed plot is shown in Figure 81. From

the plot of the 103 kPa (15 psia) case, it is apparent that a strong detonation is not 

initiated. The peak pressure is around 4800 kPa (700 psia) with a maximum velocity of 

1200 m/s obtained at the throat. The 207 kPa (30 psia) case shows a peak pressure of 

7200 kPa (1040 psia) with an accelerating wave reaching a velocity of 3900m/s by the 

throat. Figure 79 shows the 345 kPa (50 psia) case with a peak pressure around 10340 

kPa (1500 psia). The pressure histories are detonation-like in nature and show almost no 

sign of precompression by the fourth transducer. The wave speed plot in Figure 81 

shows that after an initial acceleration the velocity levels off slightly higher than the CJ 

velocity of 2900 m/s. Figure 80 shows the pressure histories from the 483 kPa (70 psia) 

initial fill pressure case. The wave quickly accelerates to the overdriven detonation 

regime before it begins to converge to the CJ velocity. This type of behavior is very 

similar to the previous runs and the large velocities that were measured are a result of the 

regions of localized mixing created by the coils of the spiral. In the third plot of Figures 

77-79 some very large pressure spikes are recorded. As mentioned earlier these are due 

to a loose cable connecting the transducer to the signal conditioner. 

44
The same set of tests was repeated using actuator C, with the 1 cm (0.394 in) 

constant area throat extension with a 0.5 cm (0.197 in) diameter. The pressure histories 

are shown in Figures 82-85 and the wave speeds are shown in Figure 86. Comparison of 

the pressure histories from this actuator to the previous one shows few differences. The 

addition of the constant area section appears to lower the pressure in all four cases. From

Figure 86, it is apparent that it also lowered the velocity when the wave was already 

supersonic. The 103 kPa (15 psia) case shows an increase in velocity, however, the wave 

is still well below the CJ velocity. The 483 kPa (70 psia) case follows the same trends as 

the previous three cases; however, it is right above CJ velocity when it exits the actuator 

after being overdriven before the throat. 

As a comparison, a spiral made from copper wire with a diameter of 4.8 mm

(0.1875 in) was installed in actuator B and tested at various fill pressures. The pressure 

history plots are shown in Figures 87-89 and the wave speed plot is shown in Figure 90. 

The spiral was tested at initial pressures of 103 (15), 207 (30), and 345 kPa (50 psia). 

From the wave speed plot it can be noted that the larger diameter does not provide an 

advantage over the thinner version, shown in Figure 81. In both cases, the 103 kPa (15 

psia) initial fill pressure mixture is not capable of producing a CJ detonation. In addition, 

the 207 (30) and 345 kPa (50 psia) cases develop into CJ detonations by the throat of the 

actuator. From these results, it was concluded that the thinner spiral worked equally well 

at accelerating the DDT process and no further testing of the thicker diameter was 

completed. The large pressure spikes in the third plot of Figures 87-89 are again due to 

the loose cable. 

45
5.2.4 Summary of Detonation Actuator Tests 

Of all the detonation actuator tests, the cases where the Shchelkin spiral was used 

proved the most capable of developing a CJ detonation before the exit of the actuator. 

Overdriven detonations were present in all three actuators at initial fill pressures 207 kPa 

(30 psia) or greater. The tests varying the initial fill pressure with no spiral failed to 

develop a CJ detonation and in only one case was the velocity approaching the CJ value. 

Actuator B and C appeared to constrict the flow to the point where the wave speeds 

decreased as the wave propagated downstream. The results from the variation of the 

equivalence ratio showed no development of a CJ detonation. In almost every case, only 

deflagration combustion was present. 

