investigation of pulse detonation engines; theory, design
TRANSCRIPT
Dissertations and Theses
Spring 2013
Investigation of Pulse Detonation Engines; Theory, Design and Investigation of Pulse Detonation Engines; Theory, Design and
Analysis Analysis
Jeff Vizcaino Embry-Riddle Aeronautical University - Daytona Beach
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INVESTIGATION OF PULSE DETONATION ENGINES; THEORY, DESIGN,
AND ANALYSIS
By
Jeff Vizcaino
A Thesis Submitted to the Graduate Studies Office in Partial Fulfillment of the Requirements for
the Degree of Master of Science in Aerospace Engineering
Embry-Riddle Aeronautical University
Daytona Beach, FL
iii
ACKNOWLEDGEMENTS
I would like to thank Dr. Magdy Attia for all the support, guidance, and education provided
through our interactions. Additionally I would like to extend my gratitude to Dr. William Engblom
and Dr. Eric Perrell for their assistance and support throughout my graduate career. Francisco
Romo, Darrell Stevens for their assistance and all my coworkers in the Embry-Riddle Gas Turbine
Lab. None of my work would have been possible without the tireless efforts of those mentioned
above.
iv
ABSTRACT
Author: Jeff Vizcaino
Title: Investigation of Pulse Detonation Engines; Theory, Design and Analysis
Institution: Embry-Riddle Aeronautical University
Degree: Master of Science in Aerospace Engineering
Year: 2012
Detonation and constant volume combustion has been known to the scientific community for some
time but only recently has active research been done into its applications. Detonation based
engines have received much attention in the last two decades because of its simple design and
potential benefits to the aerospace industry. It is then the goal of this study to provide a background
into detonation theory and application and establish the basis for future detonation based research
at Embry-Riddle Aeronautical University. In this paper we will discuss the experimental aspects
of building, testing, and analysis of a pulsed detonation tube including the development of a pulsed
detonation testbed and analysis via computational fluid dynamics.
v
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ..........................................................................................................................................iii
ABSTRACT iv
TABLE OF CONTENTS .............................................................................................................................................. v
LIST OF FIGURES ...................................................................................................................................................... ix
LIST OF TABLES...................................................................................................................................................... xiv
NOMENCLATURE .................................................................................................................................................... xv
1 PROBLEM STATEMENT ........................................................................................................................................ 1
2 BACKGROUND AND THEORY ............................................................................................................................. 2
2.1 Deflagration ...................................................................................................................................................... 2
2.2 Detonation ......................................................................................................................................................... 3
2.3 Chapman-Jouguet Condition ............................................................................................................................. 4
2.4 ZND Model ....................................................................................................................................................... 6
2.5 Detonation Waves ............................................................................................................................................. 9
Detonation Wave Formation ...............................................................................................10
Detonation Propagation .......................................................................................................10
2.6 Detonation Cells .............................................................................................................................................. 11
2.7 Thermodynamic Cycles .................................................................................................................................. 15
Humphrey Cycle ..................................................................................................................15
Fickett-Jacobs Cycle ............................................................................................................16
3 PULSE DETONATION ENGINE DESIGN CONSIDERATIONS ........................................................................ 19
3.1 Oxidizer and Fuel Selection ............................................................................................................................ 19
3.2 Detonation Initiation ....................................................................................................................................... 19
Spark Initiation ....................................................................................................................20
Deflagration to Detonation Transition (DDT) .....................................................................24
vi
Methods of Flame Acceleration ..........................................................................................26
Shchelkin Spiral ..................................................................................................................26
4 PRACTICAL APPLICATIONS OF DETONATION THEORY ............................................................................ 33
4.1 Overview ......................................................................................................................................................... 33
4.2 Existing Designs ............................................................................................................................................. 35
Valved Pulsed Detonation Engines .....................................................................................35
Valveless Pulsed Detonation Engines .................................................................................35
Rotating Detonation Engines (RDE) ...................................................................................36
5 NUMERICAL ANALYSIS ..................................................................................................................................... 38
5.1 Case Studies .................................................................................................................................................... 38
5.2 Validation Case 1: 1-Dimensional Detonation Propagation............................................................................ 39
5.3 Validation Case 2: 2-Dimensional Propagation .............................................................................................. 48
6 TEST EQUIPMENT AND METHODOLOGY....................................................................................................... 59
6.1 Experimental Method ...................................................................................................................................... 59
6.2 Experimental Hardware .................................................................................................................................. 59
7 EXPERIMENTAL RESULTS ................................................................................................................................. 65
7.1 Theoretical results ........................................................................................................................................... 65
7.2 Uncertainty ...................................................................................................................................................... 66
Calculation of Uncertainty ..................................................................................................66
7.3 Low Frequency Tube Testing ......................................................................................................................... 67
7.4 High Frequency Tube Configuration I Testing ............................................................................................... 71
Pressure Trends ...................................................................................................................71
Wavespeed Trends ..............................................................................................................74
7.5 High Frequency Tube Configuration II Testing .............................................................................................. 78
Results .................................................................................................................................78
vii
Detonation Performance ......................................................................................................82
Thermal Performance ..........................................................................................................87
Sound Levels .......................................................................................................................90
Observations & Issues .........................................................................................................91
8 Conclusions, Recommendations, and Guidelines for future studies ........................................................................ 94
8.1 Recommendations for Numerical Studies ....................................................................................................... 94
Chemical Kinetics ...............................................................................................................94
Adaptive Meshing ...............................................................................................................94
Possible applications and future studies ..............................................................................96
8.2 Recommendations for Experimental Studies .................................................................................................. 97
Filling & Purging .................................................................................................................97
Obstacle Configuration ........................................................................................................98
Sound Insulation and isolation ............................................................................................98
High Speed Digitizers .........................................................................................................99
Ion Sensing ..........................................................................................................................99
Possible applications and future studies ............................................................................100
9 REFERENCES ...................................................................................................................................................... 101
10 APPENDIX A: DETAILED EXPERIMENTAL SETUP ........................................................................... 107
10.1 Sensors and Instrumentation ......................................................................................................................... 108
10.2 Hardware ....................................................................................................................................................... 110
10.3 Data Acquisition and Instrumentation Wiring .............................................................................................. 113
10.4 Test Procedure............................................................................................................................................... 121
11 APPENDIX B: CALCULATION OF FILLING PARAMETERS ............................................................. 122
12 APPENDIX C: DRAWINGS AND DIAGRAMS ...................................................................................... 126
viii
13 APPENDIX D: RAW DATA & RESULTS................................................................................................ 148
ix
LIST OF FIGURES
Figure 1: Control volume used in CJ Model (4) 4
Figure 2: Hugoniot Curve for CJ Theory (4) 5
Figure 3: ZND vs. CJ properties 7
Figure 4: Physical properties of the 1-D Detonation Wave Structure 7
Figure 5: Soot image of detonation propagation (H2 + O2) (4) 9
Figure 6: Schematic of Detonation Cell 11
Figure 7: Soot foil device for visualization 12
Figure 8: Cell size vs. Equivalence Ratio (14) 14
Figure 9: PV diagram for Humphrey Cycle (1) 15
Figure 10: TS diagram for Humphrey Cycle (1) 15
Figure 11: PV diagram for Fickett-Jacobs Cycle (7) 16
Figure 12: FJ Thermal Efficiency (7) 16
Figure 13: Physical Steps that make up the Fickett-Jacobs Cycle (7) 17
Figure 14: Planar Detonation Wave through use of a Planar Initiator (9) 21
Figure 15: Cylindrical Detonation 21
Figure 16: Critical Energy vs. Equivalence Ratio (Tetryl: 4.2kJ/g) (10) 22
Figure 17: Critical Tube diameter vs. Equivalence Ratio (Dc = 13λ) (10) 22
Figure 18: Critical energy vs. Discharge time (11) 24
Figure 19: Critical Energy vs. Spark Gap Length (11) 23
x
Figure 20: Shchelkin Spiral Concept 26
Figure 21: Shchelkin Spiral after testing (18) 27
Figure 22: Dynamic Planar Initiator 30
Figure 23: Dynamic Toroidal Initiator 30
Figure 24: Chemiluminescence Images of Toroidal Initiator (9) 31
Figure 25: Crossover Detonation Tube Internal Configuration 31
Figure 26: Configuration of a typical thrust producing PDE (21) 33
Figure 27: Valveless PDE Design by Brophy et al. (24) 36
Figure 28: Valve-less PDE by Shimo & Heister (23) 36
Figure 29: Initial Conditions for Case 1 39
Figure 30: Expected ZND Profile for Case 1 41
Figure 31: Pressure Distribution for 1-D simulation 42
Figure 32: Peak Pressure Region for 1-D simulation 43
Figure 33: Temperature Distribution for 1-D Simulation 44
Figure 34: Peak Temperature Region for 1-D simulation 45
Figure 35: Pressure vs. Temperature in Peak Region for 1-D Simulation 45
Figure 36: Adaptive Meshing Grid 49
Figure 37: Initialization region for Case 2 49
Figure 38: Expected ZND Profile for Case 2 50
Figure 39: Pressure Wave Propagation separated by 100 s 51
Figure 40: Pressure vs. X Location for Case 2 at 50s intervals for constant Y = 0.14 52
Figure 41: Temperature vs. X Location for Case 2 at 50s intervals for constant Y = 0.14 52
xi
Figure 42: Comparison of data measurement locations for Case 2 54
Figure 43: Pressure vs. X Location for Case 2 at 50s intervals behind shock 55
Figure 44: Temperature vs. X Location for Case 2 at 50s intervals behind Shock 55
Figure 45: Numerical evaluation of cell sizes for Case 2 57
Figure 46: Cell size measurements and comparison for Case 2 57
Figure 47: Low Frequency Tube Setup 60
Figure 48: Ethylene Cell Size vs. Equivalence Ratio 61
Figure 49: High Frequency Tube Experimental Setup 62
Figure 50: Interior Geometry for High Frequency Tube 63
Figure 51: High Frequency Tube Overview 63
Figure 52: High Frequency Tube Measurement Section 64
Figure 53: High Frequency Tube Interior Obstacle Configuration 64
Figure 54: Injection plate for High Frequency Tube 64
Figure 55: Expected Range of Detonation Velocities 65
Figure 56: Expected Range of Detonation Pressures 65
Figure 57: Low Frequency Tube pressure traces with Ethylene gas 69
Figure 58: Low Frequency Tube pressure traces with Propane gas 70
Figure 59: Maximum Pressure vs. Fill percentage trends for configuration I 72
Figure 60: Maximum pressure vs. Pulsing Frequency trends for configuration I 73
Figure 61: Maximum Pressure vs. Equivalence Ratio trends for configuration I 74
Figure 62: Velocity vs. Fill Percentage trends for configuration I 75
Figure 63: Velcoity vs. Frequency trends for configuration I 76
xii
Figure 64: Velocity vs. Equivalence ratio trends for configuration I 77
Figure 65: Typical Deflagration Sensor Traces 79
Figure 66: Typical Detonation Sensor Traces 80
Figure 67: Detonation Sensor traces at 350KS/s 82
Figure 68: Combustion Sensor Mounting 82
Figure 69: Spark Plug Electrode uncertainty 82
Figure 70: Normal distribution of measured Deotonation pressures 83
Figure 71: Normal distribution of all measured Detonation Velocities 84
Figure 72: Normal distribution of measured Detonation Velocities from Pressure Transducers 85
Figure 73: Normal distribution of measured Detonation Velocities from Ion Sensors 86
Figure 74: Normal distribution of Detonation Transition Times 87
Figure 75: Temperature (F) Distribution along Detonation Tube after testing 88
Figure 76: Thermal Imaging of Detonation Tube Transition Section 89
Figure 77: Thermal Imaging of Detonation Tube Measurement Section 89
Figure 78: Sound Levels (dBa) during testing near Detonation Tube 90
Figure 79: Frozen condensation on Pressure Regulator 92
Figure 80: Long Electrode Spark Plug 93
Figure 81: Density Gradient vs. Density 95
Figure 82: Adaptive Meshing Control 96
Figure 83: Labview Virtual Instrument 113
Figure 84: Input Control Panel for LabView VI 114
Figure 85: Data logging and Timing Panel for LabView VI 115
xiii
Figure 86: Graph Output Panel 116
Figure 87: Fuel Control System 117
Figure 88: Spark Plug Ignition Control System 118
Figure 89: Mathscript Node for LabView VI 119
Figure 90: Ignition Control Wiring 120
Figure 91: Injector Wiring 120
Figure 92: Mass vs. Pulse Width curves for Propane 125
Figure 93: Mass vs. Pulse Width curves for Air 125
xiv
LIST OF TABLES
Table 1: Detonation vs. Deflagration properties burned/unburned gasses (2 p. 262) 3
Table 2: Typical Hydrocarbon Chapman-Jouguet Parameters (1 bar, 295K) 6
Table 3: Conditions for Validation Case 1 40
Table 4: CJ conditions for Case 1 40
Table 5: ZND Conditions for Case 1 40
Table 6: Wavespeed measurements for Case 1 44
Table 7: Numerical results comparison for 1-D simulation 46
Table 8: Initiation conditions for Case 2 49
Table 9: CJ Conditions for Case 2 50
Table 10: ZND Conditions for Case 2 50
Table 11: Post Detonation Conditions along X = 0.014 m 52
Table 12: Wavespeed measurements for Case 2 53
Table 13: Post Detonation Conditions behind Shock 55
Table 14: Wavespeed measurements and comparsion for Detonation and Deflagration 81
xv
NOMENCLATURE
Kj / mol
s-1
U(x) Uncertainty of variable x Varies
1
1 PROBLEM STATEMENT
Detonation combustion research has traditionally been limited to single shot pulses of detonations
utilizing highly reactive mixtures such as hydrogen and oxygen due to the difficulty of initiating
a detonation, however any practical implementation would require a nearly steady or continuous
flow exiting the combustion chamber and combined with the utilization of common aviation and
transportation fuels. Due to the supersonic nature of detonation waves, the entire combustion
region must be filled and mixed prior to detonation which effectively determines the maximum
rate at which a detonation can be repeated. In this quasi steady flow, a device downstream of the
flow will experience periodic bursts of high amplitude pressure waves followed by nearly zero
gauge pressure (in some cases a vacuum). To mitigate this effect it is then necessary to minimize
the periodic nature by increasing the detonation cycle frequency. A device downstream of the flow
would then see an ever increasingly steady flow. Increasing the detonation cyclic frequency
depends on three primary variables: filling time, detonation transition time, and purging time.
Filling time and purging time are directly influenced by the internal volume of combustion
chamber and how fast “uniform” mixing can be achieved. Detonation transition time on the other
hand is affected by internal geometry, fuel and oxidizer selection, initial spark energy and ambient
conditions. For these reasons detonation transition time has the largest impact on detonation cycle
time. It is then the intent of the research to identify the chief variables that govern detonation
transition and overall filling time in an effort to achieve quasi-steady flow for integration into
more advanced designs applicable to propulsion and shaft power.
2
2 BACKGROUND AND THEORY
Combustion can occur in two distinct modes, one is a deflagration and the other is detonation.
Each mode has its own characteristic behavior which differs radically in their respective final
thermodynamic states. Deflagration is typically what most people imagine when they think of
combustion and explosions; it is the subsonic, constant pressure consumption of reactants into
products resulting in a high temperature gas. A detonation is a violent supersonic combustion that
releases an incredible amount of energy in a rather short period. Detonation is commonly referred
to as knocking or pinging in traditional internal combustion engines and can lead to disastrous
consequences if left unchecked. In industrial situations, detonations can occur when gasses are
transported along extended lengths of pipes and can lead to accidental and sometimes fatal
explosions. In the aerospace industry however, the explosive power of detonations can be
harnessed for thrust or shaft power production.
2.1 Deflagration
Deflagration is the subsonic combustion of a fuel and oxidizer mixture usually producing a small
pressure drop with significant temperature increases. Deflagration can be modeled as an isobaric
process in most cases as the pressure loss that occurs during combustion is negligible. Deflagration
is typical in internal combustion engines (Otto and Diesel thermodynamic cycles) and aircraft
turbine engines (Brayton Cycle) and what is classically observed when a fuel and oxidizer is
ignited. The flame front or reaction usually propagates through its fuel mixture at a rate of nearly
1 m/s. If the combustion is confined to a closed volume, i.e. a cylinder, thermodynamics dictates
that there must be a corresponding increase in pressure from which mechanical work can be
extracted.
3
2.2 Detonation
Detonation is the supersonic ignition of a combustible mixture where a shock wave is fueled by
an exothermic (heat generating) reaction. Detonation waves propagate at supersonic speeds on the
order of 2000 m/s. Detonations, which are modeled as a constant volume combustion (Humphrey
and Fickett-Jacobs thermodynamic cycles) produce a higher thermal efficiency (1.3 -1.5 times)
than that of a constant pressure combustion cycle at an equivalent pressure ratio and thus can
result in a similar increase in fuel efficiency provided that other mechanical and related
efficiencies can be maintained (1). The formation and propagation of a detonation wave compresses
the gas ahead of it causing a dramatic increase in pressure and temperature after the combustion
process. This process can be described by the one dimensional Chapman-Jouguet theory and the
ZND model.
Shown in Table 1 is a list of the quantitative differences between detonations and deflagrations. A
subscript of “u” designates properties of the unburned gas and a subscript of “b” denotes properties
of the burned gas. One can see that the Mach number of the wave front ( ⁄ ) is much higher
for detonations than deflagrations (5-10 vs. 0.0001 - 0.03) a similar trend is shown for pressure,
temperature, and density.
Table 1: Detonation vs. Deflagration properties burned/unburned gasses (2 p. 262)
Table 5.1 Qualitative Differences Between Detonations and Deflagration in Gases
Usual magnitude of Ratio
Ratio Detonation Deflagration
Uu/Cua 5-10 0.0001-0.03
Ub/uu 0.4-0.7 4-16
Pb/Pu 13-55 0.98-0.976
Tb/Tu 8-21 4-16
1.4-2.6 0.06-0.25
aCu is the acoustic velocity in the unburned gasses. Uu/Cu is the Mach number of the wave.
4
2.3 Chapman-Jouguet Condition
Formulated by assuming that the detonation wave is steady, planar and one dimensional, the
Chapman-Jouguet (CJ) theory states that the flow behind the supersonic detonation wave travels
at sonic speed in reference to the combusted products, i.e. Mach 1 with respect to the gas mixture.
The CJ model has four main assumptions (3):
The detonation approaches a steady state.
The flow is laminar and one-dimensional.
The detonation products approach a state of chemical equilibrium some distance behind the
detonation front.
The detonation velocity is the minimum permitted by the conservation conditions.