5.3 Comparison of the Constant Area Tube and Actuators 

The time to detonation, distance to detonation and the amplitude of the wave were 

considered when comparing the results from the constant area tube and the actuators. As 

mentioned in a previous section, the pressure histories recorded in the tube and various 

actuators for an initial pressure of 103 kPa (15 psia) are shown in Figures 13, 45, 50, and 

55, respectively. As discussed earlier, no CJ detonations are formed in the actuators 

before the wave exits, however the pressure amplitude of ~4800 kPa (700 psia) is 

obtained in actuator B by 0.078 m (3.07 in) downstream of the ignition end wall. This 

amplitude is not reached until 0.762 m(30.0 in) downstream in the tube. Pressure histories 

of the 207 kPa (30 psia) case are shown in Figures 14, 46, 51, and 56, respectively. As 

the pressure histories show, the actuators do not accelerate the transition to detonation as 

well as the constant area tube. A CJ detonation has formed by the first transducer located 

0.457 m (18 in) downstream of the ignition end wall in the tube. No CJ detonations are 

46
even formed in the actuators. In addition, the peak pressures seen in the constant area 

tube are greater than the amplitudes recorded in the actuators. 

The results from the addition of the Shchelkin spiral are discussed next. A vast 

improvement in the performance of the actuators can be noted from these plots. Figures 

41, 72, 77, and 82 show the cases with an initial pressure of 103 kPa (15 psia) for both 

the actuators and the constant area tube, respectively. No CJ detonation is present in this 

case and the actuator’s only advantage appears to be in the large increase in pressure that 

results from the wave being compressed in the convergent section of the actuator. The 

pressure amplitudes reach levels not seen in the constant area tube until a CJ detonation 

has almost formed toward the end of the tube. The 207 kPa (30 psia) fill pressure cases 

are presented Figures 42, 73, 78, and 83. CJ detonations have formed in each actuator by 

the throat located approximately 0.102 m (4 in) downstream of the ignition end wall. A 

detonation is not formed until 0.305 m (12 in) downstream in the tube case. In addition 

to the improvement in the DDT location, the DDT time is also decreased in the actuator 

runs. Pressure histories from the 345 kPa (50 psia) cases are shown in Figures 43, 74, 79, 

and 84. The same can be said about these plots as the previous one. CJ detonation 

occurs in each case in less distance and time for each of the actuators as compared to the 

constant area tube. In the 483 kPa (70 psia) fill pressure cases, shown in Figures 16, 75, 

80, and 85, the deflagration in the constant area tube with out a spiral transitions to a 

detonation occurs faster than in the actuators with spirals. A CJ detonation is formed in 

less time and possibly less distance, although it is impossible to say due to pressure 

transducers only being located every 0.152 m (6 in) in the tube. 

47
In summary, DDT occurs in a shorter distance in the constant area tube than in the 

actuators, when no spiral is installed. Without the spiral, CJ detonations do not occur in 

the actuators at all fill pressures; however, in some cases the pressure amplitudes are 

greater than in the tube. When a spiral is added to the actuators, their performance 

surpasses that of the tube for certain initial fill pressures. The 207 (30) and 345 kPa (50 

psia) cases both produced CJ detonations in less distance and time than required by the 

constant area tube. Therefore, which configuration helps produce the quickest detonation 

depends on the initial conditions. 

48
CHAPTER 6 

DISCUSSION OF NUMERICAL RESULTS 

Computational fluid dynamic (CFD) analysis was conducted to help understand 

and validate the flow processes observed in the laboratory experiments. The 2-

dimensional, time-accurate SPARK code was chosen for the numerical study of the 

detonation actuators. It solves the elliptic Navier Stokes and energy equations as well as 

the species continuity equations. SPARK was developed by Drummond [21] to study 

supersonic reacting flowfields, which lends itself directly to the development of the 

actuators. 

The constant area tube and the three actuator concepts were all evaluated using 

the SPARK code. An axisymmetric grid was used to model the actuators. An ignition 

spark was simulated by adding a specified spark energy to the source terms in a region 

near the centerline at the wall. The size of the region and the amount of energy were 

varied to understand their effect. It was found that above a certain spark energy for a 

given region size, all cases, including both H2/O2 and H2/Air mixtures, a ChapmanJouguet detonation was formed immediately. Below this energy value no ignition 

occurred. This being the case, a good comparison between the experimental and 

computational results could not be made. There are a few possibilities to the reason why 

the SPARK code predicted immediate initiation of CJ detonations. The first was the size 

of the grid that was used to study the various cases. Shapiro [22] states the width of the 

leading shock wave to be 1.4x10-7 m. A grid of this spacing would be needed to resolve 

the detailed structure of the shock wave coupled to the reaction zone. Resolving this 

structure is imperative to observing the DDT process, which is not seen in the coarser 

49
grids. A grid of the spacing recommended by Shapiro would result in almost 800,000 

nodes in the x-direction of the detonation actuators. The computer resources allotted for 

this study only allowed spacing on the order of 1x10-4 m. A method of adaptive grid 

refinement would have to be implemented in SPARK to ensure the grid was adequately 

spaced in the vicinity of the shock/flame front. In addition, the system of equations being 

solved is numerically stiff and as the grid became finer, the computational times 

increased dramatically. 

Due to the number of grid points required to resolve the detonation front and the 

lack of adequate computer resources, the results of computations performed on much 

coarser grids will not be discussed. 

50
CHAPTER 7 

EXPERIMENTAL UNCERTAINTIES 

The experimental studies were not error-free and some uncertainties did exist. 

The first group of uncertainties deals with the injection of the fuel-oxidizer mixtures. 

Before each run, the tube and actuators were evacuated of any air and/or combustion 

products from previous runs. Ideally, the vacuum pump would evacuate the entire 

contents of the chamber; however, the pump was only able to evacuate the chamber to 

103-207 Pa (0.015-0.030 psia). Although this amount was very small, it contaminated 

the fuel and oxidizer that was injected into the chamber. In addition, the tube and 

actuator assembly would ideally be airtight but some small leaks did develop at times. 

The leak rate could be reduced to approximately 2.06 Pa/sec (0.018 psia/min). Therefore, 

during mix times the initial fill pressure was not maintained. A third source of

uncertainty deals with the injection of the fuel and oxidizer. It was controlled by turning 

valves and then monitoring the pressure on the Mensor pressure gauge. Since this was 

not automated, the partial pressures were not exact every time. This error was not 

significant since the actual partial pressures achieved varied by much less than 1% from

the stated values. In addition, the fuel and oxidizer were not premixed before they were 

injected in the tube. As discussed in Chapter 2, the fuel and oxidizer were allowed to mix 

by waiting five minutes before they were ignited. Based on the mixing study results, it 

was assumed that each run was repeatable. 

The PCB pressure transducers added more uncertainty to the experiments. Due to 

the sensitive nature of the transducers, they were susceptible to errors due to large 

accelerations caused by the violent explosions with in the chamber. These errors caused 

51
overshoots in the pressure readings as well as noise to occur in the signals that was later 

removed with filtering. The filtering itself added more uncertainties because the low-pass 

filter did not allow anything over 300kHz to pass through. Any part of the signal above 

this cutoff frequency was eliminated whether it was noise or not. Therefore, the pressure 

histories that were obtained may not replicate the combustion process in the detonation 

chamber. The time of flight velocities should still be accurate since they do not depend 

on the pressure magnitude, only on the time of arrival. 

Finally, the ignition energy stated may not exactly match with the value actually 

achieved. The Spectralite 919 flash lamp power supply was calibrated by technicians at 

Wyle Laboratories before and during the experimental studies and should have provided 

accurate energies. The components that were added to boost the maximum energy were 

not monitored and it was assumed that the stated energy was achieved if the 5 μF 

capacitor was completely discharged after each firing. This was checked when the 

equipment was installed, but was discontinued during the actual runs, therefore, actual 

energies may have varied. 

52
CHAPTER 8 

CONCLUSIONS AND RECOMMENDATIONS

An experimental investigation was performed in support of the development of 

actuators utilizing detonation for flow control. These actuators hold the promise of

controlling high speed flows, including the transonic and supersonic flow regimes. 