Figure 1: Control volume used in CJ Model (4)
The CJ model uses a control volume surrounding a planar shock wave to determine the gas
dynamic properties after the wave from those before it. A Hugoniot relationship is used to
determine the region of possible solutions for a steady detonation wave. The information, plotted
on a P - diagram shown in Figure 2, is representative of these solutions. The dashed lines that
are tangent to Hugoniot curve represent the Rayleigh line and where they intersect is called the
Chapman-Jouguet point with the upper representing the detonative region and the lower
representing the deflagrative region.
5
Figure 2: Hugoniot Curve for CJ Theory (4)
The properties for the CJU point are as follows and are normally found through an iterative
calculation process. The CJ conditions can be easily calculated and plotted for most gasses using
the CEA (Chemical Equilibrium w/ Applications) program referenced in this research.
( )
(
)
(
)
( )
Where √
√
and ( )
6
Table 2 below shows some sample data for hydrogen, ethylene and propane. On average, air-fuel
mixtures produce a significantly lower pressure and temperature ratio as well as lower detonation
velocities when compared to oxygen-fuel mixtures although both result in pressure and
temperature ratios ten or more times greater than ambient conditions.
Table 2: Typical Hydrocarbon Chapman-Jouguet Parameters (1 bar, 295K)
Mixture P/P1 T/T1 /1 MCJ UCJ (m/s)
Hydrogen-Air (H2) 15.8 10 1.8 4.9 1965
Methane-Air (CH4) 17.4 9.4 1.8 5.1 1800
Propane-Air (C3H8) 18.4 9.6 1.8 5.3 1796
Ethylene-Air (C2H4) 18.5 9.6 1.8 5.3 1821
Acetylene-Air (C2H2) 19.3 10.6 1.8 5.4 1864
Hydrogen-O2 (H2) 19.0 12.5 1.8 5.3 2836
Methane-O2 (CH4) 29.6 12.6 1.9 6.8 2390
Ethylene-O2 (C2H4) 33.8 13.3 1.9 7.3 2374
Acetylene-O2 (C2H2) 34.2 14.3 1.8 7.4 2426
Propane-O2 (C3H8) 36.6 13 1.9 7.7 2357
2.4 ZND Model
The Zel’dovich-von Neumann-Döring model features a shock wave traveling at the Chapman-
Jouguet (CJ) velocity followed by a thin reaction zone. The conditions behind the leading shock
wave differ from the CJ final equilibrium conditions in that the pressure and density are much
7
higher than that of a CJ detonation wave while temperature tends to be much lower. The ZND
structure is shown quantitatively in Figure 4.
P/P1 T/T1 /1
Hydrogen-Air (ZND) 27.4 5.1 5.4
Hydrogen-Air (CJ) 15.8 10.0 1.8
Figure 3: ZND vs. CJ properties
Figure 4: Physical properties of the 1-D Detonation Wave Structure
The planar shock wave brings the gas to the post-shock, or von Neumann, state followed by a
planar wave. The ZND model assumes that the flow is one-dimensional, and models the shock
wave as a discontinuity, neglecting transport effects (diffusion, conduction, etc.). Zel’dovich, von
Neumann, and Döring proposed that the detonation wave could be viewed as three distinct regions
8
whose widths are dependent on the mixture equivalence ratio and the chemical kinetics of the gas
mixture in which the detonation wave is propagating.
The first region, the shock wave, has a width of just a few tenths of a nanometer, yet delivers a
tremendous amount of energy into the unburned reactants. This energy input results in immediate
and dramatic increases in pressure, density and temperature that increase the chemical reaction
rates and enhance the energy release phase of the wave structure.
The deflagration region consists of two zones that dictate the final conditions of detonation wave.
The first, which is known as the induction zone, is the region in which the chemical reaction rates
are insignificant and have not produced an appreciable change in thermodynamic state. The
induction zone transitions to the reaction zone when the reaction rate begins to increase
exponentially, drastically raising temperatures while stabilizing pressure and density to their final
equilibrium value. The total width of the three zones is on the order of a few centimeters and
varies with fuel type and fuel equivalence ratio. Each zone is dependent on the previous zone
ahead of it to sustain the detonation wave.
9
2.5 Detonation Waves
In a self-sustaining detonation, the shock and reaction zone propagate with a nearly identical speed
that is approximated by the Chapman-Jouguet (CJ) theory. The ZND theory is often used to
represent the one dimensional detonation structure although in reality its structure is anything but.
The detonation wave has a complex 3D structure which is the result of transverse shock waves
that propagate behind the leading normal shock wave. The intersection of the transverse waves
with the leading normal shock wave results in localized high-pressure, high-temperature regions
known as triple points (Figure 6). The extreme heating that occurs at these points greatly accelerate
the local reaction rates and ensures that the heat release region is closely coupled to the leading
normal shock wave. The rapid oscillation of the triple points across the leading shock wave
promotes the stability of the detonation wave and results in the characteristic “fish scale” patterns
(5) that can be seen on soot images and walls of detonation tubes.
Figure 5: Soot image of detonation propagation (H2 + O2) (4)
10
Detonation Wave Formation
In the instant immediately preceding the onset of a detonation wave, a detonation kernel (a
miniature explosion) occurs, which cause a blast wave that accelerates the local reaction rate and
leads to the formation of an unstable detonation wave. This explosion can either occur as an
interaction between the leading shock and the flame, at the flame front, at the shock front, or at
the merging of shock waves that precede the flame. The occurrence of a localized explosion
generates a strong shock wave travelling back through the burnt reactants, referred to as a
retonation wave which can in some case reflect and merge with the leading shock front. If the
initial shock wave is strong enough then the accompanied rise in temperature may be able to
trigger auto ignition behind the shock front. Once the auto ignition has occurred a stable detonation
can be formed in which the shock waves are sustained by the energy of the chemical reaction that
has been initiated by shock compression and heating.
Detonation Propagation
Detonation propagation in a confined tube will continue as long as there is enough unburned
reactants ahead of it and no radical geometry changes occur. Detonation waves expanding abruptly
into a large area however behave differently than those propagating in confined spaces. When a
detonation wave propagates from a confined tube into an unconfined space, it has to overcome the
sharp corners and one of three outcomes occur. In the supercritical regime, detonations
successfully transmit into the unconfined space when the energy release rate overcomes the effects
of the expansion waves. The subcritical regime is where a complete detonation failure occurs as
the shock decouples from the reaction zone and the detonation continues as a shock wave followed
by a deflagration. The critical regime is seen to occur when the detonation wave initially fails but
detonation wave re-initiation is observed due to shock interactions produced by the transverse
waves travelling through the mixture. (6)
11
2.6 Detonation Cells
Figure 6: Schematic of Detonation Cell
A detonation wave form cells as it travels leaving behind the characteristic "fish scale" pattern
seen in Figure 5. These are formed by the oscillations of the triple point region occurring between
the leading shock and the transverse waves. Figure 6 above is a depiction of that pattern with
major features labeled. The cell width is the maximum distance between triple points and is
representative of the sensitivity of the mixture to detonation. Mixtures with small cell widths are
more sensitive and likely to detonate than mixtures with larger cell widths. The cell width of a
mixture is generally determined experimentally through the use of soot foil traces like in Figure
7, laser shadowgraphs, or schlieren photographs.
12
Figure 7: Soot foil device for visualization
The cell size can be approximated by the formula where is the induction zone length and
is an empirical proportionality constant. The proportionality constant varies strongly with the
equivalence ratio, between 10 and 50 for common fuel-air mixtures at stoichiometric conditions,
and between 2 and 100 for off-stoichiometric mixtures. The cell size of a mixture increases with
decreasing initial pressure and increases with lower oxygen mass fraction which in turn makes
fuel-air mixtures less sensitive than fuel-oxygen mixtures. A plot of cell size vs. equivalence ratio
exhibits a U-shaped curved typical of many detonation trends and is shown in Figure 8. In
descending order of detonation sensitivity (lowest to highest cell size):
1. C2H2 (acetylene)
2. H2 (hydrogen)
3. C2H4 (ethylene)
4. C3H8 (propane)
13
5. C2H6 (ethane)
6. C4H10 (butane)
7. CH4 (methane)
Many of the “dynamic parameters” of detonations are largely affected by the cell size and because
it is one of the most readily observable aspects of the wave, it is used in empirical relations for
critical tube diameter, critical energy and minimum tube diameter. As a general rule it is necessary
to have a minimum tube diameter on the order of 1/3 the cell width for air fuel mixtures
propagation unimpeded and at least 1 cell with for obstacle filled tubes.
14
Figure 8: Cell size vs. Equivalence Ratio (14)
15
2.7 Thermodynamic Cycles
Typical internal combustion engines and gas turbine engines use constant pressure combustion
cycles. Detonations are attributed with an increase in pressure during combustion while
maintaining a constant volume. The Humphrey cycle and Fickett-Jacobs cycle both model
detonations as a constant volume combustion process but differ in overall thermal efficiency and
theoretical work output.
Humphrey Cycle
The Humphrey cycle is generally the most frequently used to estimate the thermal efficiency of a
PDE because it is essentially the Brayton cycle modified for a constant volume compression
process. Shown below in Figure 9 and Figure 10 are the PV and TS diagrams for the Brayton and
Humphrey cycles.
An ideal Humphrey cycle with states 0-1-2-3-0 can be divided into the following segments:
(0-1) Compression
(1-2) Detonation
(2-3) Expansion
(3-0) Exhaust
Figure 9: PV diagram for Humphrey Cycle (1)
Figure 10: TS diagram for Humphrey Cycle (1)
16
Humphrey Cycle Thermal Efficiency (
) [
( )
( )
] (1)
Brayton Cycle Thermal Efficiency ( )
Referencing the preceding equations one can notice that the difference between the Humphrey
and Brayton thermal efficiencies is a single group of terms which is always less than one leading
to the conclusion that for equivalent ratios of temperature and specific heat a Humphrey Cycle
will always have a higher thermal efficiency.
Fickett-Jacobs Cycle
The FJ cycle is based on the piston-cylinder analogy used commonly in thermodynamics and
based on the works of Fickett and Davis in "Detonation Theory and Experiment" and Jacobs in
"The Energy of Detonation". It dictates the
Figure 11: PV diagram for Fickett-Jacobs Cycle (7) Figure 12: FJ Thermal Efficiency (7)
From reference (7) the thermal efficiency of the cycle is:
17
[
(
)
]
Where √ √ and ( )
Figure 13: Physical Steps that make up the Fickett-Jacobs Cycle (7)
18
1. The cycle starts with the system at the initial state. (State 1).
2. Reactants are isentropically compressed. ⁄ . (State 2).
3. External work to move the piston on the left at velocity up instantaneously initiates a
detonation front at the piston surface.
4. Detonation propagates to the right and the detonation products following the wave are in a
uniform state at a velocity up. (State 3).
5. Energy of this mechanical motion is converted to external work (step e) by adiabatically
and reversibly bringing the detonation products to rest maintaining the distance between
the two pistons. (State 4.)
6. Then the products are isentropically expanded to the initial pressure. (State 5).
7. Heat is extracted by reversibly cooling the products at constant pressure. (State 6).
8. Cycle is completed by converting products (State 6) to reactants (State 1) at constant
temperature and pressure.
19
3 PULSE DETONATION ENGINE DESIGN CONSIDERATIONS
3.1 Oxidizer and Fuel Selection
Selections of a fuel and oxidizer affect net thrust or work produced by a PDE cycle due to the
large variation in detonation velocities, compression ratios, and temperatures produced by various
types of fuels. It is typically best to use gaseous form reactants because of their lower detonation
energy requirements although liquid fuels can be used if atomized prior to ignition. Even after
atomization though, liquid fuels would require more power from a direct ignition system or a
longer deflagration-to-detonation transition section. As shown in Figure 8, Figure 16 and
Figure 17, there is a strong dependence on stoichiometric ratio for cell size, initiation charge, and
critical tube diameter. It is thus important to ensure stoichiometric or near stoichiometric fuel
balances entering the combustion chamber.
3.2 Detonation Initiation
Detonation initiation is currently one of the most critical problems in contemporary PDE
development. Initiation of a detonation requires significantly more input energy than that of
deflagration. For detonations there exists a critical initiation energy for which it is the smallest
amount of energy deposition that will cause a direct initiation of a detonation.
A detonation will be initiated if the energy release couples with the generated shock waves. If
energy release occurs too far behind the shock wave or if the shock waves are weak, a detonation
will not be initiated and result in a deflagration with modest pressure increases. There are generally
two types of initiation modes, direct initiation and detonation transition. Direct initiation is usually
20
caused by blast waves created by rapid energy addition either from the discharge of solid or
gaseous explosives, exploding wires or high energy spark discharges. Detonation transition is
usually carried out by means of flame acceleration via obstacle-wave interaction.
Spark Initiation
Many experimental direct initiation tests are conducted through the use of solid explosives and are
based on the equivalent mass of explosive tetryl (C7H5N5O8) with a blast energy value of 4.2
MJ/kg. Varying the amount of explosive material can then be used to equate the energy required
for direct ignition to other methods of initiation. For "sensitive mixtures" like ethylene the required
energy can be in the tens of kilojoules and less sensitive mixtures can scale up to the hundreds or
even thousands of kilojoules. Direct initiation of detonation then can require very large power
input for high cycle frequencies.
Confinement by tubes or channels will decrease the critical energy required since blast waves
decay more slowly when compared to unconfined cases. Increasing initial pressure or temperature
will also slow the decay and reduce critical energy requirements. Experimental result have shown
that critical initiation energy is observed to scale as follows (8):
Increase with the cube of the induction zone length (l) or detonation cell width ( ) for
spherical geometry.
Increase with the square for cylindrical geometry
Increase linearly for pseudo-planar geometry
21
Spherical detonations are typically encountered when using spark ignitions sources, cylindrical
with exploding wire discharges, and planar when using a planar detonation initiation device.
Figure 14: Planar Detonation Wave through use of a Planar Initiator (9)
Figure 15: Cylindrical Detonation
In detonation transition, a detonation wave can be created either by deflagration-to-detonation
transition (DDT) or shock-to-detonation transition (SDT). DDT employs the use of obstacles in
the path of combustion wave to accelerate it to CJ velocity. SDT uses directed or focused
shockwaves along with obstacles to initiate a detonation wave. Detonation transition generally
requires a large pre-detonation section or transition section for a self-sustaining wave to form and
can be impractical for many applications.
22
In general, detonation initiation (direct or through transition) is sensitive to the following
conditions:
Detonation Cell Size ( A function of the fuel and oxidizer combination)
Initial Temperature
Initial Pressure
Geometrical cross-sectional area
Wall porosity
Figure 16 and
Figure 17 following show a characteristic U-shaped dependence on equivalence ratio for
detonation energy and critical tube diameter.
Figure 16: Critical Energy vs. Equivalence Ratio
(Tetryl: 4.2kJ/g) (10)
Figure above using spherical strong blast theory;
( )
Figure 17: Critical Tube diameter vs. Equivalence
Ratio (Dc = 13λ) (10)
23
Spark ignition
Direct initiation is typically instigated by means of spark ignition or other electrical discharge.
The igniter must be able to initiate a detonation wave before the shockwave decays. If the spark
energy is below the critical energy, the blast wave generated will eventually separate from the
reaction front and decay into a sound wave resulting in an ordinary deflagration. In Lee’s
“Initiation of Gaseous Detonation” (11) he noted that the “critical energy decreases with the
duration of the energy release” and “only the energy released before the igniter attains maximum
power is important in the initiation process”. One reason he is cited for these observations was
that “for very small electrode spacing, the losses to the electrodes become important, and the
critical energy sharply [increases] to compensate for the losses.” These conclusions can be seen in
Figure 18 and Figure 19 below.
Figure 19: Critical Energy vs. Spark Gap Length (11)
24
Figure 18: Critical energy vs. Discharge time (11)
Calculation of the direct initiation is very much an empirical science and while formulas do exist,
many still rely on equipment, specific data and correlations to predict critical initiation energy.
Traditionally, empirical equations are used to predict the general magnitude of the energy required
(100 J, 101 J, 102 J, etc.) and then experiments are carried out to determine whether or not
detonation was successful. One formula as described by Radelescu (12) is shown in the next
section. Detailed critical energy data can be found online via the web at California Institute of
Technology Explosion Dynamics Laboratory’s (EDL) homepage (13).
Deflagration to Detonation Transition (DDT)
In some situations the energy required for direct initiation of detonation may be prohibitively high.
This can be due to large combustion chamber sizes, particularly insensitive fuel choices, very low
temperature conditions, or low pressures. Deflagration-to-detonation transition (DDT) and shock-
to-detonation transition (SDT) are two methods commonly employed to achieve the detonation
with significantly reduced energy requirements. In some cases an overdriven detonation wave,
one that propagates at a speed greater than the speed of a CJ detonation wave, can also be used to
reduce the critical diameter requirement needed for successful transition of a detonation wave
from a tube of small diameter to a tube of larger diameter. (14)
Critical conditions for DDT require that the cell width be smaller than a specified fraction of the
tube or obstacle dimensions, the expansion ratio (ratio of burned to unburned gas volume) must
be larger than a minimum value, and that the deflagration speed exceed a minimum threshold. For
simple situations, transition to detonation is possible only if the detonation cell width is smaller
25
than the tube diameter (unobstructed tube) or smaller than the obstacles' aperture (obstructed tube).
For a successful transfer of a detonation wave from one section to a larger or essentially
unconfined volume, there exists a critical tube diameter which is generally accepted to be on the
order of thirteen times the detonation cell width (13λ), (though in some cases it can be higher).
In DDT a subsonic combustion wave (deflagration or flame) is accelerated to a supersonic
combustion wave (detonation). The DDT process can be divided into four phases as described in
(15):
Deflagration initiation - A relatively weak energy source such as an electric spark is used to
create a flame.
Flame acceleration - Increasing energy release rate and the formation of strong shock waves
are caused by flame acceleration.
Formation and amplification of explosion centers - One or more localized explosion centers
form as pockets of reactants reach critical ignition. The explosion centers create small blast
waves which rapidly amplify in the surrounding mixture.
Formation of a detonation wave. The amplified blast waves and existing shock-reaction
zone complex merge into a supersonic detonation front which is self-sustaining.
26
Methods of Flame Acceleration
The exact physics of flame acceleration are unknown yet recent work into studying detonation
transitions has yielded a new explanation of the role that obstacles play in flame acceleration.
Simulations from (16) and (17) showed that the deflagration propagates along the unobstructed
center of the orifice plates leaving the mixture between orifice plates untouched near the wall. Gas
expansion due to delayed burning in the pockets produces a jet flow in the unobstructed part of
the tube. This jet flow allows the flame tip to propagate faster which then produces new pockets
and creates a chain reaction leading to flame acceleration. The simulation also showed a strong
reduction in the acceleration rate with higher initial flow Mach numbers and mitigation of flame
acceleration was observed as soon as the flame speed became comparable to the gas speed of
sound.