Parametric studies were completed using a 1.22 m (48 in) long constant area tube 

and three actuator concepts. From the tube tests, initial fill pressure was found to have a 

large effect on the detonation process, as higher fill pressures decreased the time and the 

distance required to transition to a CJ detonation. The equivalence ratio of the fuel and 

oxidizer mixture was varied between 0.3 and 1.3 and it was found that the DDT time 

could be minimized by a fuel-lean mixture with φ = 0.7. The energy used to ignite the 

mixture in the tube was varied from 0.025J to 15J in an attempt to accelerate the DDT 

process. It was found that increasing energy increased the initial wave speeds; however, 

the wave could not maintain the velocities and the final values behave randomly with 

spark energy. It was concluded that the ignition energy within the range tested did not 

significantly improve the detonation process. The composition of the oxidizer was varied 

from pure oxygen to air. As the oxidizer composition approached air, the wave speeds 

decrease and the likelihood of DDT decreases. A composition fraction of 0.75 still 

allowed a CJ detonation to develop but the wave speeds were lower than in the pure 

oxygen case. In the final attempt to accelerate the DDT process, a Shchelkin spiral was 

added to the tube. It was tested at initial fill pressures ranging from 103 (15) to 345 kPa 

(50 psia). The presence of the spiral helped to decrease the DDT distance from 1.07 m

(42 in) to 0.914 m (36 in) in the 103 kPa (15 psia) case and from 0.914 m (36 in) to 0.457 

53
m (18 in) in the 207 kPa (30 psia) case. The 345 kPa (50 psia) case transitioned at the 

same point in both cases. 

Of the variable values tested in the constant are tube, those that helped to 

transition deflagrations to detonations were also studied in the evaluation of the three 

detonation actuators. The initial fill pressure was varied from 103 (15) to 483 kPa (70 

psia) using each of the actuators. Actuator A was the only one to produce supersonic 

wave speeds. No CJ detonations were developed and in most cases, only deflagration 

combustion was present. The equivalence ratio was varied to understand its effect on the 

flow processes in the actuators. The values tested ranged from 0.7 to 1.3, however, no CJ 

detonations developed in any of the runs attempted. A Shchelkin spiral was then 

installed in the actuators and initial fill pressures of 103 (15) to 483 kPa (70 psia) were 

used to evaluate its performance. Only the 103 kPa (15 psia) cases did not produce 

strong detonations. Most of the other three fill pressure cases had at least overdriven 

detonations from the throat of the actuator on downstream. Of the three actuators, only 

actuator B helped to transition waves to just below the CJ point. Overdriven detonations 

were present at the exit for fill pressures 207 kPa (30 psia) and greater. Actuator A had 

CJ or overdriven wave speeds for fill pressures of 345 kPa (50 psia) and greater. 

Actuator C had strong detonations present at the throat, but the constant area throat 

extension weakened the wave by lowering its wave speed. 

When the constant area tube and the actuators are compared, the tube generates 

CJ detonations quicker than the actuators when no spiral is installed. The actuators are 

not capable of creating CJ detonations at any of the fill pressures tested; however, in 

some cases the pressure amplitudes are greater than in the tube. When a spiral is added to 

54
the actuators, they are capable of developing CJ detonations faster than the tube for 

certain initial fill pressures. The 207 (30) and 345 kPa (50 psia) cases both produced CJ 

detonations in less distance and time than required by the constant area tube. Therefore, 

the initial conditions must be considered when deciding whether the actuators perform

better than the constant area tube. 

It should be noted that the actuator shape was not optimized in this study. The 

three geometries that were found to work well in simulations were studied 

experimentally. The results show that actuators with increasing throat diameters may be 

more favorable. More studies will have to be completed to optimize the design of the 

actuator. 

The goal of this study was to obtain CJ detonations in the actuators and this was 

achieved with the help of the Shchelkin spiral. The results from the single shot 

experiments prove that the actuators are capable of producing CJ detonations or in some

cases overdriven detonations. A multicycle version needs to be developed so that the 

actuator can be tested in a high speed cross flow to determine its effectiveness in flow 

control. 