Shchelkin Spiral
Figure 20: Shchelkin Spiral Concept
27
The Schelkin spiral named after Russian physicist Kirill Ivanovich Shchelkin proposed in "Gas
Dynamics of Combustion". The effectiveness of the spiral is based on its blockage ratio which is
the area of the cross section cover by spring divided by total internal area of cross section.
Figure 21: Shchelkin Spiral after testing (18)
The Aerodynamic Research Center (ARC) at the University of Texas at Arlington tested pulse
detonation equipment to produce thrust utilizing Shchelkin spirals of different dimensions and in
tubes of different lengths to measure its effectiveness. Tables of the experiments and graphs of the
results can be found in (18). As a result, it was concluded that shorter PDEs, which can run at
higher frequencies due to their shorter filling times, may use shorter Shchelkin spirals with higher
BRs to achieve detonations. Longer PDEs, which have higher filling times and hence can’t run at
higher frequencies, can achieve successful detonation using spirals with smaller BRs and
increased lengths. (18)
According to Kuhl, Leyer and Borisov, the mechanism by which transition was facilitated was
credited to the generation of turbulence by the obstacles, promoting flame acceleration by
increasing the surface area of the flame front. However, more recent experiments have
demonstrated that it is due to the effect of pressure waves generated by the obstacles rather than
turbulent flame wrinkling. Shchelkin spirals when inserted into PDEs causes a reduction in the
efficiency of exhausting the burnt gas and introducing new the fresh mixture. Furthermore, these
28
obstacles are generally attached to the tube walls and are thus not suitable for large-diameter tubes
where the delay in development of turbulence causes a reduction in flame acceleration. Practical
implementation of these devices is also limited as reconfiguring obstacle geometry is difficult and
time consuming and have limited lifespans as demonstrated in Figure 21.
Orifice Plates
Similar to the Schelkin spiral, orifice plates introduce flow blockage cause turbulence and pressure
perturbations that can trigger a transition to detonation. Orifice plates have the advantage of being
much more resilient than spirals. In general orifice plates can be of stronger construction while
maintaining the same blockage ratio, additionally spacing and inner diameter are much easier to
modify than schelkin spirals. It is for these reasons that most recent detonation transition studies
utilize series of orifice plates to induce a detonation wave.
Pre-Detonator
Another common approach for detonation involves the utilization of an “initiator” which contains
a highly detonable fuel/oxygen mixture to generate a strong detonation that propagates into a less
sensitive mixture. Another reason to have a pre-detonator is to use fuels that are already regulated
and accepted in the industry but do not easily detonate. However the use or onboard storage of
highly reactive gases is prohibited or impractical in many situations.
29
Initiators or pre-detonator units work as follows: a deflagration is initiated in a small-diameter
detonation chamber usually filled with a fuel-oxygen mixture which then undergoes a rapid
transition to detonation. The detonation wave then exits from the small chamber into a larger
diameter filled with a less sensitive mixture. If the new diameter is larger than the critical tube
diameter of the mixture or roughly 13 times the cell width than a stable detonation wave will
continue to propagate in the larger tube or reinitiate itself farther down the tube.
Transient Plasma Ignition (TPI)
In TPI, a pseudo-spark discharges in tens of nanoseconds time scale to generate a power blast
wave that will detonate highly insensitive mixtures when used in conjunction with DDT. The
amount of power required though makes this method more impractical than a direct spark ignition.
The transient plasma pulse generator outlined in (19) was designed to deliver pulses of 70 kV to
100 kV with currents ranging between 450 A and 600 A, all within 50 to 100 nanoseconds.
Results from (19) showed that the TPI system was more effective than conventional spark ignition
systems resulting a nearly 20% improvement in DDT distances and up-to 2.5 reduction factor in
DDT times. In addition, at high flow rates, where the flames normally extinguished itself using
the spark ignition system, the TPI system was able to ignite mixtures and effectively initiate
detonation waves. Detonation initiation success rates greater than 94% were obtained at cycle
frequencies of up-to 40Hz. (19)
Shock to Detonation transition (SDT)
Shock to detonation transition (SDT) uses shock wave focusing to create a region of high pressure
and temperature that is capable of initiating insensitive fuel-air mixtures. In shock wave focusing,
30
this high-energy density region is generated by a converging wave or by the collision of two or
more shock waves (20). Two examples are shown below, a planar initiator and toroidal. The planar
concept is more or less a proof of concept device while the toroidal is an advanced implementation
of the planar concept. One can notice that the toroidal initiator is simply a planar initiator with its
pattern around a cylinder.
Figure 22: Dynamic Planar Initiator
Figure 23: Dynamic Toroidal Initiator
The toroidal initiator works by first filling it with a detonable mixture and then igniting by a
relatively weak spark (mJ). The ignited gas / flame front undergoes DDT carried out by a series
of miniature obstacles that result in the creation of a detonation wave. The detonation wave is
directed through the channels then deflected inward toward the test section where the wave
continues to propagate as an imploding detonation wave (see Figure 24 below) similar to the
predetonator.
31
Figure 24: Chemiluminescence Images of Toroidal Initiator (9)
Crossover Branching
Figure 25: Crossover Detonation Tube Internal Configuration
32
Detonation branching via crossover tube is a setup in which a propagating detonation initiated in
the donor tube via the methods mentioned above and transferred to the receiving tube through a
small crossover tube. In this setup both tubes have a stable detonation wave propagating towards
the end of the tube at slightly delayed intervals.
33
4 PRACTICAL APPLICATIONS OF DETONATION THEORY
4.1 Overview
Figure 26: Configuration of a typical thrust producing PDE (21)
Pulse detonation engines (PDE) operate through the use of supersonic combustion rather than
subsonic combustion of its fuel. The speed of combustion refers to the speed of flame propagation
through a combustible mixture. Pulse Detonation engines have gained much appeal in recent
years, particularly in the aerospace field where simplified mechanical operation and lower
operational weight have been the principal motivators. The majority of research into detonation is
being conducted by universities under direct funding from government agencies such as the
Department of Energy (DOE), and the military (USAF, Navy). Applications in aerospace
propulsion have thus far operated on the basis of cyclic detonation of fuel and air to produce thrust.
A detonation based engine has the potential to create high compression ratios (~15-20) from
combustion alone without the use of rotary blades or moving pistons, while simultaneously using
less fuel. Because of this, applications in other areas such shaft power production and supersonic
combustors for scramjet vehicles, show promise as well. Currently, there are no production
vehicles or engines in use today, with the exception of a modified Rutan Long-EZ with an
operating frequency of 80 Hz that flew for 10 seconds under its own power at a height of 100 ft.
and produced 200 lbf of thrust.
34
A typical setup as shown in Figure 26 involves the use a cylindrical tube to serve as the combustion
chamber, fuel and oxygen feed lines and an ignition source. A typical detonation cycle is as
follows: (1)
The detonation combustion chamber is filled with an oxidizer/fuel mixture. This is typically
air (or oxygen) for the oxidizer and fuel is generally a simple hydrocarbon based fuel (CH4,
C2H2, C3H8, JP10, etc.)
Detonation is initiated at the ‘closed’ end of the combustor by some method.
The detonation wave propagates through the combustor and exits and the open end.
The burned gases in the combustor are exhausted.
Pulsed detonation Engines are cyclic in nature which means that the process is characterized as
unsteady and its performance and efficiency are dependent on its operating frequency, or the
number of pulses per second. In general, higher thrust and energy are produced at higher operating
frequencies. The maximum operating frequency is determined by the time necessary for the
engine to complete the detonation process laid out above. Most advanced research PDE’s operate
in the range of 50-100 Hz or 10-20 ms per cycle (22) using oxygen. The specific cycle time is
determined by the mechanical properties of the device (how fast purge air can be introduced,
mixing times, detonation method, etc.) and the chemical properties of the oxidizer and fuel
combination (critical detonation energy, detonation velocity, etc.).
35
4.2 Existing Designs
Valved Pulsed Detonation Engines
Of the test engines in development today, many of them fall in to the category of using a valved
thrust wall. That is to say that when detonation is initiated, one end of the combustion chamber is
closed while the other is open. The valved design simplifies the combustion process because a
simple rotary plate or solenoid can be used to shut off flow of the reactants to the combustion
chamber, completely prevent back flow and acting as a thrust wall. A drawback of a valved design
implementation is that its simplified operation also limits the maximum effective cycle frequency,
as many mechanical parts may not be able to operate at the higher frequencies necessary for
commercial applications of PDEs. In addition, longevity and durability are also an issue as any
valved system will generally take the full force of the detonation wave expansion when acting as
the thrust wall.
Valveless Pulsed Detonation Engines
The primary issue with any valve-less design is to effectively minimize or prevent back flow when
detonation is initiated. Two experimental designs are shown below utilizing different schemes for
valveless operation; Brophy’s method employed the use of ‘sufficiently high’ air pressure and a
choke point located somewhere within the isolator section to prevent blast waves from propagating
backward. Shimo and Heister successfully used what they called a ‘fluid diode’ which “emulates
an aerodynamic check valve providing the lowest possible resistance to inflow and the highest
possible resistance to backflow.” (23)
36
Figure 27: Valveless PDE Design by Brophy et al. (24)
Figure 28: Valve-less PDE by Shimo & Heister (23)
Rotating Detonation Engines (RDE)
37
The rotating detonation engine is fundamentally different from traditional detonation engines in
that is does not rely on pulsed combustion but rather a continuously rotating detonation wave. In
this setup fuel and oxidizer are injected axially into the chamber and ignited by a detonation wave
travelling circumferentially around the core section. The design shown above currently in testing
by the Air Force Research Laboratory uses a modular design in which each individual section can
be varied to suit different fuel / air configurations and filling methods. The oxidizer spacer height
and number of injection ports can be varied to control the mass flow rate of air / oxygen delivered.
The fuel injection plate can have the size, number, and array of fuel inlet holes varied to control
overall mass flow rate. Finally, the center body can be swapped for different size diameters to
control the channel width to accommodate varying cell sizes of different fuels. This configuration
has the ability to provide continuous detonation level pressure at the exhaust if a stable detonation
can be maintained. A detonation still has to be initiated externally and then directed into the
channel but does not require continuous pulsing.
38
5 NUMERICAL ANALYSIS
5.1 Case Studies
Several numerical analyses were performed on detonation phenomena to gauge the current
capabilities of commercial computational fluid dynamics solvers. ANSYS Fluent software has
been chosen for use in the following studies because of its robustness, scalability, and availability,
at the time of writing the latest version is ANSYS Fluent 14.0. Two case studies are used to verify
the software’s capability, a 1-Dimensional analysis and a 2-Dimensional Analysis. A 3-
Dimensional simulation was not performed due to computational cost and limited resources
available. The end results of these validation studies are to provide the basis for simulating
detonation events in innovative and unconventional types for qualitative analysis.
39
5.2 Validation Case 1: 1-Dimensional Detonation Propagation
Based on reference (25), “Numerical Investigation of Detonation in Premixed Hydrogen –Air
Mixture- Assessment of Simplified Chemical Mechanisms” and simulates a lean hydrogen air
mixture propagation through an open ended tube. The main objective of the 1-D simulation was
to determine if ANSYS Fluent was able to accurately calculate CJ and ZND detonation conditions
using simplifying assumptions. The grid is setup as a uniform structured grid with 10-4 meter
spacing and divided in two flow domains. An initial thin region of reacted gases is patched near
the left closed end to initiate the detonation wave and a lean mixture of hydrogen and air is
initialized in the remainder of the tube for detonation propagation. The lean mixture was chosen
because of its effect on increasing the induction zone length and trying to resolve the ZND
conditions of the detonation wave. The condition for both regions are shown below in Table 3 and
Table 4. All solid boundaries were set as adiabatic walls with the outlet set as a standard pressure
outlet with one atm absolute back pressure. To compare to with CJ detonation theory, turbulence
modelling was set to laminar. The reaction set was chosen to be a global one step mechanism to
save computational resources.
Figure 29: Initial Conditions for Case 1
40
Setup and initialization
Table 3: Conditions for Validation Case 1
Initial Conditions (Unburned Gas)
1 atm Initial Pressure
298 K Initial Temperature
1.314 % H2 Mass Fraction
22.99 % O2 Mass Fraction
75.69 % N2 Mass Fraction
0.000 % H2O Mass Fraction
Initial Conditions (Ignition Region)
30 atm Initial Pressure
3000 K Initial Temperature
0 H2 Mass Fraction
0 O2 Mass Fraction
0 N2 Mass Fraction
1 H2O Mass Fraction
Table 4: CJ conditions for Case 1
Chapman-Jouguet Detonation Conditions (CJ)
P2/P1 11.05 Pressure Ratio
T2/T1 6.95 Temperature Ratio
UCJ 1556.7 m/s Detonation Velocity
Table 5: ZND Conditions for Case 1
Post Shock Conditions (Von Nuemann)
Pvn/P1 20.05 Post Shock Pressure
Tvn/T1 4.042 Post Shock Temperature
i 10.7 mm Induction Zone Length
41
An
Figure 30: Expected ZND Profile for Case 1
Results
Once the solution was fully developed and sufficiently along the tube certain trends started to
emerge and the thermodynamic properties of interest such peak pressures and temperatures, and
reaction zone propagation could be determined.
Pressure
Peak and steady state pressure was shown to be roughly constant after the wave had traveled
approximately 50 mm from the end wall and its trend is shown in Figure 31. Peak Pressure hovered
around 17.25 atm rapidly trailing off and to CJ level pressures in approximately 5 mm eventually
reaching an expanded gas state at around 3.3 atm. For the shown timestep this peak value happens
at x = 0.200 meters which also corresponds to the maximum rate of reaction. Figure 32 shows a
zoomed in region with the kinetic rate of reactions for the global 1-step mechanism superimposed
on top.
0 0.002 0.004 0.006 0.008 0.01 0.012
1200
1400
1600
1800
2000
2200
Distance; = 0.0107 m
Te
mp
era
ture
Final T = 2078.2 K; Max T = 2104.1 K
0 0.002 0.004 0.006 0.008 0.01 0.012
10
12
14
16
18
20
Distance
Pre
ssu
re
Final P = 11 atm; Max P = 20.1 atm
42
Figure 31: Pressure Distribution for 1-D simulation
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
2
4
6
8
10
12
14
16
18
20
X Location (m)
Pre
ssu
re (
atm
)
43
Figure 32: Peak Pressure Region for 1-D simulation
Wavespeed
Wavespeed was calculated by measuring the time it took the peak pressure wave to pass through
several different locations then calculating its average speed with simple kinematics. The resulting
average of speeds from 5cm to 45 cm away from the end wall was found to be approximately
1570 m/s which happens to be very near to the CJ value of 1557 m/s.
0.195 0.196 0.197 0.198 0.199 0.2 0.201 0.202 0.203 0.204 0.2050
2
4
6
8
10
12
14
16
18
20
X Location (m)
Pre
ssu
re (
atm
)
0.195 0.196 0.197 0.198 0.199 0.2 0.201 0.202 0.203 0.204
0
0.5
1
1.5
2
2.5
x 104
X Location (m)
Ra
te o
f R
ea
ctio
n
Pressure Reaction
44
Table 6: Wavespeed measurements for Case 1
D (m) t (s) Velocity (m/s)
0.05 0.0000307 ----
0.100 0.0000621 1592
0.150 0.0000941 1563
0.200 0.0001257 1582
0.250 0.0001575 1572
0.300 0.0001894 1567
0.350 0.0002214 1563
0.400 0.0002535 1558
0.450 0.0002855 1563
Temperature
The temperature distribution showed the same trend as the pressure distribution, sharply rising to
a peak and then trailing off to a constant value. The large discontinuous jump near the end wall (x
= 0) is the expansion of the initial high temperature ignition region used to simulate the detonation
ignition. The temperature corresponding to the peak pressure at x = 0.2002 meters is
approximately 1695 K and settles to a near CJ Value within 5 mm.
Figure 33: Temperature Distribution for 1-D Simulation
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
500
1000
1500
2000
2500
3000
X Location (m)
Te
mp
era
ture
(K
)
45
Figure 34: Peak Temperature Region for 1-D simulation
Figure 35: Pressure vs. Temperature in Peak Region for 1-D Simulation
0.195 0.196 0.197 0.198 0.199 0.2 0.201 0.202 0.203 0.204 0.2050
500
1000
1500
2000
2500
3000
X Location (m)
Te
mp
era
ture
(K
)
0.195 0.196 0.197 0.198 0.199 0.2 0.201 0.202 0.203 0.204
0
0.5
1
1.5
2
2.5
x 104
X Location (m)
Ra
te o
f R
ea
ctio
n
ReactionTemperature
0.195 0.196 0.197 0.198 0.199 0.2 0.201 0.202 0.203 0.204 0.2050
2
4
6
8
10
12
14
16
18
20
X Location (m)
Pre
ssu
re (
atm
)
0.195 0.196 0.197 0.198 0.199 0.2 0.201 0.202 0.203 0.204
0
500
1000
1500
2000
2500
3000
X Location (m)
Te
mp
era
ture
(K
)
TemperaturePressure
46
Simulation vs. Theory
If one were to assume that the point where reaction go to zero as the end of the detonation wave
then we can approximate this as the location where we would expect to find the CJ conditions. In
Figure 32 and Figure 34 these point is around 0.198 meters. The resultant pressure and temperature
at these points is 10.97 atm and 2136 K.
Table 7: Numerical results comparison for 1-D simulation
X (m) Pressure (atm) Temperature (K) Velocity (m/s)
0.2002 17.25 1695.13 1570
0.1980 10.97 2136.61 1570
Pvn (atm) Tvn (K)
20.05 1212.49
PCJ (atm) TCJ (K) UCJ (m/s)
11.05 2084.22 1557
Comparing the CJ values at the approximated CJ point with theoretical analysis yields a -0.7 %
difference for pressure, 2.5% difference for temperature, and a 0.8% difference for detonation
velocity. However comparing the post shock conditions reveals that -14% difference in pressure
and 38% difference in temperature. This is also readily seen in the pressure and temperature plots
as there is no define ZND structure evident (recall Figure 4: Physical properties of the 1-D
Detonation Wave Structure). In Figure 32 we can see within the resolution of the cell size that the
discontinuous jump signaling the detonation wave happens at the same point for the reaction and
pressure waves and that they reach a maximum at the same point. In the ZND model we would
expect an induction period after the shock where there are no reactions occurring. Similarly for
the temperature in Figure 34 we see the discontinuity occurring at the same point. The temperature
increase that would be associated with the reaction zone occurs after the majority of the reaction
has completed rather than coincidentally.
47
It can be concluded then base on the findings above that the 1-Dimensional model is useful in
simulating stable CJ conditions for a propagating wave but not determining its structure. This
method of simulation would then be useful in creating a stable detonation for entering into
complex geometries in which only detonation entrance conditions are necessary such as the inlet
to a turbine or nozzle.