 

55
REFERENCES 

[1] Gad-el-Hak, E., Bushnell, D., “Status and Outlook of Flow Separation Control,” 

AIAA Paper 91-0037, Jan 1991. 

[2] Jacobs, J.W., James, R.D., Ratliff, C.T., and Glezer, A., “Turbulent Jets Induced by 

Surface Actuators,” AIAA Paper 93-3243, AIAA Shear Flow Conference, 1993. 

[3] McManus, K., Ducharme, A., Goldey, C., and Magill, J., “Pulsed Jet Actuators for 

Suppressing Flow Separation,” AIAA Paper 96-0442, Jan. 1996. 

[4] Funk, R., Parekh, D., Glezer, A., and Crittenden, T., “Transient Separation Control 

Using Pulse Combustion Actuation,” AIAA Paper 02-3166, June 2002. 

[5] Grossman, K.R., Cybyk, B.Z., and VanWie, D.M., “Sparkjet Actuators for Flow 

Control,” AIAA Paper 03-0057, Jan. 2003. 

[6] Beck, B.T., Cutler, A.D., Drummond, J.P., and Jones, S.B., “A Resonant Pulse 

Detonation Actuator for High-Speed Boundary Layer Separation Control,” 

Proceedings of the 11th International Symposium on Flow Visualization, August 

9-12, 2004. 

[7] Miller, D.N., Yagle, P.J., Bender, E.E., Smith, B.R., and Vermeulan, P.J., “A 

Computational Investigation of Pulsed Injection into a Confined Expanding 

Crossflow,” AIAA Paper 01-3026, June 2001. 

[8] Kanury, A.M., Introduction to Combustion Phenomena, Vol. 2, Gordan and Breach, 

New York, 1982. 

[9] Glassman, I., Combustion, Academic Press, Inc., New York, 1977. 

[10] Bussing, T.R.A., and Pappas, G., “An Introduction to Pulse Detonation Engines,” 

AIAA Paper 94-0263, Jan. 1994. 

56
[11] Hinkey, J.B., Bussing, T.R.A., and Kaye, L., “Shock-Tube Experiments for the 

Development of a Hydrogen-Fueled Pulse Detonation Engine,” AIAA Paper 95-

2578, July 1995. 

[12] Li, C., and Kailasanath, K., “Detonation Initiation in Pulse Detonation Engines,” 

AIAA Paper 03-1170, Jan. 2003. 

[13] Schauer, F., Stuturd, J., and Bradley, R., “Detonation Initiation Studies and 

Performance Results for Pulsed Detonation Engine Applications,” AIAA Paper 

01-1129, Jan. 2001. 

[14] Meyer, T.R., Hoke, J.L., and Brown, M.S., “ Experimental Study of DeflagrationTo-Detonation Enhancement Techniques in a H2/Air Pulsed-Detonation Engine,” 

AIAA Paper 02-3720, July 2002. 

[15] Shchelkin, K.L., Soviet Journal of Technical Physics, Vol. 10, pp. 823-827, 1940. 

[16] Urtiew, P.A., and Oppenheim, A.K., “Experimental Observations of the Transition 

to Detonation in an Explosive Gas,” Proc. Royal Society London, A291:13. 

[17] Gordon, S., and McBride, B.J., “Computer Program for Calculation of Complex 

Chemical Equilibrium Compositions, Rocket Performance, Incident and 

Reflecting Shocks, and Chapman-Jouguet Detonations,” NASA SP 273, 1971. 

[18] Lee, J.H., Knystautas, R., and Chan, C.K., “Turbulent Flame Propagation in 

Obstacle-Filled Tubes,” 20th International Symposium on Combustion, The 

Combustion Institute, Pittsburg, 1984, pp. 1663-1672. 

[19] Nettleton, M.A., Gaseous Detonations: Their Nature, Effects, and Control, 

Chapman and Hall, NY, NY, 1987. 

57
[20] Ting, J.M., Bussing, T.R.A., and Hinkey, J.B., “Experimental Characterization of 

the Detonation Properties of Hydrocarbon Fuels for the Development of a Pulse 

Detonation Engine,” AIAA Paper 95-3154, July 1995. 

[21] Drummond, J.P., “A Two-Dimensional Numerical Simulation of a Supersonic, 

Chemically reacting Mixing Layer,” NASA TM-4055, 1988. 

[22] Shapiro, A.H., The Dynamics and Thermodynamics of Compressible Fluid Flow, 

Ronald Press Company, New York, 1953. 

58
Figure 1. Simplified detonation actuator. 

59
1/ρ1

P1

V

III

IV

II

I

A

P2

J

Figure 2. The Hugoniot plot divided into five regions. 

60
Figure 3. Characteristic detonation profile in a constant area tube [10]. 

61
1⁄4 NPT Vent

1⁄4 NPT Fuel Supply

Figure 4. Detonation tube in initial and actuator configurations. 

62
Detonation Tube

Actuator

Electrodes

Signal Conditioner Pressure 

Gauge 

Figure 5. Detonation tube with an actuator installed. 

63
Pressure 

Taps Exit 

Inlet 

Figure 6. Detonation actuators. 

64
(a) Detonation Actuator A 

(b) Detonation Actuator B 

Figure 7. Simplified schematics of detonation actuators. 

65
(c) Detonation Actuator C 

Figure 7. Simplified schematics of detonation actuators, cont. 

66
Figure 8. Simplified schematic of the detonation tube facility setup. 

67
Figure 9. Simplified schematic of the initial and high-energy ignition systems. 

68
Wire Diameter = 

1.6 mm (.0625 in) Wire Diameter = 4.8 mm (.1875 in) 

Figure 10(a). Shchelkin spirals used in the actuators. 

69
Wire Diameter = 

1.6 mm (.0625 in) 

Figure 10(b). Shchelkin spirals used in the constant area tube. 

70
Al Tape Spiral 

Figure 11. Shchelkin spiral installed in a detonation actuator. 

71
Figure 12. Wave speeds for various mixing techniques. 

72
Figure 13. Pressure histories in the tube for a 103 kPa (15 psia) fill pressure 

73
Figure 14. Pressure histories in the tube for a 207 kPa (30 psia) fill pressure. 

74
Figure 15. Pressure histories in the tube for a 345 kPa (50 psia) fill pressure. 

75
Figure 16. Pressure histories in the tube for a 483 kPa (70 psia) fill pressure. 

76
Figure 17. Wave speeds in the tube for various fill pressures. 

77
Figure 18. Distance required for DDT versus fill pressure. 

78
0

0.20.40.60.8

1

1.21.40.00E+00 1.00E+05 2.00E+05 3.00E+05 4.00E+05 5.00E+05 6.00E+05

Fill Pressure, pa

Timeto transition toa detonation, ms

Figure 19. Time required for DDT versus fill pressure. 