48
5.3 Validation Case 2: 2-Dimensional Propagation
Case 2 based on reference (26) by Taylor, Kessler, Gamezo, and Oran, evaluates the transient
propagation of a detonation wave in an opened end tube using a stoichiometric hydrogen and air
mixture.
Setup and initialization
The simulation region is a 4cm x 128 cm planar tube initialized with a 0.3125mm grid spacing
throughout. The ignition region was created by patching 4 separate regions (shown in Figure 37)
with high temperature and pressure combustion cases to simulate a direct detonation, these
conditions are shown in Table 8. The transient simulation was run at a constant 0.1 ms time
interval to ensure that forwarded reaction rates for combustion kinetics were not too large.
Adaptive meshing was employed in this simulation due to the grid density required to resolve the
transient features of the detonation front and the overall length of the simulation region. ANSYS’
Fluent built in gradient based adaptive meshing was employed every 10 time steps with a
maximum level of refinement of 5 and maximum cell count of 2.5 million total cells. Density
gradients and reaction rate gradients were determined to be best suited for detonation regions of
interests such as the reaction and shock fronts. Fluent only allows for single variable adaptive
meshing thus a compromise was made and it was determined that density based adaptive meshing
would be best suited to resolve the high pressure and temperature regions found near the
detonation front. Shown in Figure 36 is a sample of the adaptive grid near the detonation front.
One can see that the region immediately downstream of the flow where it is still at ambient
conditions has been unaffected by the adaption whereas the regions near the shock intersection
49
has been heavily refined. Additionally areas of relatively constant pressure have been coarsened
after the detonation front has past.
Figure 36: Adaptive Meshing Grid
Figure 37: Initialization region for Case 2
Table 8: Initiation conditions for Case 2
Initial Conditions (Unburned Gas)
1 atm Initial Pressure
298 K Initial Temperature
2.852 % H2 Mass Fraction
22.64 % O2 Mass Fraction
74.51 % N2 Mass Fraction
0.000 % H2O Mass Fraction
50
Initial Conditions (Ignition Region)
90 atm Initial Pressure
3500 K Initial Temperature
0 H2 Mass Fraction
0 O2 Mass Fraction
0 N2 Mass Fraction
1 H2O Mass Fraction
Table 9: CJ Conditions for Case 2
Chapman-Jouguet Conditions (CJ)
P2/P1 15.45 Pressure Ratio
T2/T1 9.8 Temperature Ratio
UCJ 1968 m/s Detonation Velocity
Table 10: ZND Conditions for Case 2
Post Shock Conditions (Von Nuemann)
Pvn/P1 27.4 Post Shock Pressure
Tvn/T1 5.1 Post Shock Temperature
i 0.16 mm Induction Zone Length
Figure 38: Expected ZND Profile for Case 2
0 0.5 1 1.5 2 2.5 3
x 10-3
1400
1600
1800
2000
2200
2400
2600
2800
3000
Distance; = 0.00016 m
Te
mp
era
ture
Final T = 2920.2 K; Max T = 2947 K
0 0.5 1 1.5 2 2.5 3
x 10-3
14
16
18
20
22
24
26
28
Distance
Pre
ssu
re
Final P = 14.9 atm; Max P = 27.4 atm
51
Results
The transient simulation was run until it was determined that the solution had reached a pseudo
steady state and the detonation propagation was stable.
Figure 39: Pressure Wave Propagation separated by 100 s
Pressure and Temperature
The two dimensional simulation shows multiple detonation fronts evolving within the tube with
transverse shockwaves propagating backwards through the simulation which make it difficult to
accurately determine post detonation conditions. Shown in Figure 40 and Figure 41 Similar to the
one dimensional the CJ conditions were examined at the point when the reaction rates fell to near
zero values. The data points were sampled at 50s intervals along a constant horizontal line at Y
= 0.14m.
It is immediately obvious that the pressure and temperature spikes fluctuate largely and do not
correspond with post shock ZND conditions. The peak pressures range from 25 to 55 atm when
ZND predicts only 27 atm pressure rise. The initial temperature rises to a value between 3000K
and 3500K peaking shortly after to a value a few hundred kelvin higher. The post detonation
conditions along the constant Y location are shown in Table 11with their respective locations. The
average pressure is approximately 16 atmospheres and with a temperature near 3400K. The
average pressure is represents a 3.6% difference and average temperature represents a 16%
difference in temperature.
52
Figure 40: Pressure vs. X Location for Case 2 at 50s intervals for constant Y = 0.14
Figure 41: Temperature vs. X Location for Case 2 at 50s intervals for constant Y = 0.14
Table 11: Post Detonation Conditions along X = 0.014 m
Time
(s) X Location
(m) Pressure
(atm) Temperature
(K)
0 0.2 0.4 0.6 0.8 1 1.20
10
20
30
40
50
60
X Location (m)
Pre
ssu
re (
atm
)
0 0.2 0.4 0.6 0.8 1 1.20
500
1000
1500
2000
2500
3000
3500
4000
4500
X Location (m)
Te
mp
era
ture
(K
)
53
122 0.217 16.8 3475
172 0.331 16.0 3465
222 0.421 16.6 3498
272 0.514 16.4 3381
322 0.621 15.9 3443
372 0.733 15.2 3337
422 0.822 15.0 3280
Average 16.0 3411
Wavespeed
Wavespeed measurement was calculated by analyzing the locations where the pressure was first
seen to rise significantly, i.e. where the shock front first cross the line at Y = 0.014m. Shown in
Figure 40 is an overlay of the pressure traces at 50 s intervals. The average wavespeed was
computed to be approximately 2192 m/s differing from the theoretical CJ value of 1968 m/s by
11%.
Table 12: Wavespeed measurements for Case 2
D (m) t (ms) Velocity (m/s)
0.294 122 ----
0.405 172 2227
0.517 222 2225
0.628 272 2231
0.736 322 2163
0.843 372 2132
0.950 422 2144
Average 2187
Similar to the one dimensional simulation the numerical values for CJ pressure, temperature, and
wavespeed compare favorable to the theoretical values calculated by Chapman-Jouguet theory but
did not agree well with the ZND model predictions. Additionally the point of zero reaction was
found to be well after the initial shockwave had passed rather than closely coupled with it like the
54
one 1-D model and theory predict. Examining the location of the shockwave in Table 12 and the
location of the zero reaction point in Table 11 one can see that there is a difference of several
centimeters between the recorded X locations for the selected time steps and is shown in Figure
42 as Location 1. For comparison, data points were extracted by visually determining the location
of shock fronts and then estimating where the reaction zone ended which is shown as Location 2.
The new pressure and temperature traces show the same trend as those in Figure 40 and Figure 41
but tend to average much higher than those along the Location 1 points. Sampling points
immediately after the detonation wave results in an average value of 23.1 atm and 3960K the
corresponding to a 50% overestimation of pressure and a 34% overestimation of temperature with
wavespeed remaining unaffected.
Figure 42: Comparison of data measurement locations for Case 2
55
Figure 43: Pressure vs. X Location for Case 2 at 50s intervals behind shock
Figure 44: Temperature vs. X Location for Case 2 at 50s intervals behind Shock
Table 13: Post Detonation Conditions behind Shock
Time
(s) X Location
(m) Pressure
(atm) Temperature
(K)
0 0.2 0.4 0.6 0.8 1 1.20
5
10
15
20
25
30
35
40
X Location (m)
Pre
ssu
re (
atm
)
0 0.2 0.4 0.6 0.8 1 1.20
500
1000
1500
2000
2500
3000
3500
4000
4500
X Location (m)
Te
me
pe
ratu
re (
K)
56
122 0.293 22.1 3958
172 0.405 20.7 3975
222 0.517 22.2 3936
272 0.627 27.8 4138
322 0.735 25.6 4022
372 0.843 28.4 4022
422 0.945 14.8 3689
Average 23.1 3963
Given the large disparity between results at the two sampling locations it is difficult to determine
exactly which set of results represent post detonation conditions. The CJ and ZND models which
are used to predict theoretical performance are based on 1-Dimensional modelling only and do not
account for shock wave interactions that cause the fish scale cell patterns or localized hot spots
that are seen in experimental testing. It may then not be correct in judging the accuracy of the
simulation solely on theoretical detonation conditions.
Detonation Cells
Image stacking of individual pressure contours for each time step was performed on the extracted
data to show a time history of the oscillating wave front and evaluate detonation cell regularity
and size. A time accurate overlay of pressure contours is shown for the first few centimeters in
Figure 45. It is immediately obvious that a regular detonation cell pattern exists shortly after the
simulated initiation of detonation. The fish scale pattern formed by the intersecting shockwaves
create an average of 3-4 cells in the tube at every time instant coinciding with an approximate
average cell width of 1 – 1.33 cm per cell. Analyzing a region of the stack image we can see that
this is indeed the case where the measured cell width ranges from 1.10 cm to 1.52 cm or roughly
7/16” to 19/32”. The expected cell width of stoichiometric hydrogen-air obtained from
experimental results 0.8 cm – 1.5 cm which agrees well with the numerical results.
57
Figure 45: Numerical evaluation of cell sizes for Case 2
Figure 46: Cell size measurements and comparison for Case 2
Simulation vs. Theory
The two dimensional case showed correct trends for detonation pressure, temperature, velocity
and detonation structure though not necessarily in line with theoretical CJ and ZND properties.
There was good agreement when compared to locations far behind the leading detonation front
where reactions were determined to cease. The difference between theoretical and numerical
results was found to be significantly higher than that of the one dimensional simulation though
varying by as much 11% for detonation velocity and 16% for temperature. The theoretical one
dimensional ZND and CJ models predict the location of detonation properties to be immediately
following the initial shock and following the detonation wave respectively and so an effort was
made to sample results immediately after the detonation wave for comparison. In doing so
58
detonation pressure and temperature were found to differ significantly with velocity remaining
unaffected. It was determined that variance was caused by the complex two dimensional nature of
the numerical simulation in which shock interaction and chemical kinetics lead to large variations
in pressures and temperatures. There is no known theory that predicts the transient thermodynamic
property distribution for two and three dimensional detonation propagations. The accuracy of the
predicted detonation cell sizes and propagation velocity in conjunction with detonation level
pressures and temperatures would indicated that the simulation accurately captured a stable
detonation propagating in a confined tube. For all intensive purpose of this study it is has been
deemed accurate for application in future studies.
Based on the results obtained from this simulation it can be concluded that Fluent it is indeed
capable of predicting and defining detonation cell propagation and is best suited to simulated
detonation propagation and transference in combined geometries. The results from this simulation
can be used to study detonation propagation into large tubes, converging- diverging tubes, and
those with arbitrary geometries.
59
6 TEST EQUIPMENT AND METHODOLOGY
6.1 Experimental Method
Experimental tests were conducted to first establish baseline performance with stoichiometric
conditions then parametrically changing targeted decision variables to evaluate their effect on
performance. A typical experiment would proceed by starting with a stoichiometric fuel / air
mixture with a pulse width designed to fill 100% of the tube volume at single 1 Hz pulses.
Equivalence ratio would then be varied to its upper and lower limits of combustion from lean to
rich mixtures. The input variables would then be reset to vary volume fill percentage and run until
its combustion limits were met as well. Lastly pulsing frequency was evaluated using initial
stoichiometric conditions at 100% fill and then varied from 1Hz to its maximum operating
frequency. If certain inputs were noticed to have a significant effect on performance such as
ignition time and pulse width, they too were varied to dial in performance and examine trends if
any existed.
6.2 Experimental Hardware
Two different detonation systems were used in this study: a large diameter tube initially tested
with propane gas and a smaller tube designed to run on ethylene gas. The large tube was built as
part of previous research by a past researcher and the author as the initial testbed for detonation
research. The small tube was a redesigned version of the original detonation system built to
address several issues experienced during testing namely size, weight, and detonation
performance. The larger tube had issues with volume fill rate that limited the maximum frequency
that could be achieved to 1Hz or less while the smaller tube had a maximum filling frequency of
60
10 Hz or greater and it is for this reason that future references to the large and small tubes will be
referred as the low and high frequency tubes respectively from this part forward.
The low frequency tube used a system of threaded rods and custom manufactured orifice plates to
generate the obstacles used in detonation transition. Filling and ignition was performed only in the
beginning section near the end wall and thus required a long initial spark delay to ensure proper
mixing and fuel / air travel.
Figure 47: Low Frequency Tube Setup
The high frequency detonation tube used in this study was designed to use Ethylene (C2H4) / Air
mixtures to achieve detonation via detonation transition utilizing orifice plates. The primary intent
61
of this design was to use a sufficiently light fuel that was sensitive enough to use with smaller tube
diameters to promote higher filling frequencies utilizing onsite resources. The average cell width
at stoichiometric conditions is approximately 1 inch and thus the detonation tube was chosen to
be approximately 2 inches in diameter. The optimum blockage ratio was determined from past
studies to be approximately 45% yielding an interior diameter of 1.5 inches which should enable
us to achieve detonation over a wide range of equivalence ratios and ensure a stable detonation
propagation as shown in Figure 48.
Figure 48: Ethylene Cell Size vs. Equivalence Ratio
62
The tube is composed of three sections in which ignition is initiated, detonation transition occurs,
and pressure and combustion conditions are measured. To facilitate high frequency pulsing of fuel
and air both gases are injected at the interfaces between the different sections. This is seen also as
a way to control mixing times as the adequate mixing is crucial to successful detonation
propagation. Additionally the tube is mounted to a sliding rail systems which allows it to move
axially with respect to its exhaust direction should propulsion testing need to be performed.
The measurement section was modified from the low frequency system to allow for two ion
sensors spaced 90 degrees opposed from the pressure sensors at the last two pressure sensor
locations. The interior obstacles were manufactured stainless steel thin discs and spaced by thin
wall pipe to allow for easier reconfiguration when compared to the low frequency tube cartridge
system.
Figure 49: High Frequency Tube Experimental Setup
63
Figure 50: Interior Geometry for High Frequency Tube
The high frequency tube used exhaust vents mounted near the end of the tube to ensure excess
combustion gases are removed and not vented into the closed lab facility. Additionally a retention
barrel was placed in front of the exhaust to capture soot particles and any potential debris that may
be liberated during testing.
Figure 51: High Frequency Tube Overview
64
Figure 52: High Frequency Tube Measurement Section
Figure 53: High Frequency Tube Interior Obstacle Configuration
Figure 54: Injection plate for High Frequency Tube
65
7 EXPERIMENTAL RESULTS
7.1 Theoretical results
Ethylene gas and gaseous air was used in testing all configurations of the low and high frequency
tubes and the expected trends for detonation velocity and pressures are shown below. The right
secondary axis on both figures shows cell width in inches with a horizontal line marking the upper
limit for the high frequency tube and two vertical lines denoting the boundaries for the velocities
and pressures. An equivalence ratio between 0.70 and 2.0 bounds the theoretical detonation
velocities between 1692 m/s and 1885 m/s and the pressure from 15.87 psia to 19.56 pisa.
Figure 55: Expected Range of Detonation Velocities
Figure 56: Expected Range of Detonation Pressures
66
7.2 Uncertainty
With any experimental system there is a certain degree of uncertainty inherent in the measurement
process. Uncertainty comes for the measurement and manufacturing process where precision is
limited to the instruments available and manifests itself in pressure and wavespeed measurement.
Sources of uncertainty for pressure and velocity come from:
Mounting locations for sensors
DAQ Sampling Rate
Pressure Transducer rise time and resolution
Calculation of Uncertainty
Wavespeed
The calculation of wavespeed for both numerical and experimental studies uses the simple
kinematic formula for velocity. Unlike numerical simulations, in which the exact time and position
are known, experimental precision was limited by manufacturing tolerances and sampling rates.
Modifying the original equation to account for this we get:
⁄ ( )
⁄ ( )
U(d) is the uncertainty created by the tolerances in position of the sensor mounting holes relative
to each other. U(s) is the uncertainty created by the maximum sampling rate of digital acquisition
device (DAQ). The stated spacing for hole locations was 2.00” +/- .01” representing a 0.5%
uncertainty in distance. By itself the mounting location only contributes a difference of 9 m/s for
a calculated wavespeed of 1800m/s. The maximum sampling rate of DAQ with 6 sensors in
67
differential mode is 233 KHz leading to a sampling time of 4.29s and an uncertainty of +/-
2.1459s.
⁄
⁄
( ) √( ( )
)
( ( )
)
( ) √(
)
(
)
( )
( )
With only 4 sensors connected the uncertainty is reduced to 91 m/s and 2 sensors at 46 m/s.
Pressure
The PCB 111A24 sensors have a published resolution of 20 mpsi and a reflected rise time of 1.5
s. Given the level of pressure ranges experienced in testing sensor resolution was not an issue.
The reflected rise time taken to go from a nearly zero level voltage region to some nearly constant
value when the sensor is oriented in line with the pressure wave. The reflected rise time in all
measurements was then less than half the sampling time in all detonation cases and thus did not
contribute to any erroneous measurements. It was determined that there was no significant amount
of uncertainty inherent in the pressure measurements.
7.3 Low Frequency Tube Testing
In previous testing utilizing propane-air combinations detonation was never achieved in any
configuration, it was only until the air supply was switched to oxygen that detonation level
pressures and velocities were obtained. Even then measured detonation pressures and velocities
were not consistent with CJ theory.
68
The low frequency tube was then tested with ethylene (C2H4) fuel instead of the propane (C3H8)
with a DDT section consisted of 14 total discs with a blockage ratio of 45% and a spacing of 3”.
The objective of this experiment was to determine if the failure to transition to detonation was due
to either cell size limitations or transition length. Propane has a detonation cell size of roughly 2 –
4 inches depending on equivalence ratio while ethylene is roughly half that with a cell size of
approximately 1 – 2 inches. Referencing Figure 57 and Figure 58, measurements showed that
ethylene lead to a higher pressure and velocity at the test measurement section than the best
propane tests but ultimately did not detonate. With roughly four cell widths available for
detonation propagation one would have expected a stable wave at the end of the measurement
section if DDT had been achieved but the lack of any substantial improvements in wavespeed
would support the conclusion that transition length and not cell size was ultimately the factor that
prevented detonation transition. The effect of an increased L/D ratio was not pursued during this
study due to the large size and overall length needed to increase transition length. Doubling the
transition length would have required another four feet of schedule 80 pipe which the stand and
filling arrangement was not designed for and incapable of accommodating.
69
Figure 57: Low Frequency Tube pressure traces with Ethylene gas
26.7 26.8 26.9 27 27.1 27.2 27.3 27.4 27.5 27.6
0
20
40
60
80
100
120
Time (ms)
Pre
ssu
re (
PS
I g)
Speed:(m/s)1-2: 769.72-3: 1043.93-4: 952.5Avg: 922.01TR1 (us): 15TR1 (us): 5TR1 (us): 5TR1 (us): 6Max P1: 108.8Max P2: 96.71Max P3: 101.71Max P4: 91.1
70
Figure 58: Low Frequency Tube pressure traces with Propane gas
71
7.4 High Frequency Tube Configuration I Testing
The first configuration consisted of a 30 inch long ddt section with a maximum of 12 thin discs
and two end discs spaced two inches apart from one another. The L/D ratio in this configuration
was approximately 14:1
Pressure Trends
The following figures show the influence modifying fill percentage, fill frequency, and
equivalence on maximum recorded pressure for the short tube configuration I. The fill percentage,
which is the percentage of volume at a given equivalence ratio and tube length, had the greatest
effect on pressure ratio, followed by equivalence ratio and then lastly pulsing frequency. As the
fill percentage increased one can see that so did the maximum required pressure ratio to the point
where it started leveling off. Not shown in the plots however is the issue of combustion failure
that occurred at higher fill ratios. The fuel-air mixture often failed to ignite or lead to low pressure
and speed deflagration at fill ratios of 120% and greater. Increasing the firing rate at 100% fill and
a stoichiometric lead to a gradual decrease in maximum recorded pressure ratio though not as
dramatic as that in the equivalence ratio tests or fill percentages test. This would seem to indicate
that residual combustion products left over after ignition and the slow speed of the deflagration
interfered with the next pulse cycle. This interference gradually had a greater effect as the time
between pulses grew smaller. This would indicate the need for a purging cycle between pulses
though the implementation of one would effectively cut the pulsing frequency in half.
In Figure 61 a second data set was added for comparison, the same tube length and internal spacing
but reducing the number of obstacles and thus the L/D ratio for DDT section. The reduction of
obstacle number change the overall L/D ratio from 14:1 to roughly 9:1. The clear difference in
peak pressures illustrates the effect of obstacle count on flame acceleration. Interestingly enough
72
both data sets do not peak at the same equivalence ratio but are instead separated by a large gap.
The 13 disc configuration peaks at an equivalence ratio of 0.75 whereas the 8 disc configuration
does so at an equivalence ratio of 1.0.
Figure 59: Maximum Pressure vs. Fill percentage trends for configuration I
0 20 40 60 80 100 120 140 160 180 2000
10
20
30
40
50
60
70
Fill Percentage (%)
Pre
ssu
re (
PS
I g)
73
Figure 60: Maximum pressure vs. Pulsing Frequency trends for configuration I
0 1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
60
70
Frequency (Hz)
Pre
ssu
re (
PS
I g)
74
Figure 61: Maximum Pressure vs. Equivalence Ratio trends for configuration I
Wavespeed Trends
The variation of filling parameters showed the same trend as the maximum pressure readings save
for the effect of filling frequency on calculated wavespeed. Wavespeed was seen to increase up
to 100 percent fill then leveled off to a nearly constant value. Wavespeed when compared against
equivalence ratio, approached a maximum at a value of 0.8 for the 13 discs case and a lower
maximum at an equivalence ratio of 1.1 for the 8 discs case. Similar to the maximum pressure
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
10
20
30
40
50
60
70
Equivalence Ratio
Pre
ssu
re (
PS
I g)
13 Discs
8 Discs
75
cases, the increase in L/D ratio led to an increase in wavespeed. It is also worth noting that the
maximum pressure condition in Figure 61 for both the 13 and 8 disc configuration did not coincide
with the maximum velocity cases. Curiously, the change in pulsing frequency saw no appreciable
difference in computed wavespeed whereas the same conditions caused a severe drop in peak
pressures.
Figure 62: Velocity vs. Fill Percentage trends for configuration I
0 20 40 60 80 100 120 140 160 180 2000
200
400
600
800
1000
1200
Fill Percentage (%)
Wa
ve
Ve
locity (
m/s
)
76
Figure 63: Velcoity vs. Frequency trends for configuration I
0 1 2 3 4 5 6 7 8 9 100
200
400
600
800
1000
1200
Frequency (Hz)
Wa
ve
Ve
locity (
m/s
)
77
Figure 64: Velocity vs. Equivalence ratio trends for configuration I
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
200
400
600
800
1000
1200
Equivalence Ratio
Wa
ve
Ve
locity (
m/s
)
13 Discs
8 Discs
78
7.5 High Frequency Tube Configuration II Testing
The second configuration containing twice the number of total discs and the same obstacle spacing
increased the L/D ratio from 14 to 28. This increase in L/D ratio led to successful transition to
detonation.
Results
The increased L/D led to detonation in most conditions and was found to be stable however it is
interesting to note that not every combination of equivalence ratio, volume and delay time led to
successful transition. Some tests resulted in fast deflagrations with high pressure ratios like those
shown in Figure 65 while some failed to ignite entirely. The cases that showed fast deflagrations
were easy to identify as deflagrations rather than weak detonation in part due to the addition of
ion sensors at the last two pressure sensor locations. The ion sensors allowed for the determination
and differentiation of the flame front. In the figure below the four positive traces are the pressure
sensors while the negative two are the ion sensors. The ion sensors only measure a voltage drop
when the gap across the spark plug has been closed. The ionized gas caused by chemical reactions
during combustion closes this gap and creates a short circuit when the flame passes by the
electrodes.
Figure 65 confirms that the measured data was a deflagration rather than a detonation in three
ways. Firstly the peak pressures which reach a maximum of roughly 100 psig are much lower than
the expected 230-290 psig that we expect from stoichiometric detonation. Secondly the computed
wavespeeds at roughly 1000 m/s are approximately half that of the CJ values. Lastly the delay
between the last two pressure sensors and the ion sensors shows that the combustion wave actually
79
trails the pressure wave by a significant amount of time rather than coupled with it like ZND
theory predicts.
Figure 65: Typical Deflagration Sensor Traces
Figure 66 is typical example of a detonation, when compared to deflagrations it is immediately
obvious that the time between pressure measurements is much smaller, the peak pressure ratios
are much higher, and the time between pressure and ion sensors are negligible.
0.433 0.4332 0.4334 0.4336 0.4338 0.434 0.4342 0.4344 0.4346 0.4348
-60
-40
-20
0
20
40
60
80
100
120
80
Figure 66: Typical Detonation Sensor Traces
In Table 14 the observed differences between deflagrations and detonations are observed
numerically. The difference between a fast deflagration and a detonation is shown clearly in the
wavespeed, pressure, and ion sensor data. The ion sensor measured speeds are consistent with the
pressure transducer speeds in the detonation case and the measured time between combustion and
pressure waves is 25 time less than that of the deflagration case.
It is interesting to note however that the ion sensors actually detect the combustion wave prior to
the pressure wave rather than immediately after like theorized in the ZND model. The measured
time between the pressure front and flame front is calculated to be 4.3 microseconds which at the
calculated wavespeed for the pressure sensors is a separation of about 8.5 mm. The difference is
exactly equal to 1 time step difference at the current sampling rate, i.e. 6 sensors / 1.4MS/s = 4.286
s. When sampling time was increased to 2.85 s the flame was still found to lead the pressure
wave by exactly one time step and is shown in Figure 67. Additionally the spark plug mounting
0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404-150
-100
-50
0
50
100
150
200
250
300
81
has an uncertainty of + /- 0.02 inches of .5 mm and although the center point of the electrode was
designed to be aligned with center of the pressure transducer the actual location that the
combustion wave cross the electrode gap can be anywhere across the prong. It is entirely possible
within the uncertainty of the measurement system that the combustion wave is actually much
closer to the pressure sensors or possibly even after it. However for the purposes of this study the
confirmation of combustion wave travelling at detonation speeds couple very closely to the
pressure wave is adequate.
Table 14: Wavespeed measurements and comparsion for Detonation and Deflagration
Deflagration Detonation
V2,pcb 1075.8 1972.8 m/s
V32,pcb 1076.0 1691.1 m/s
V43,pcb 986.4 1972.8 m/s
V43,ion 696.3 1972.8 m/s
tC2-P2 116 -4.3 s
tC1-P1 137 -4.3 s
DC2-P2 80.7 -8.5 mm
DC1-P1 95.6 -8.5 mm
82
Figure 67: Detonation Sensor traces at 350KS/s
Figure 68: Combustion Sensor Mounting
Figure 69: Spark Plug Electrode uncertainty
Detonation Performance
Testing was conducted with constant LabView VI inputs to measure the variability of the
detonation wave measured at the end of the tube. The following figures show the pressure,
wavespeed, and transition time distribution and its comparison to a normal distribution. Recalling
that for an ethylene-air detonation the CJ pressure is approximately varies between 230 psi and
83
290 psi and the detonation velocity varying between 1640 m/s – 1880 m/s with stoichiometric
conditions yielding a CJ pressure of 274 psi and a detonation velocity of 1821m/s.
Figure 70: Normal distribution of measured Deotonation pressures
The average of 404 separate pressure measurements was found to be 251 psi with a standard
deviation 72 psi. Figure 70 shows that most of the samples collected were within one standard
deviation of the average (354 samples equaling 88%). With a small percentage being two standard
deviations or more greater than the average and the least being within two standard deviations less
than the average. The value of 251 psig represents an absolute pressure value of 265 psia which
is slightly less than the stoichiometric detonation pressure and well within the expected ranges. It
is important to note that since 88% of the values fall within the 178 psig – 323 psig range it is
impossible to determine the variation of detonation pressure with equivalence ratio as any
pressures outside of this range would not correspond to a stable detonation wave.
0
50
100
150
200
250
300
34 106 178 251 323 395 467 More
Sam
ple
Fre
qu
ency
Pressure (PSIg)
Pressure Distribution
84
Figure 71: Normal distribution of all measured Detonation Velocities
The next three figures show the normal distribution of all recorded speed calculations, one for the
pressure sensors and combustion sensors combine and then two for each one individually. The
average of all combined and individual wavespeeds was 1871 m/s which is very nearly the
maximum expected velocity and has a standard deviation of 137 m/s. The standard deviation is
relatively small when compared to that of the pressure measurements and interestingly enough it
is actually equal to that of the measurement uncertainty. However, the distribution of all measured
velocities is more random than that of the pressures with 71% falling within +/- one standard
deviation and 22% less than one standard deviation and more than two standard deviations below
the average velocity. Only 32% of the measured wavespeeds lie within the expected range with
the majority of them trending much higher. If we are to keep the same scale as Figure 71 but plot
just the distributions of pressures sensors calculated wavespeeeds or just the ion sensor calculated
0
50
100
150
200
250
1459 1597 1734 1871 2008 2146 2283 More
Freq
uen
cy
Velocity Distribution
85
wavespeed an interesting trend appears. The randomness apparent in the overall plot of velocities
seems to be inherited from the pressure sensors as it shows the same degree of randomness. The
ion sensors however show a much more even distribution with 96% of the calculated velocities
compared to the 63% with the pressure sensors. This would seem to indicate that the ion sensors
are a more accurate way of measuring wave velocities. The disparity between the pressure sensors
and ion sensors is most likely due to the inherent error in the way the quartz pressure sensors
work, i.e. the reflected rise time which is the maximum response time for the signal to reach a
certain percentage of its maximum value from a zero voltage level. The ion sensors have a constant
voltage and instantly measure a change when it is discharged.
Figure 72: Normal distribution of measured Detonation Velocities from Pressure Transducers
0
20
40
60
80
100
120
140
160
1459 1597 1734 1871 2008 2146 2283 More
Freq
uen
cy
Velocity Distribution (Pressure Sensors)
86
Figure 73: Normal distribution of measured Detonation Velocities from Ion Sensors
The transition time values were measured from the point of the ignition signal to the first recorded
pressure wave and are shown in Figure 74. One can immediately note a near perfect normal
distribution indicating that there exists a large degree of randomness in transition although the
standard deviation is only 6 ms for an average value of 17.6 ms transition time. This deviation is
likely cause by inconsistencies in filling as well as slight differences in the timing control system.
0
10
20
30
40
50
60
1459 1597 1734 1871 2008 2146 2283 More
Freq
uen
cyVelocity Distribution (Ion Sensors)
87
Figure 74: Normal distribution of Detonation Transition Times
Thermal Performance
The entire length of the detonation tube was painted with a high temperature black matte finish to
simulate a black body with emissivity of 1.00. Temperature levels were measured using a
handheld infrared gun after continuous testing had performed for several minutes. The variation
of temperature is shown along the whole pipe length In Figure 75 and visual readings from a FLIR
camera are shown in Figure 76 and Figure 77. The temperature levels steadily rose from the end
wall of the tube towards 30” from the end wall, peaking 340 F and gradually decreasing after that.
This was most likely due to the increasing effect of flame acceleration and decreased residence
time in that area. The flanges show a large dip temperature but has an outer diameter of roughly
6” and is not in direct contact with the flow. The check valves leading to the injection ports on the
end wall and injection plates were cool to the touch but were not directly measured because its
emissivity coefficient was not known. The temperature near the pressure measurement section
0
5
10
15
20
25
30
35
40
45
0.0 5.8 11.7 17.6 23.5 29.5 35.4 More
Freq
uen
cyTransition Time Distribution
88
was found to decrease rapidly and hovered around 150 F which was below the 275 F limit for
steady state temperatures of the pressure sensors. The Flir imaging for the transition and
measurement sections showed the same trends but were useful only as a qualitative tool as the
model used only had a maximum range of 200 F.
Figure 75: Temperature (F) Distribution along Detonation Tube after testing
89
Figure 76: Thermal Imaging of Detonation Tube Transition Section
Figure 77: Thermal Imaging of Detonation Tube Measurement Section
90
Sound Levels
Figure 78: Sound Levels (dBa) during testing near Detonation Tube
The above figure is measurement of recorded sound pressure levels using a sound level meter with
an “A” frequency weighting. The A frequency rating however may not represent the true sound
pressure level that exists when the detonation tube is firing. Typically a “C” frequency rating
would measure peak sound levels. Of the commercial equipment available at the time neither “A”
or “C” meters had fast enough rise times (125 ms max) to truly capture the peak pressure wave
which rose from 0 to maximum and lower within the span of 10 ms. The importance of Figure 78
then to illustrate the regions of high levels and its attenuation through walls and doors.
Inside the testing area of the gas turbine lab where the detonation tube is housed one can see that
sound pressure levels fluctuate +/- 3 dBs. Immediately outside the walls of the gas turbine lab
however there is a significant drop of 20 dBs which is equivalent to using a low amount of hearing
protection. It is important to note that attenuation only occurs when the pressure wave passes
91
through walls or solid bodies. Measured sound pressure levels in the corridors immediately outside
the testing area were found to be constant regardless of distance.
The need for hearing protection within the testing area should be clear, anyone inside or
immediately outside of the area would require hearing protection in the form headsets and/or ear
plugs.
Observations & Issues
Air and Fuel
During testing of the high frequency tube configuration II setup several unforeseen issues and
interesting side effects were observed. Most notably was the effect of incoming air pressure on
successful detonation transition. Large drops in air pressure at the regulator were noticed when air
was being injected which made it difficult to determine the incoming air pressure and thus the
amount of mass being injected. This effect was constant throughout testing however and could be
corrected for by increasing incoming air pressure above the desired level. During continuous
pulsed testing a steady decline in maximum air pressure at the regulator was also noticed. It was
determined that the offsite air compressor used for air delivery was being discharged before the
automatic compressor was being triggered to refill the compressed air tank. The effect that this
issue had on testing was dramatic when combined with the pressure drops during filling. The
pressure drops were so severe that the equivalence ratio of gas was richer than intended and led
not only to detonation failure but also combustion failure.
It is important to note that the fuel delivery system did not experience pressure drops in the line
when filling as pressure at the regulator was not shown to vary at all. One issue that the fuel supply
92
did have was the static temperature decrease when discharging fuel. It was repeatedly observed
that condensation and sometimes ice would form on the pressure regulator at the fuel tank.
Figure 79: Frozen condensation on Pressure Regulator
Filling issues
The switch from the short tube to the long tube configuration brought about unexpected issues in
the filling performance of the tube. Introduction of the longer transition section increased both the
required filling time and mixing time. In the short tube configuration ignition was always initiated
immediately after filling had completed to minimize cycle time. A spark delay had to be added in
the long tube configuration to ensure that combustion or detonation occurred. The additional
length of tube combined with the presence of a larger number of obstacles required an additional
mixing delay time on the order of 100ms. The delay time was found to be consistent for a specific
fuel / air mixtures but not so for all combinations of equivalence ratio and fill rate which is to be
expected.
Spark Plug Ignition
93
Initial testing was performed using a long electrode oil heater spark plug as it was assumed that
the deeper penetration in the mixture would allow for a more uniform ignition and aid in
detonation initiation. However several runs showed that the use of the extended electrode plug
actually resulted in weaker ignitions, more failed detonations and lower pressure deflagrations
when compared to a traditional automotive spark plug.
Figure 80: Long Electrode Spark Plug
Spark plug ignition time also seemed to effect combustion strength as a relatively short spark time
of 5ms was found to produce weak deflagrations or no ignition whereas longer 10ms and 15ms
ignition times produced stronger blast waves and led to more reliable and successful detonations.
94
8 CONCLUSIONS, RECOMMENDATIONS, AND GUIDELINES FOR
FUTURE STUDIES
8.1 Recommendations for Numerical Studies
From the results presented in the previous sections we have inferred certain methods for
simulating detonation events in different configurations. Generally speaking it is not practical to
perform numerical analysis with full reacting chemistry sets and the necessary grid spacing to
resolve the reaction zones of detonation cells. In many cases the complexity of the system can be
condensed through reduced reaction sets (even global 1-step mechanisms) and adaptive meshing
techniques.
Chemical Kinetics
Validation case 1 showed that the use of a 1-step reaction mechanism in numerical simulations
accurately determined the CJ detonation velocity, pressure, and temperature conditions after the
shock. The one dimensional nature of the simulation allowed for very low mesh cell counts and in
turn short simulation times. The 1 step mechanism however was unable to resolve the long
induction time associated with ZND model. It was determined that this was an appropriate tradeoff
given the accuracy of the CJ conditions and the requirements of this study. The simplicity of the
global one step will lend greatly to simulation efficiency and speed.
Adaptive Meshing
Adaptive meshing in the two dimensional simulation greatly reduced the overall mesh size needed
to define the simulation. The computational resources needed to dynamically adapt a large mesh
are still significant and thus it is best used sparingly. In order for adaptive meshing to be truly
effective it must be correctly set to refine the areas of interest. The figure below shows a plot of
density gradient superimposed upon a density contour plot to illustrate the region of interest. In
95
this situation density gradient was selected to capture regions of high pressure and temperature
gradient as either will lead to large gradients. Specifically for detonations there are immediate
rises in temperature and pressure near the shock front and for transition cases these locations are
not overlapping but rather separated by a large distance. It is recommended that normalized
density gradient adaption be used because it requires only setting the relative level of density
gradient rather than a maximum or minimum, ideal for large discontinuous regions of
thermodynamic properties.