79
Figure 20. Pressure histories in the tube with an equivalence ratio of 0.3. 

80
Figure 21. Pressure histories in the tube with an equivalence ratio of 0.5. 

81
Figure 22. Pressure histories in the tube with an equivalence ratio of 0.7. 

82
Figure 23. Pressure histories in the tube with an equivalence ratio of 0.9. 

83
Figure 24. Pressure histories in the tube with an equivalence ratio of 1.1. 

84
Figure 25. Pressure histories in the tube with an equivalence ratio of 1.3. 

85
Figure 26. Wave speeds in the tube for various equivalence ratios. 

86
Figure 27. Time required for DDT versus equivalence ratio. 

87
Figure 28. Pressure histories in the tube with an ignition energy of 0.025J. 

88
Figure 29. Pressure histories in the tube with an ignition energy of 0.25J. 

89
Figure 30. Pressure histories in the tube with an ignition energy of 2.5J. 

90
Figure 31. Pressure histories in the tube with an ignition energy of 5.0J. 

91
Figure 32. Pressure histories in the tube with an ignition energy of 10.0J. 

92
Figure 33. Pressure histories in the tube with an ignition energy of 15.0J. 

93
Figure 34. Wave speeds in the tube for various ignition energies. 

94
Figure 35. Pressure histories in the tube with a composition fraction of 0.25. 

95
Figure 36. Pressure histories in the tube with a composition fraction of 0.50. 

96
Figure 37. Pressure histories in the tube with a composition fraction of 0.75. 

97
Figure 38. Wave speeds in the tube for various composition fractions. 

98
Figure 39. Time required for DDT versus the composition fraction. 

99
Figure 40. Distance required for DDT versus composition fraction. 

100
Figure 41. Pressure histories in the tube at a 103 kPa (15 psia) fill pressure using a spiral. 

101
Figure 42. Pressure histories in the tube at a 207 kPa (30 psia) fill pressure using a spiral. 

102
Figure 43. Pressure histories in the tube at a 345 kPa (50 psia) fill pressure using a spiral. 

103
Figure 44. Comparison of wave speeds in the tube with and without a spiral. 

104
Figure 45. Pressure histories in actuator A with a 103 kPa (15 psia) fill pressure. 

105
Figure 46. Pressure histories in actuator A with a 207 kPa (30 psia) fill pressure. 

106
Figure 47. Pressure histories in actuator A with a 345 kPa (50 psia) fill pressure. 

107
Figure 48. Pressure histories in actuator A with a 483 kPa (70 psia) fill pressure. 

108
Figure 49. Wave speeds for each fill pressure case using actuator A. 

109
Figure 50. Pressure histories in actuator B with a 103 kPa (15 psia) fill pressure. 

110
Figure 51. Pressure histories in actuator B with a 207 kPa (30 psia) fill pressure. 

111
Figure 52. Pressure histories in actuator B with a 345 kPa (50 psia) fill pressure. 

112
Figure 53. Pressure histories in actuator B with a 483 kPa (70 psia) fill pressure. 

113
Figure 54. Wave speeds for each fill pressure case using actuator B. 

114
Figure 55. Pressure histories in actuator C with a 103 kPa (15 psia) fill pressure. 

115
Figure 56. Pressure histories in actuator C with a 207 kPa (30 psia) fill pressure. 

116
Figure 57. Pressure histories in actuator C with a 345 kPa (50 psia) fill pressure. 

117
Figure 58. Pressure histories in actuator C with a 483 kPa (70 psia) fill pressure. 

118
Figure 59. Wave speeds for each fill pressure case using actuator C. 

119
Figure 60. Exit wave speeds for each actuator at various fill pressures. 

120
Figure 61. Pressure histories in actuator A with an equivalence ratio=0.7. 

121
Figure 62. Pressure histories in actuator A with an equivalence ratio=0.9. 

122
Figure 63. Pressure histories in actuator A with an equivalence ratio=1.1. 

123
Figure 64. Pressure histories in actuator A with an equivalence ratio=1.3. 

124
Figure 65. Wave speeds for each equivalence ratio case using actuator A. 

125
Figure 66. Pressure histories in actuator B with an equivalence ratio=0.7. 

126
Figure 67. Pressure histories in actuator B with an equivalence ratio=1.3. 

127
Figure 68. Wave speeds for each equivalence ratio case using actuator B. 

128
Figure 69. Pressure histories in actuator C with an equivalence ratio=0.7. 

129
Figure 70. Pressure histories in actuator C with an equivalence ratio=1.3. 

130
Figure 71. Wave speeds for each equivalence ratio case using actuator C. 

131
Figure 72. Pressure histories in actuator A with spiral added at 103 kPa (15 psia). 

132
Figure 73. Pressure histories in actuator A with spiral added at 207 kPa (30 psia). 

133
Figure 74. Pressure histories in actuator A with spiral added at 345 kPa (50 psia). 

134