Figure 81: Density Gradient vs. Density
Additionally control the level of refinement and maximum / minimum number of cells will allow
for optimum resolution of areas of interest while keeping simulation time and mesh count within
the limits of current hardware.
96
Figure 82: Adaptive Meshing Control
Possible applications and future studies
The 1-Dimensional simulation applicability and potential lies in its ability to accurate simulate CJ
detonation conditions. A small tube section could be used to simulate detonations propagating into
open spaces, nozzles, or turbine geometry where only the entrance conditions are important and
no necessarily the wave structure.
The 2-dimensional simulation is best suited for detonation propagation and transition studies
where it is desired to know whether a stable detonation can be achieved and transferred. Such
applications would include innovative transition sections, delivery systems, and power extraction
devices.
97
8.2 Recommendations for Experimental Studies
Filling & Purging
It was seen that decreasing the time between pulses in the short tube configuration had an adverse
effect on maximum recorded pressure but not wavespeed. The decrease in pressure was attributed
to the decrease in purge time leading to a buildup of residual combustion gases. Rather than being
able to propagate through a combustible mixture the pressure and reaction wave were decouple
and thus lead to blow outs. To mitigate this effect, a purging cycle will need to be added between
pulsing cycles to ensure that only a fresh combustible mixture exists inside the tube at the moment
of ignition. The purging cycle would consist of a single air pulse of sufficient width to deliver the
oxidizer mass that would fill the tube volume. Introduction of a purging pulse however would
effectively cause the pulsing frequency to decrease however as the oxidizer injection time is the
limiting factor in filling time.
It was observed during testing that the onset of detonation was very sensitive to initial air pressure,
a low pressure condition resulted in a lower amount of mass delivered to the tube and thus an off-
stoichiometric mixture of fuel and air that would either fail to detonate or become inconsistent and
unreliable. The chief cause of the low pressure conditions was the offsite air compressor used to
deliver the air supply to the tube. During the filling process pressure inside the line and at the
pressure regulator often fluctuated by 10 – 20 psi and after several sequential pulses the pressure
at the regulator would decrease from it set value to one much lower. This trend would continue
until a trigger began to refill the compressed air tank.
The combination of a need to deliver air faster and more reliably to the detonation tube necessitates
a larger compressed air storage system and quick release system. A larger tank with a higher
98
minimum pressure would alleviate any filling air consistencies while a quick release system would
eliminate the air supply fluctuations seen during the filling process as well as decrease the overall
filling time and increase the cycle frequency. The quick release system for air delivery could be
as simple as using larger solenoids or utilizing timed and motorized valving systems.
Obstacle Configuration
Although detonation was not achieved, the short tube was able to achieve a higher filling a pulsing
rate than the long tube configuration due reduced volume. An effort to minimize the transition
length by altering the parameters of DDT would reduce the total volume and therefore the filling
time necessary to create a stoichiometric mixture. Previous studies showed that certain
configurations of obstacle placement and blockage ratio produced consistently higher pressures
and measured velocities and while the result of these tests were adapted to the design of the high
frequency tube it is possible that further optimization can be achieved.
Sound Insulation and isolation
The high and damaging sound levels produced by a detonation pulse must be accounted for in any
further experimental setup especially those operating at higher pulsing frequencies. OSHA
regulations dictate that the noise dose be limited to some finite value per day for continuous pulses
and exposure limited to peak sound level pressures whenever possible. For the safety of
researchers and those near the testing area all efforts must be made to minimize noise exposure.
Established safety procedures require that hearing protection be worn by all persons within the lab
testing area. A sound suppressing enclosure must be used to minimize noise exposure to those
outside of this area without actively prohibiting access. The high velocity and pressure created at
the exhaust plate (2000 m/s and nearly 16x ambient pressure) cause a potential hazard should
anything be expelled during a detonation pulse and consequently requiring some form of blast
protection / deflection. The creation of simple test cell within the laboratory area could satisfy
99
these requirements and enable further testing of pulse detonation experiments and other
combustion related studies.
High Speed Digitizers
High speed digitizers are similar to a DAQ in that they can record and convert analog voltage data
into digital signals. However digitizers are much more specialized in their function in that they do
not support pulse generation or pulse width modulation and thus cannot be used to control other
devices such digital solenoids and ignition systems. The tradeoff however is that they tend to have
much higher sampling rates accompanied by larger onboard memory to log and buffer data faster.
Digitizers typically record in the megasample (millions of samples / second) range as opposed to
the current DAQ’s kilosample range (thousands of samples/second), for example the National
Instruments USB-5133 digitizer is able to record 100MS/s on two channels simultaneously
resulting in over 400 times the sensor resolution of the current setup. An ideal measurement setup
for the current system would comprise of a DAQ control the ignition, fuel, and air pulses for the
spark and solenoids and recording digital pulse and an array of ion sensors that do not require high
frequency measurements and digitizers recording measurements from the pressure sensors.
Ion Sensing
The ion sensors used in this study were shown to be very successfully at measuring detonation
wavespeeds. The sensors were shown to have less of a standard deviation when compared to the
measurements obtained by the pressure transducers while simultaneously prevent any false
positive detonation velocities i.e. recording an expanding pressure wave instead of the actual flame
velocity. The combustion sensors are only able record the propagation of ionized gas which occurs
during the multiple chemical reactions of a combustion event, prior to and after that there is no
significant electrical charge in the gas to cause the stored potential in the senor to discharge. The
sensors also proved to be extremely cost effect since no modification was needed to original spark
100
plug that was used as the combustion sensor and only minor electrical wiring was needed. It is
then the recommendation of this author that the combination of the LabView DAQ used in testing
plus a large array of combustion sensors strategically placed throughout the length of a detonation
tube can provide valuable insight into the study of deflagration to detonation transition. Ion sensors
spaced regularly throughout a detonation tube and between obstacles could be used to precisely
show the effect of obstacle geometry on detonation transition and aid in parametric study of new
configurations.
Possible applications and future studies
With a reconfigurable and reliable pulse detonation engine system developed further research can
now be focused on integration and optimization studies. The potential application of pulsed
detonation engines for thrust applications can be explored with the introduction of a supersonic
nozzle section. A custom designed or off-the-shelf turbine can be integrated at the exhaust to
evaluate power extraction capability and efficiency. The high enthalpy flow can also be used in
non-detonation applications such as shock tube testing.
101
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18. New, Dr. Daniel T. H., Lu, Dr. Frank K. and Tsai, Dr. H. M. Experimental
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19. Sinibaldi, Jose O., et al. Investigation of Transient Plasma Ignition for Pulse
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22. Wintenberger, E. and Shepherd, John E. Detonation Waves and Pulse Detonation
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25. Numerical Investigation of Detonation in Premixed Hydrogen-Air-Mixture - Assesment
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27. Khemani, Haresh. The Stoichiometric Air-Fuel Ratio. Bright Hub. [Online]
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105
37. Kailasanath, K. Research on Pulse Detonation Combustion Systems - A Status Report.
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Aksenov, V. S. and Shamshin, I. O. s.l. : Proceedings of the Combustion Institute
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41. Numerical simulations of flame propagation and DDT in obstructed channels filled
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in obstructed channels filled with hydrogen-air mixture, , 2007, Vol. 31.
42. Deflagration-to-Detonation Transition in Premixed H2-Air in Channels with
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107
10 APPENDIX A: DETAILED EXPERIMENTAL SETUP
108
10.1 Sensors and Instrumentation
Dynamic pressure transducers
PCB Piezotronic model 111A24 pressure transducers were used for dynamic pressure and velocity
measurement. The sensors have a maximum measurement range of 2000 psi at 5.0mv per psi at a
resolution of 20 millipsi and a rise time of less than 1.5 microseconds. They can withstand flash
temperatures of 3000F and static pressures of 10,000 psi however steady state operating
temperature is limited to 275F.
Combustion (Ion) Sensors
The Ion sensors were constructed from Autolite brand number 26 spark plugs unaltered and
connected to a PCB signal conditioner to provide a constant voltage potential across the electrodes.
The post was connected to the positive supply voltage of the signal conditioner and the body was
grounded to the common system ground and the signal conditioner ground. The default
configuration
Sound Level Meter
CEM DT-85A with an “A” frequency rating was used to measure sound levels at the detonation
tube and its surrounding area. The sound level meter has a measurement range of 35-130 dB and
an accuracy of +/- 3.0 dB and has a frequency range of 31.5Hz to 8KHz.
Infrared Handheld Gun
Extech 42545 high temperature infrared handheld thermometer was used to obtain surface
temperature measuments. The thermometer has a measurement range -58F to 1832F with
adjustable emissivity ratios and a narrow 50:1 distance to target ratio
109
Signal Conditioner
The high frequency and low frequency tubes utilizes a PCB 482C15unit for signal conditioning
which supports up to 4-channels and individually adjustable voltage gain settings. The signal
conditioner provides a constant current source needed for the pressure transducers.
Data Acquisition Board (DAQ)
A National Instruments USB-6351 DAQ was used for the experiments, Figure 16. Out of all the
unit’s features, only the analog inputs and timers were used for testing. The analog inputs are
capable of sampling at a rate of up to 1.25 MHz (multichannel aggregate) with 16-bit resolution
and range of ±10 V. They were used to record the pressure signals. The 32-bit counter/timers
were used as control lines to trigger the injection solenoids and ignition system. The actual
sampling throughput was slightly higher due to the short sampling periods of approximately 100
ms. A short wire harness using an AMP multi-pin connector was used to easily transport /
separate the DAQ from the main wiring harness.
Fuel Supply
The fuel used for all configurations in this research was ethylene research gas (EY R200) provided
by Airgas. Stored in a size 200 high pressure tank with a CGA 350 connection and regulated by
an Airgas two stage 100 psi output regulator (PN Y12215D350).
Power Supply
An adjustable 3-15 VDC 40A B&K Precision 1692 switching power supply was used to power
the igniter, coil, and the injector driver box. The unit has a fixed-voltage mode (at 13.9 VDC),
used for testing. A digital display on the unit’s front panel shows the output voltage and instant
current draw.
110
Injector Solenoids
The injector valves are manufactured by AFS, model Gs-series. They are ‘peak-and-hold’ type
valves. In order for them to have a fast response (opening/closing time), a high current must be
initially applied. Once the valve is open, a lower ‘hold’ current is sufficient to keep them open.
This avoids overheating the units. The manufacturer published mass flow vs. time curves were
obtained by using an AFS injector driver box. Therefore, to be able to properly correlate injector
opening time with mass flow, an AFS injector driver box was used.
Injector Driver
The injector driver box is an AFS 8-channel unit. It was powered by 13.8 VDC from the power
supply. It automatically provided the peak-and-hold output needed to trigger the injectors, based
on logic-level input signals from the DAQ.
Ignition coil and Igniter
The ignition module and coil were BOSCH units, fitted to several European cars. They were
powered by the 13.8VDC power supply, using heavy wire as described before. The ignition
module is of the ‘dumb’ type: i.e. coil charge time was directly controlled by the DAQ. A
wirewound noise suppression cable was used to connect the coil to the spark plug. The spark plug
used for all experiments is a standard Autolite 26 spark plug.
10.2 Hardware
The detonation tube was constructed from schedule 80 stainless steel 304 with a nominal
diameter of 2” and meets ASTM standard A312. Strength and temperature response of the
material is shown below.
111
Nom. ID, inches 2.0 Outer Diameter, inches 2.375
Wall thickness, min., inches 0.189 Wall thickness, nominal, inches 0.216
Working Pressure PSI (ambient T) 3,411 Yield strength, min, PSI 30,000
Burst pressure PSI (ambient T) 13,642 Tensile strength, min, PSI 75,000
Melting Point 2550-2640
Maximum Service Temperature 1380-1700
Obstacles
The obstacles were made from stainless steel 304 round tube and manufactured to the desired
tolerances shown in Appendix C.
Flanges
112
The flanges were socket-weld, class 300, conforming to MSS SP-6, SP-25, ASTM A182, and
ANSI/ASME B16.5 standards.
Flange gaskets
The flange gaskets were chosen to be full face class 300 gaskets conforming to ASME B16.20
standards and manufactured from NOVATEC engineered graphite and able to withstand
continuous temperatures of 925 degrees Fahrenheit
Bolts and Nuts
Bolts were chosen to be grade 2 stainless steel bolts with a minimum tensile strength of 70 Kpsi
Check valves
Check valves were of the Fluorelastomer seal type with a maximum pressure rating of 1000 psi
at 70 degrees Fahrenheit and have and can operate at temperatures of up to 400 degrees
Fahrenheit.
Injection block and Fuel Manifold
The injection blocks and fuel manifold delivery systems were machined from 6061 aluminum.
113
10.3 Data Acquisition and Instrumentation Wiring
Shown in Figure 90 is the ignition coil setup, the primary power supply provides a DC voltage
source of 13.8V to an automotive ignition coil. The power supply and coil both share a common
ground.
LabView Frontend
The control panel which controls the fuel, air, and spark timing as well as data measurement was
created using NI LabView 2011 and interfaces with the NI USB-6351 digital acquisition system
used in analog to digital conversion (ADC). The virtual instrument (VI) is designed to control all
the parameters that govern the filling and detonation of the fuel / air mixture save for the fuel and
air pressures which must be manually set at their respective regulators.
Figure 83: Labview Virtual Instrument
114
Figure 84: Input Control Panel for LabView VI
The Input control panel controls all the filling parameters for the fuel / air mixture supplied to gas
injectors and subsequently the spark pulse. Fuel Type and Oxidizer Type control the fuel and
oxidizer values used to calculate stoichiometric Air to Fuel ratio (AFR) and the appropriate
injector curvefit in the mathscript node located withing the LabView backend. Fuel and Oxidizer
pressure controls are used to determine the injector curvefits for injected mass vs. pulse width, in
the above figures these are grayed out to allow for maximum filling rates and minimum filling
time. Equivalence ratio, fill percentage, and tube length control the injected mass of fuel and air.
Modifying the equivalence ratio directly adjust the amount of fuel delivered to the detonation
tube while keeping the amount of air constant. Modifying the fill percentage and tube length
controls the overall volume used to calculate the mass of fuel and air needed. Increasing the fill
percentage multiplies the volume by the appropriate constant whereas modifying the tube length
will modify the volume by a ratio of L/Lo as governed by the equation V = R2L. Modifying the
pulse number directly changes the number of fuel, air, and spark On/Off pulse while System
pulse frequency will determine how closes those pulses are to each other. The system pulse
frequency effectively controls the time between one pulse and the next. Injector numbers tell the
mathscript code how to divide the total pulse time, if 2 oxygen injectors are used instead of 4 the
115
total required fill time for air will double and likewise with the fuel. Start delay and spark delay
control the time between when the user presses the run button and the appropriate signal is
generated. In the current implementation all timing is triggered by the air high pulse (the digital
on signal) which means that the initial delay is actually the air delay and the spark delay is the
time between when the air injectors are closed and when the spark is ignited. Spark time controls
how long the spark plug is firing which directly controls the energy deposition rate. The air, fuel,
and ignition toggle buttons control whether or not the digital pulses are sent to the injector and
spark devices. By default these buttons are set to on but can be set to default off if needed.
Figure 85: Data logging and Timing Panel for LabView VI
The logging and timing panel control the data logging features of the VI. It allows for controlling
the sampling rate, recording time, and whether or not to log data to a file. The timing panel
displays the calculated data from the given inputs such as estimated fuel and air mass delivered
and pulse widths. It is important to not however that the sample rate of the daq is limited to 1.4
million samples per second total across all ports which means that if six sensors are connected and
recorded then the maximum sample rate is 1.4MS/6 or 233.33 KHz. To remove sensors from
being recorded one needs to remove it from the DAQMX node in the LabView backend.
116
Figure 86: Graph Output Panel
The graph output panels show all the current sensors traces being used during the run. Recording
is started when the simulation is started although it can be changed to start when any of the injector
control pulses are fired or turned off. The top left corner shows just the scaled pressure sensor
traces, bottom left shows just ion sensor traces, top right shows the combined raw data from both
pressure and ion sensors and bottom left shows the digital pulses sent to the injectors and spark
plugs.
LabView Injector control system
The HFT VI employed in the experimental setup employs the use of pulse width modulation
(PWM) to deliver the precise amount of fuel desired for the inputs in the LabView frontend.
Each pulse time is calculated by the process outlined in APPENDIX B: CALCULATION OF FILLING
PARAMETERS, and then controlled by three independent hardware counters supplied by the NI
daq. The VI uses the inputs from the frontend panel to determine the required filling time for
both the fuel and air injectors. Adjusting the equivalence ratio, fill percentage, volume, and
number of injectors controls modify the width of the pulses (the “on times”) while pulse number
and frequency modify the spaces between pulses or the “off times”. Spark delay time will modify
117
the distance between the last fuel / air pulse and the ignition pulse. Start delay will modify the
time between when the user press the run button and the first pulse starts.
The LabView code following the mathscript node is necessary to convert the desired pulse times
into digital on off signals and is created in three parts. First a pulse generator node is created
which tells the daq a digital pulse needs to be generated and on what channel. After the pulse is
generated the daq is then informed of how many pulses need to be generated and in what mode
to run them. Lastly the signal is when to start whether is triggered on run, external signal, or
from internal digital signal. The pulse is then generated based on the rising or falling action of
the signal, i.e. on or off. If the triggering is set on rising then the pulse is simultaneous with the
trigger start and if set to falling it simultaneous with the end of a trigger.
Figure 87: Fuel Control System
118
Figure 88: Spark Plug Ignition Control System
119
Figure 89: Mathscript Node for LabView VI
120
Figure 90: Ignition Control Wiring
Figure 91: Injector Wiring
121
10.4 Test Procedure
WARNING: Before Continuing ensure that those involved in testing are wearing appropriate
safety gear. For those in the immediate vicinity hearing and eye protection is required, additionally
it is recommended that ear plugs be used to supplement hearing protection. For those not involved
in testing but are in close proximity hearing protection is still mandatory.
1) Connect required fuel / air hose lines ensuring that all connections are tight and leak free.
If lines are damaged discontinue testing immediately and repair.
2) Check to make sure all safety devices are functioning correctly, check valves, flashback
arrestors, etc.
3) Ensure that air pressure are set to appropriate levels as determined by the filling rate
required. (Visible on the LabView Front Panel).
4) Ensure all wiring from pressure transducers are connected to the signal conditioner.
5) Ensure all wiring to the DAQ system is connected
6) Turn on system power from the B&K Precision 1695 DC power supply.
7) Turn on PCB Piezotroncs signal conditioners
8) Turn on the USB-X6351 DAQ
9) Load the “HFT_VI” LabView Front Panel
10) Press “Run Once” to purge the fuel and air lines ensuring that there is no pressure in the
fuel line. If there is make sure the spark ignition is either turned off on the front panel or
the spark plug has been disconnected manually.