Figure 75. Pressure histories in actuator A with spiral added at 483 kPa (70 psia). 

135
Figure 76. Wave speeds using actuator A with spiral added. 

136
Figure 77. Pressure histories in actuator B with spiral added at 103 kPa (15 psia). 

137
Figure 78. Pressure histories in actuator B with spiral added at 207 kPa (30 psia). 

138
Figure 79. Pressure histories in actuator B with spiral added at 345 kPa (50 psia). 

139
Figure 80. Pressure histories in actuator B with spiral added at 483 kPa (70 psia). 

140
Figure 81. Wave speeds using actuator B with spiral added. 

141
Figure 82. Pressure histories in actuator C with spiral added at 103 kPa (15 psia). 

142
Figure 83. Pressure histories in actuator C with spiral added at 207 kPa (30 psia). 

143
Figure 84. Pressure histories in actuator C with spiral added at 345 kPa (50 psia). 

144
Figure 85. Pressure histories in actuator C with spiral added at 483 kPa (70 psia). 

145
Figure 86. Wave speeds using actuator C with spiral added. 

146
Figure 87. Pressure histories with a 4.8 mm (.1875 in) spiral installed in Actuator B at 103 kPa (1

147
Figure 88. Pressure histories with a 4.8 mm (.1875 in) spiral installed in Actuator B at 207 kPa (3

148
Figure 89. Pressure histories with a 4.8 mm (.1875 in) spiral installed in Actuator B at 345 kPa (5

149
Figure 90. Wave speeds in actuator B with 4.8 mm (.1875 in) spiral installed. 

150
. 

Appendix A 

Detailed Engineering Drawings 

151
Figure A1. Detailed engineering drawing of the detonation tube. 

152
Figure A2. Detailed engineering drawing of the 

modifications to the ignition end blind flang

153
Figure A3. Detailed engineering drawing of the detonation tube injection system. 

154
Figure A4. Detailed drawing of the electrodes and installation assembly. 

155
Figure A5. Detailed drawing of the three-electrode ignition system. 

156
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Contractor Report

 4. TITLE AND SUBTITLE

Development of an Actuator for Flow Control Utilizing Detonation

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Lonneman, Patrick J.; and Cutler, Andrew D.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center The George Washington University

Hampton, VA 23681-2199 Joint Institute for Advancement of

 Flight Sciences

 Langley Research Center, Hampton, VA 23681

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National Aeronautics and Space Administration

Washington, DC 20546-0001

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

 

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

Thesis by the first author to the Faculty of the School of Engineering and Applied Science, The George Washington University in partial 

fulfillment of the requirements for the Degree of Master of Science, October 2004. Langley Technical Monitor: J. P. Drummond

An electronic version can be found at http://techreports.larc.nasa.gov/ltrs/ or http://ntrs.nasa.gov

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Availability: NASA CASI (301) 621-0390

19a. NAME OF RESPONSIBLE PERSON

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14. ABSTRACT

Active flow control devices including mass injection systems and zero-net-mass flux actuators (synthetic jets) have been employed to delay 

flow separation. These devices are capable of interacting with low-speed, subsonic flows, but situations exist where a stronger crossflow 

interaction is needed. Small actuators that utilize detonation of premixed fuel and oxidizer should be capable of producing supersonic exit 

jet velocities. An actuator producing exit velocities of this magnitude should provide a more significant interaction with transonic and 

supersonic crossflows. This concept would be applicable to airfoils on high-speed aircraft as well as inlet and diffuser flow control. The 

present work consists of the development of a detonation actuator capable of producing a detonation in a single shot (one cycle). Multiple 

actuator configurations, initial fill pressures, oxidizers, equivalence ratios, ignition energies, and the addition of a turbulence generating 

device were considered experimentally and computationally. It was found that increased initial fill pressures and the addition of a turbulence 

generator aided in the detonation process. The actuators successfully produced Chapman-Jouguet detonations and wave speeds on the order 

of 3000 m/s.

15. SUBJECT TERMS

Detonations; Nozzles; Flow control; Actuators

18. NUMBER

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175

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01- 12 - 2004