11) Once the lines have been purged the testing system is ready to be used.
122
11 APPENDIX B: CALCULATION OF FILLING PARAMETERS
123
Given: Liquefied Propane Gas (LPG) + Air
Composition
Gas Formula Mass
Fraction
Molecular
Weight
(g/mol)
Density
(kg/m3) @
SLS
Stoichiometric
O/F
Mass AFR
@ Stoich.
Propane 90.0 44.096 1.865 5:1 15.64
Propylene 5.0 42.080 1.780 9:2 14.75
Butane 3.5 58.122 2.458 13:2 15.425
Methane 1.5 16.042 0.678 2:1 17.195
Calculating density at specified conditions
has a molecular weight of 44.096 g/mol, using ideal gas law we have
, where
.
Volumetric Air – to – Fuel Ratio is simply the ratio of the number of moles in a balanced chemical
equation, i.e.
( )
And the Volumetric AFR is then for pure oxygen is
To find AFR by Mass
124
*Note we use divide by 0.232 because air is roughly 23.2% oxygen by mass.
We then do this for every constituent of the gas to find the overall AFR which is simply the mass
fraction of each fuel multiplied by is respective mass AFR.
∑
To determine mass of air required to fill volume:
Total mass of mixture is then equal to
Where is equal to the tube volume
Noting that
and we have
( )
Or
( )
Solving for we get:
( )
Accordingly is simply:
To calculate necessary pulse width for the fuel and air injectors one must reference the mass vs.
time curves provided by the manufacturer. For example, if we are to use a combination of propane
and air at 29 psig (200 kPag) and 87 psig respectively (200 kPag) to deliver 160 mg of air and 50
mg of fuel per injector. We simply reference the injector curves (shown in Figure 92and Figure
125
93) using the required mass in milligrams and pressure to find the required pulse width of air to
be roughly 18 ms and fuel to be 11ms.
Figure 92: Mass vs. Pulse Width curves for Propane
Figure 93: Mass vs. Pulse Width curves for Air
126
12 APPENDIX C: DRAWINGS AND DIAGRAMS
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
13 APPENDIX D: RAW DATA & RESULTS
149
0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334-100
-50
0
50
100
150
200
250
300
V21 = 1683.0 m/s
V32 = 1959.3 m/s
V43 = 1986.5 m/sV43
comb = 1700.6 m/s
Avg. Vel. = 1876.3 m/s
DDT Time = 12.46 ms
P1 = 229.2 psig
P2 = 267.8 psig
P3 = 226.8 psig
P4 = 270.0 psig
150
0.4284 0.4286 0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302-100
-50
0
50
100
150
200
250
300
350
V21 = 1918.7 m/s
V32 = 1701.5 m/s
V43 = 2104.2 m/sV43
comb = 1867.8 m/s
Avg. Vel. = 1908.1 m/s
DDT Time = 9.30 ms
P1 = 219.3 psig
P2 = 347.8 psig
P3 = 271.9 psig
P4 = 277.4 psig
151
0.4282 0.4284 0.4286 0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43-100
-50
0
50
100
150
200
250
300
350
V21 = 1964.0 m/s
V32 = 1689.7 m/s
V43 = 1965.8 m/sV43
comb = 1931.7 m/s
Avg. Vel. = 1873.2 m/s
DDT Time = 9.15 ms
P1 = 241.0 psig
P2 = 289.6 psig
P3 = 194.7 psig
P4 = 324.3 psig
152
0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404-100
-50
0
50
100
150
200
250
300
350
V21 = 1995.2 m/s
V32 = 1688.9 m/s
V43 = 1959.5 m/sV43
comb = 1938.3 m/s
Avg. Vel. = 1881.2 m/s
DDT Time = 19.58 ms
P1 = 250.0 psig
P2 = 225.2 psig
P3 = 253.8 psig
P4 = 319.5 psig
153
0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338-100
-50
0
50
100
150
200
250
300
V21 = 1731.5 m/s
V32 = 1899.8 m/s
V43 = 1990.0 m/sV43
comb = 1957.8 m/s
Avg. Vel. = 1873.8 m/s
DDT Time = 12.92 ms
P1 = 240.0 psig
P2 = 261.4 psig
P3 = 278.3 psig
P4 = 248.6 psig
154
0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334-100
-50
0
50
100
150
200
250
300
350
V21 = 1957.7 m/s
V32 = 1807.6 m/s
V43 = 1891.9 m/sV43
comb = 1919.3 m/s
Avg. Vel. = 1885.7 m/s
DDT Time = 12.51 ms
P1 = 244.4 psig
P2 = 244.0 psig
P3 = 340.6 psig
P4 = 312.7 psig
155
0.4436 0.4438 0.444 0.4442 0.4444 0.4446 0.4448 0.445 0.4452 0.4454-40
-20
0
20
40
60
80
100
V21 = 988.9 m/s
V32 = 919.0 m/s
V43 = 909.7 m/sV43
comb = 539.6 m/s
Avg. Vel. = 939.2 m/s
DDT Time = 24.46 ms
P1 = 84.7 psig
P2 = 89.1 psig
P3 = 99.3 psig
P4 = 90.7 psig
156
0.4464 0.4466 0.4468 0.447 0.4472 0.4474 0.4476 0.4478 0.448 0.4482-40
-20
0
20
40
60
80
100
120
V21 = 930.7 m/s
V32 = 996.1 m/s
V43 = 925.3 m/sV43
comb = 497.8 m/s
Avg. Vel. = 950.7 m/s
DDT Time = 27.26 ms
P1 = 87.5 psig
P2 = 87.1 psig
P3 = 111.9 psig
P4 = 93.5 psig
157
0.4312 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433-100
-50
0
50
100
150
200
250
300
350
400
V21 = 1691.3 m/s
V32 = 1932.7 m/s
V43 = 1983.4 m/sV43
comb = 1960.9 m/s
Avg. Vel. = 1869.1 m/s
DDT Time = 12.16 ms
P1 = 265.3 psig
P2 = 216.3 psig
P3 = 235.3 psig
P4 = 399.1 psig
158
0.4414 0.4416 0.4418 0.442 0.4422 0.4424 0.4426 0.4428 0.443 0.4432-100
-50
0
50
100
150
200
V21 = 1001.1 m/s
V32 = 679.4 m/s
V43 = 1850.0 m/sV43
comb = 3862.5 m/s
Avg. Vel. = 1176.8 m/s
DDT Time = 22.25 ms
P1 = 101.1 psig
P2 = 90.4 psig
P3 = 104.7 psig
P4 = 184.0 psig
159
0.4376 0.4378 0.438 0.4382 0.4384 0.4386 0.4388 0.439 0.4392 0.4394-100
-50
0
50
100
150
200
250
300
V21 = 1686.9 m/s
V32 = 1946.4 m/s
V43 = 1751.5 m/sV43
comb = 1772.6 m/s
Avg. Vel. = 1795.0 m/s
DDT Time = 18.57 ms
P1 = 282.1 psig
P2 = 238.6 psig
P3 = 230.0 psig
P4 = 178.4 psig
160
0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338 0.434 0.4342-80
-60
-40
-20
0
20
40
60
80
100
120
V21 = 1060.4 m/s
V32 = 738.5 m/s
V43 = 1827.0 m/sV43
comb = 822.8 m/s
Avg. Vel. = 1208.6 m/s
DDT Time = 13.17 ms
P1 = 98.1 psig
P2 = 102.4 psig
P3 = 118.9 psig
P4 = 104.1 psig
161
0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338 0.434 0.4342-100
-50
0
50
100
150
200
V21 = 1081.2 m/s
V32 = 992.1 m/s
V43 = 1055.9 m/sV43
comb = 5.2 m/s
Avg. Vel. = 1043.1 m/s
DDT Time = 13.21 ms
P1 = 125.0 psig
P2 = 133.8 psig
P3 = 141.7 psig
P4 = 158.0 psig
162
0.445 0.4452 0.4454 0.4456 0.4458 0.446 0.4462 0.4464 0.4466 0.4468-100
-50
0
50
100
150
200
250
300
350
400
V21 = 1708.4 m/s
V32 = 1942.3 m/s
V43 = 1745.4 m/sV43
comb = 1912.1 m/s
Avg. Vel. = 1798.7 m/s
DDT Time = 25.90 ms
P1 = 225.6 psig
P2 = 207.0 psig
P3 = 371.2 psig
P4 = 267.1 psig
163
0.4264 0.4266 0.4268 0.427 0.4272 0.4274 0.4276 0.4278 0.428 0.4282-100
0
100
200
300
400
500
V21 = 1958.9 m/s
V32 = 2344.2 m/s
V43 = 1341.7 m/sV43
comb = 1904.0 m/s
Avg. Vel. = 1881.6 m/s
DDT Time = 7.21 ms
P1 = 228.5 psig
P2 = 297.7 psig
P3 = 490.3 psig
P4 = 310.3 psig
164
0.4312 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433-100
0
100
200
300
400
500
V21 = 1668.6 m/s
V32 = 1962.8 m/s
V43 = 1835.0 m/sV43
comb = 1936.6 m/s
Avg. Vel. = 1822.1 m/s
DDT Time = 12.08 ms
P1 = 299.0 psig
P2 = 319.0 psig
P3 = 226.0 psig
P4 = 412.5 psig
165
0.4384 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402-100
-50
0
50
100
150
200
250
300
350
400
V21 = 1956.3 m/s
V32 = 1945.7 m/s
V43 = 1715.5 m/sV43
comb = 1690.0 m/s
Avg. Vel. = 1872.5 m/s
DDT Time = 19.28 ms
P1 = 228.0 psig
P2 = 266.4 psig
P3 = 384.9 psig
P4 = 193.2 psig
166
0.43 0.4302 0.4304 0.4306 0.4308 0.431 0.4312 0.4314 0.4316 0.4318-100
-50
0
50
100
150
200
250
300
V21 = 1945.7 m/s
V32 = 1715.6 m/s
V43 = 1855.3 m/sV43
comb = -15030.8 m/s
Avg. Vel. = 1838.9 m/s
DDT Time = 10.82 ms
P1 = 228.7 psig
P2 = 241.8 psig
P3 = 256.1 psig
P4 = 213.8 psig
167
0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404 0.4406-100
-50
0
50
100
150
200
250
300
V21 = 1693.1 m/s
V32 = 1978.4 m/s
V43 = 1720.9 m/sV43
comb = 1696.9 m/s
Avg. Vel. = 1797.4 m/s
DDT Time = 19.73 ms
P1 = 254.8 psig
P2 = 226.3 psig
P3 = 206.2 psig
P4 = 237.5 psig
168
0.43 0.4302 0.4304 0.4306 0.4308 0.431 0.4312 0.4314 0.4316 0.4318-100
-50
0
50
100
150
200
250
300
350
V21 = 1970.9 m/s
V32 = 1692.8 m/s
V43 = 2068.1 m/sV43
comb = 1983.1 m/s
Avg. Vel. = 1910.6 m/s
DDT Time = 10.83 ms
P1 = 206.3 psig
P2 = 317.7 psig
P3 = 229.2 psig
P4 = 308.7 psig
169
0.437 0.4372 0.4374 0.4376 0.4378 0.438 0.4382 0.4384 0.4386 0.4388-100
0
100
200
300
400
500
V21 = 1951.5 m/s
V32 = 1687.6 m/s
V43 = 2358.3 m/sV43
comb = 1958.1 m/s
Avg. Vel. = 1999.1 m/s
DDT Time = 18.00 ms
P1 = 206.2 psig
P2 = 213.6 psig
P3 = 220.1 psig
P4 = 446.9 psig
170
0.445 0.4452 0.4454 0.4456 0.4458 0.446 0.4462 0.4464 0.4466 0.4468-100
-50
0
50
100
150
200
250
300
350
V21 = 1705.7 m/s
V32 = 1949.0 m/s
V43 = 1996.3 m/sV43
comb = 1670.4 m/s
Avg. Vel. = 1883.6 m/s
DDT Time = 25.89 ms
P1 = 320.0 psig
P2 = 223.8 psig
P3 = 266.8 psig
P4 = 292.7 psig
171
0.4384 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402-100
-50
0
50
100
150
200
250
300
350
400
V21 = 1972.3 m/s
V32 = 1683.4 m/s
V43 = 1693.9 m/sV43
comb = 1936.4 m/s
Avg. Vel. = 1783.2 m/s
DDT Time = 19.21 ms
P1 = 219.2 psig
P2 = 213.3 psig
P3 = 383.7 psig
P4 = 269.5 psig
172
0.4466 0.4468 0.447 0.4472 0.4474 0.4476 0.4478 0.448 0.4482 0.4484-100
0
100
200
300
400
500
V21 = 2070.2 m/s
V32 = 1863.6 m/s
V43 = 1763.5 m/sV43
comb = 1924.8 m/s
Avg. Vel. = 1899.1 m/s
DDT Time = 27.54 ms
P1 = 482.4 psig
P2 = 208.2 psig
P3 = 190.2 psig
P4 = 246.1 psig
173
0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338-100
-50
0
50
100
150
200
250
V21 = 1942.5 m/s
V32 = 1697.4 m/s
V43 = 1983.3 m/sV43
comb = 1967.1 m/s
Avg. Vel. = 1874.4 m/s
DDT Time = 12.79 ms
P1 = 246.7 psig
P2 = 219.0 psig
P3 = 218.7 psig
P4 = 207.5 psig
174
0.4354 0.4356 0.4358 0.436 0.4362 0.4364 0.4366 0.4368 0.437 0.4372-200
-100
0
100
200
300
400
V21 = 2009.3 m/s
V32 = 1960.1 m/s
V43 = 1732.8 m/sV43
comb = 1964.5 m/s
Avg. Vel. = 1900.7 m/s
DDT Time = 16.27 ms
P1 = 368.3 psig
P2 = 224.6 psig
P3 = 239.6 psig
P4 = 356.1 psig
175
0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404-150
-100
-50
0
50
100
150
200
250
300
V21 = 1970.3 m/s
V32 = 1841.8 m/s
V43 = 1807.2 m/sV43
comb = 1942.7 m/s
Avg. Vel. = 1873.1 m/s
DDT Time = 19.59 ms
P1 = 271.2 psig
P2 = 265.7 psig
P3 = 199.2 psig
P4 = 263.6 psig
176
0.438 0.4382 0.4384 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398-100
0
100
200
300
400
500
V21 = 1695.7 m/s
V32 = 1959.7 m/s
V43 = 1954.7 m/sV43
comb = 1731.9 m/s
Avg. Vel. = 1870.0 m/s
DDT Time = 18.92 ms
P1 = 253.7 psig
P2 = 218.1 psig
P3 = 243.1 psig
P4 = 481.3 psig
177
0.4358 0.436 0.4362 0.4364 0.4366 0.4368 0.437 0.4372 0.4374 0.4376-100
0
100
200
300
400
500
V21 = 1671.4 m/s
V32 = 1984.6 m/s
V43 = 1977.2 m/sV43
comb = 1967.0 m/s
Avg. Vel. = 1877.7 m/s
DDT Time = 16.60 ms
P1 = 262.1 psig
P2 = 414.5 psig
P3 = 252.1 psig
P4 = 375.5 psig
178
0.4336 0.4338 0.434 0.4342 0.4344 0.4346 0.4348 0.435 0.4352 0.4354-100
-50
0
50
100
150
200
250
300
350
V21 = 1706.1 m/s
V32 = 1949.3 m/s
V43 = 1708.6 m/sV43
comb = 2026.3 m/s
Avg. Vel. = 1788.0 m/s
DDT Time = 14.45 ms
P1 = 211.3 psig
P2 = 181.8 psig
P3 = 233.7 psig
P4 = 309.1 psig
179
0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302 0.4304 0.4306-100
-50
0
50
100
150
200
250
300
V21 = 1703.3 m/s
V32 = 1947.5 m/s
V43 = 2021.2 m/sV43
comb = 1963.0 m/s
Avg. Vel. = 1890.7 m/s
DDT Time = 9.75 ms
P1 = 243.4 psig
P2 = 256.4 psig
P3 = 246.6 psig
P4 = 225.1 psig
180
0.431 0.4312 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328-100
-50
0
50
100
150
200
250
V21 = 1897.3 m/s
V32 = 1738.3 m/s
V43 = 1902.3 m/sV43
comb = 1670.6 m/s
Avg. Vel. = 1845.9 m/s
DDT Time = 11.96 ms
P1 = 207.8 psig
P2 = 195.1 psig
P3 = 173.5 psig
P4 = 234.2 psig
181
0.4282 0.4284 0.4286 0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43-100
-50
0
50
100
150
200
250
300
350
V21 = 1786.4 m/s
V32 = 1864.2 m/s
V43 = 2149.4 m/sV43
comb = 1982.5 m/s
Avg. Vel. = 1933.3 m/s
DDT Time = 9.06 ms
P1 = 205.6 psig
P2 = 198.1 psig
P3 = 197.4 psig
P4 = 314.6 psig
182
0.4398 0.44 0.4402 0.4404 0.4406 0.4408 0.441 0.4412 0.4414 0.4416-100
-50
0
50
100
150
200
250
300
V21 = 1977.1 m/s
V32 = 1698.3 m/s
V43 = 2351.5 m/sV43
comb = 1945.5 m/s
Avg. Vel. = 2009.0 m/s
DDT Time = 20.66 ms
P1 = 232.0 psig
P2 = 214.1 psig
P3 = 226.9 psig
P4 = 266.9 psig
183
0.4464 0.4466 0.4468 0.447 0.4472 0.4474 0.4476 0.4478 0.448 0.4482-100
-50
0
50
100
150
200
250
V21 = 1887.3 m/s
V32 = 1777.2 m/s
V43 = 1982.6 m/sV43
comb = 1945.7 m/s
Avg. Vel. = 1882.4 m/s
DDT Time = 27.22 ms
P1 = 193.8 psig
P2 = 194.6 psig
P3 = 210.4 psig
P4 = 196.4 psig
184
0.437 0.4372 0.4374 0.4376 0.4378 0.438 0.4382 0.4384 0.4386 0.4388-100
-50
0
50
100
150
200
250
V21 = 1966.3 m/s
V32 = 1959.8 m/s
V43 = 1695.6 m/sV43
comb = 1814.1 m/s
Avg. Vel. = 1873.9 m/s
DDT Time = 17.88 ms
P1 = 202.6 psig
P2 = 230.4 psig
P3 = 210.3 psig
P4 = 243.2 psig
185
0.4394 0.4396 0.4398 0.44 0.4402 0.4404 0.4406 0.4408 0.441 0.4412-100
-50
0
50
100
150
200
250
V21 = 1694.4 m/s
V32 = 2007.6 m/s
V43 = 1658.8 m/sV43
comb = 1960.3 m/s
Avg. Vel. = 1786.9 m/s
DDT Time = 20.39 ms
P1 = 241.7 psig
P2 = 207.5 psig
P3 = 191.4 psig
P4 = 191.0 psig
186
0.4368 0.437 0.4372 0.4374 0.4376 0.4378 0.438 0.4382 0.4384 0.4386-100
-50
0
50
100
150
200
250
300
V21 = 1707.3 m/s
V32 = 1961.9 m/s
V43 = 1723.9 m/sV43
comb = 1807.5 m/s
Avg. Vel. = 1797.7 m/s
DDT Time = 17.65 ms
P1 = 295.9 psig
P2 = 202.9 psig
P3 = 209.3 psig
P4 = 165.8 psig
187
0.447 0.4472 0.4474 0.4476 0.4478 0.448 0.4482 0.4484 0.4486 0.4488-100
-50
0
50
100
150
200
250
300
V21 = 2414.0 m/s
V32 = 1985.8 m/s
V43 = 1700.0 m/sV43
comb = 1690.5 m/s
Avg. Vel. = 2033.3 m/s
DDT Time = 27.97 ms
P1 = 239.2 psig
P2 = 253.6 psig
P3 = 177.1 psig
P4 = 218.6 psig
188
0.444 0.4442 0.4444 0.4446 0.4448 0.445 0.4452 0.4454 0.4456 0.4458-100
-50
0
50
100
150
200
250
300
V21 = 1673.2 m/s
V32 = 1942.4 m/s
V43 = 2038.4 m/sV43
comb = 1970.2 m/s
Avg. Vel. = 1884.7 m/s
DDT Time = 24.94 ms
P1 = 267.2 psig
P2 = 234.2 psig
P3 = 237.8 psig
P4 = 233.2 psig
189
0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332-100
-50
0
50
100
150
200
250
300
V21 = 1768.0 m/s
V32 = 1846.3 m/s
V43 = 1980.6 m/sV43
comb = 1953.9 m/s
Avg. Vel. = 1865.0 m/s
DDT Time = 12.28 ms
P1 = 250.7 psig
P2 = 222.7 psig
P3 = 189.2 psig
P4 = 206.7 psig
190
0.4482 0.4484 0.4486 0.4488 0.449 0.4492 0.4494 0.4496 0.4498 0.45-100
-50
0
50
100
150
200
250
300
V21 = 1973.0 m/s
V32 = 1970.4 m/s
V43 = 1689.3 m/sV43
comb = 1935.8 m/s
Avg. Vel. = 1877.6 m/s
DDT Time = 29.17 ms
P1 = 237.2 psig
P2 = 192.8 psig
P3 = 199.1 psig
P4 = 281.4 psig
191
0.4416 0.4418 0.442 0.4422 0.4424 0.4426 0.4428 0.443 0.4432 0.4434-100
-50
0
50
100
150
200
250
300
V21 = 1984.5 m/s
V32 = 1684.5 m/s
V43 = 1957.7 m/sV43
comb = -4.9 m/s
Avg. Vel. = 1875.6 m/s
DDT Time = 22.51 ms
P1 = 254.4 psig
P2 = 201.3 psig
P3 = 201.9 psig
P4 = 264.8 psig
192
0.4424 0.4426 0.4428 0.443 0.4432 0.4434 0.4436 0.4438 0.444 0.4442-100
-50
0
50
100
150
200
250
V21 = 1690.3 m/s
V32 = 1980.3 m/s
V43 = 1958.6 m/sV43
comb = 1984.9 m/s
Avg. Vel. = 1876.4 m/s
DDT Time = 23.30 ms
P1 = 232.3 psig
P2 = 217.8 psig
P3 = 220.9 psig
P4 = 203.7 psig
193
0.44 0.4402 0.4404 0.4406 0.4408 0.441 0.4412 0.4414 0.4416 0.4418-100
0
100
200
300
400
500
V21 = 1926.2 m/s
V32 = 1720.1 m/s
V43 = 1950.4 m/sV43
comb = 1971.7 m/s
Avg. Vel. = 1865.6 m/s
DDT Time = 20.82 ms
P1 = 207.4 psig
P2 = 166.1 psig
P3 = 229.1 psig
P4 = 415.1 psig
194
0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338 0.434 0.4342-100
-50
0
50
100
150
200
250
300
350
400
V21 = 1832.5 m/s
V32 = 1813.8 m/s
V43 = 1975.0 m/sV43
comb = 1997.2 m/s
Avg. Vel. = 1873.8 m/s
DDT Time = 13.29 ms
P1 = 355.3 psig
P2 = 175.3 psig
P3 = 239.6 psig
P4 = 212.1 psig
195
0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338 0.434-50
0
50
100
150
200
250
300
350
V21 = 1678.2 m/s
V32 = 1986.3 m/s
V43 = 1974.1 m/sV43
comb = 1677.2 m/s
Avg. Vel. = 1879.5 m/s
DDT Time = 13.00 ms
P1 = 253.9 psig
P2 = 293.8 psig
P3 = 230.0 psig
P4 = 319.1 psig
196
0.443 0.4432 0.4434 0.4436 0.4438 0.444 0.4442 0.4444 0.4446 0.4448-100
0
100
200
300
400
500
600
700
800
900
V21 = 1726.1 m/s
V32 = 1948.5 m/s
V43 = 1952.4 m/sV43
comb = 1967.5 m/s
Avg. Vel. = 1875.7 m/s
DDT Time = 23.84 ms
P1 = 264.8 psig
P2 = 162.8 psig
P3 = 225.9 psig
P4 = 808.7 psig
197
0.4394 0.4396 0.4398 0.44 0.4402 0.4404 0.4406 0.4408 0.441 0.4412-100
-50
0
50
100
150
200
250
300
V21 = 1701.1 m/s
V32 = 1981.2 m/s
V43 = 1676.3 m/sV43
comb = 1728.4 m/s
Avg. Vel. = 1786.2 m/s
DDT Time = 20.30 ms
P1 = 254.3 psig
P2 = 199.3 psig
P3 = 197.7 psig
P4 = 217.7 psig
198
0.4454 0.4456 0.4458 0.446 0.4462 0.4464 0.4466 0.4468 0.447 0.4472-50
0
50
100
150
200
250
V21 = 1910.2 m/s
V32 = 1731.6 m/s
V43 = 1936.5 m/sV43
comb = 1946.2 m/s
Avg. Vel. = 1859.4 m/s
DDT Time = 26.34 ms
P1 = 236.9 psig
P2 = 175.8 psig
P3 = 249.9 psig
P4 = 210.2 psig
199
0.43 0.4302 0.4304 0.4306 0.4308 0.431 0.4312 0.4314 0.4316 0.4318-100
-50
0
50
100
150
200
250
300
350
V21 = 1976.3 m/s
V32 = 1944.9 m/s
V43 = 1699.4 m/sV43
comb = 1942.1 m/s
Avg. Vel. = 1873.6 m/s
DDT Time = 10.81 ms
P1 = 212.6 psig
P2 = 162.1 psig
P3 = 320.2 psig
P4 = 193.2 psig
200
0.4432 0.4434 0.4436 0.4438 0.444 0.4442 0.4444 0.4446 0.4448 0.445-100
-50
0
50
100
150
200
250
300
V21 = 1937.6 m/s
V32 = 1730.4 m/s
V43 = 1908.8 m/sV43
comb = 1996.6 m/s
Avg. Vel. = 1858.9 m/s
DDT Time = 24.05 ms
P1 = 173.8 psig
P2 = 188.3 psig
P3 = 183.8 psig
P4 = 261.1 psig
201
0.4432 0.4434 0.4436 0.4438 0.444 0.4442 0.4444 0.4446 0.4448 0.445-100
-50
0
50
100
150
200
250
300
V21 = 1937.6 m/s
V32 = 1730.4 m/s
V43 = 1908.8 m/sV43
comb = 1996.6 m/s
Avg. Vel. = 1858.9 m/s
DDT Time = 24.05 ms
P1 = 173.8 psig
P2 = 188.3 psig
P3 = 183.8 psig
P4 = 261.1 psig
202
0.4338 0.434 0.4342 0.4344 0.4346 0.4348 0.435 0.4352 0.4354 0.4356-100
-50
0
50
100
150
200
250
300
V21 = 1955.3 m/s
V32 = 1949.7 m/s
V43 = 1704.3 m/sV43
comb = 1684.3 m/s
Avg. Vel. = 1869.7 m/s
DDT Time = 14.60 ms
P1 = 210.2 psig
P2 = 187.6 psig
P3 = 273.8 psig
P4 = 258.3 psig
203
0.4328 0.433 0.4332 0.4334 0.4336 0.4338 0.434 0.4342 0.4344 0.4346-100
-50
0
50
100
150
200
250
300
350
V21 = 1698.8 m/s
V32 = 2009.0 m/s
V43 = 1947.7 m/sV43
comb = 1701.3 m/s
Avg. Vel. = 1885.2 m/s
DDT Time = 13.64 ms
P1 = 238.3 psig
P2 = 304.1 psig
P3 = 208.8 psig
P4 = 197.0 psig
204
0.4436 0.4438 0.444 0.4442 0.4444 0.4446 0.4448 0.445 0.4452 0.4454-100
-50
0
50
100
150
200
250
V21 = 1644.2 m/s
V32 = 1708.5 m/s
V43 = 1778.1 m/sV43
comb = 2512.7 m/s
Avg. Vel. = 1710.3 m/s
DDT Time = 24.54 ms
P1 = 232.4 psig
P2 = 229.9 psig
P3 = 206.9 psig
P4 = 249.1 psig
205
0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336-400
-300
-200
-100
0
100
200
300
400
V21 = 1684.2 m/s
V32 = 1980.3 m/s
V43 = 1795.3 m/sV43
comb = 1697.7 m/s
Avg. Vel. = 1820.0 m/s
DDT Time = 12.79 ms
P1 = 219.2 psig
P2 = 344.2 psig
P3 = 222.6 psig
P4 = 274.7 psig
206
0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334-300
-200
-100
0
100
200
300
400
V21 = 1963.3 m/s
V32 = 1687.6 m/s
V43 = 1950.6 m/sV43
comb = -5.3 m/s
Avg. Vel. = 1867.2 m/s
DDT Time = 12.45 ms
P1 = 255.7 psig
P2 = 229.0 psig
P3 = 252.9 psig
P4 = 328.2 psig
207
0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302 0.4304 0.4306 0.4308-150
-100
-50
0
50
100
150
200
250
300
V21 = 1760.6 m/s
V32 = 2006.8 m/s
V43 = 1926.3 m/sV43
comb = 1679.9 m/s
Avg. Vel. = 1897.9 m/s
DDT Time = 9.86 ms
P1 = 221.3 psig
P2 = 257.2 psig
P3 = 174.9 psig
P4 = 228.7 psig
208
0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404-100
-50
0
50
100
150
200
250
300
V21 = 1806.7 m/s
V32 = 1967.0 m/s
V43 = 1697.6 m/sV43
comb = 1676.7 m/s
Avg. Vel. = 1823.8 m/s
DDT Time = 19.40 ms
P1 = 293.1 psig
P2 = 251.7 psig
P3 = 242.9 psig
P4 = 232.7 psig
209
0.4414 0.4416 0.4418 0.442 0.4422 0.4424 0.4426 0.4428 0.443 0.4432-100
-50
0
50
100
150
200
250
300
350
400
V21 = 1963.3 m/s
V32 = 1851.4 m/s
V43 = 1849.3 m/sV43
comb = 1988.5 m/s
Avg. Vel. = 1888.0 m/s
DDT Time = 22.24 ms
P1 = 252.2 psig
P2 = 259.4 psig
P3 = 233.5 psig
P4 = 372.0 psig
210
0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334-100
-50
0
50
100
150
200
250
300
350
400
V21 = 1923.8 m/s
V32 = 1826.1 m/s
V43 = 2165.6 m/sV43
comb = 1925.4 m/s
Avg. Vel. = 1971.8 m/s
DDT Time = 12.54 ms
P1 = 242.6 psig
P2 = 392.3 psig
P3 = 217.2 psig
P4 = 308.7 psig
211
0.4402 0.4404 0.4406 0.4408 0.441 0.4412 0.4414 0.4416 0.4418 0.442-200
-100
0
100
200
300
400
V21 = 1963.0 m/s
V32 = 1955.4 m/s
V43 = 1774.7 m/sV43
comb = 1938.0 m/s
Avg. Vel. = 1897.7 m/s
DDT Time = 20.99 ms
P1 = 235.2 psig
P2 = 255.5 psig
P3 = 224.4 psig
P4 = 310.9 psig
212
0.4348 0.435 0.4352 0.4354 0.4356 0.4358 0.436 0.4362 0.4364 0.4366-100
-50
0
50
100
150
200
250
300
V21 = 1745.7 m/s
V32 = 2234.7 m/s
V43 = 1713.1 m/sV43
comb = 1989.7 m/s
Avg. Vel. = 1897.8 m/s
DDT Time = 15.79 ms
P1 = 230.5 psig
P2 = 224.1 psig
P3 = 266.7 psig
P4 = 235.4 psig
213
0.4352 0.4354 0.4356 0.4358 0.436 0.4362 0.4364 0.4366 0.4368 0.437-100
-50
0
50
100
150
200
250
300
350
V21 = 1955.5 m/s
V32 = 1936.2 m/s
V43 = 1726.7 m/sV43
comb = 1956.6 m/s
Avg. Vel. = 1872.8 m/s
DDT Time = 16.16 ms
P1 = 242.2 psig
P2 = 309.6 psig
P3 = 229.8 psig
P4 = 219.8 psig
214
0.431 0.4312 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328-100
-50
0
50
100
150
200
250
300
350
V21 = 1986.6 m/s
V32 = 1670.1 m/s
V43 = 1968.4 m/sV43
comb = 1963.4 m/s
Avg. Vel. = 1875.1 m/s
DDT Time = 11.94 ms
P1 = 243.3 psig
P2 = 178.4 psig
P3 = 268.4 psig
P4 = 319.6 psig
215
0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332-100
-50
0
50
100
150
200
250
300
V21 = 1981.5 m/s
V32 = 1969.3 m/s
V43 = 1683.9 m/sV43
comb = 1937.3 m/s
Avg. Vel. = 1878.2 m/s
DDT Time = 12.26 ms
P1 = 277.9 psig
P2 = 204.7 psig
P3 = 296.3 psig
P4 = 249.5 psig
216
0.4356 0.4358 0.436 0.4362 0.4364 0.4366 0.4368 0.437 0.4372 0.4374-100
-50
0
50
100
150
200
250
V21 = 1926.6 m/s
V32 = 1963.6 m/s
V43 = 1704.7 m/sV43
comb = 1676.9 m/s
Avg. Vel. = 1864.9 m/s
DDT Time = 16.48 ms
P1 = 231.7 psig
P2 = 201.3 psig
P3 = 236.2 psig
P4 = 223.7 psig
217
0.4478 0.448 0.4482 0.4484 0.4486 0.4488 0.449 0.4492 0.4494 0.4496-100
-50
0
50
100
150
200
250
300
350
V21 = 1688.8 m/s
V32 = 1959.3 m/s
V43 = 1713.2 m/sV43
comb = 1705.1 m/s
Avg. Vel. = 1787.1 m/s
DDT Time = 28.72 ms
P1 = 301.8 psig
P2 = 319.6 psig
P3 = 267.8 psig
P4 = 197.6 psig
218
0.442 0.4422 0.4424 0.4426 0.4428 0.443 0.4432 0.4434 0.4436 0.4438-100
-50
0
50
100
150
200
250
300
350
V21 = 1804.0 m/s
V32 = 1845.3 m/s
V43 = 2381.6 m/sV43
comb = 1965.7 m/s
Avg. Vel. = 2010.3 m/s
DDT Time = 22.97 ms
P1 = 271.8 psig
P2 = 277.8 psig
P3 = 261.1 psig
P4 = 319.2 psig
219
0.4432 0.4434 0.4436 0.4438 0.444 0.4442 0.4444 0.4446 0.4448 0.445-100
-50
0
50
100
150
200
250
300
350
400
V21 = 1693.9 m/s
V32 = 1937.3 m/s
V43 = 2067.8 m/sV43
comb = 1772.6 m/s
Avg. Vel. = 1899.7 m/s
DDT Time = 24.08 ms
P1 = 232.4 psig
P2 = 220.1 psig
P3 = 222.9 psig
P4 = 364.9 psig
220
0.4312 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433-100
-50
0
50
100
150
200
250
300
V21 = 1966.3 m/s
V32 = 1693.8 m/s
V43 = 1937.8 m/sV43
comb = 1976.3 m/s
Avg. Vel. = 1866.0 m/s
DDT Time = 12.12 ms
P1 = 259.6 psig
P2 = 189.9 psig
P3 = 232.6 psig
P4 = 195.9 psig
221
0.4398 0.44 0.4402 0.4404 0.4406 0.4408 0.441 0.4412 0.4414 0.4416-100
-50
0
50
100
150
200
250
300
V21 = 1966.5 m/s
V32 = 1756.6 m/s
V43 = 2232.8 m/sV43
comb = -5.2 m/s
Avg. Vel. = 1985.3 m/s
DDT Time = 20.61 ms
P1 = 229.9 psig
P2 = 196.5 psig
P3 = 267.7 psig
P4 = 235.2 psig
222
0.4264 0.4266 0.4268 0.427 0.4272 0.4274 0.4276 0.4278 0.428 0.4282-100
0
100
200
300
400
500
V21 = 1977.0 m/s
V32 = 1710.7 m/s
V43 = 1810.2 m/sV43
comb = 1970.6 m/s
Avg. Vel. = 1832.7 m/s
DDT Time = 7.21 ms
P1 = 415.9 psig
P2 = 194.7 psig
P3 = 209.4 psig
P4 = 225.7 psig
223
0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334-100
-50
0
50
100
150
200
250
V21 = 1907.4 m/s
V32 = 1702.5 m/s
V43 = 1956.5 m/sV43
comb = 1963.5 m/s
Avg. Vel. = 1855.5 m/s
DDT Time = 12.53 ms
P1 = 241.0 psig
P2 = 212.2 psig
P3 = 243.1 psig
P4 = 210.7 psig
224
0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338-100
-50
0
50
100
150
200
250
300
V21 = 1705.4 m/s
V32 = 1996.4 m/s
V43 = 1687.5 m/sV43
comb = 1688.8 m/s
Avg. Vel. = 1796.4 m/s
DDT Time = 12.88 ms
P1 = 296.0 psig
P2 = 278.5 psig
P3 = 212.8 psig
P4 = 268.6 psig
225
0.4414 0.4416 0.4418 0.442 0.4422 0.4424 0.4426 0.4428 0.443 0.4432-100
-50
0
50
100
150
200
250
300
V21 = 1909.8 m/s
V32 = 1757.3 m/s
V43 = 2261.8 m/sV43
comb = 1981.5 m/s
Avg. Vel. = 1976.3 m/s
DDT Time = 22.22 ms
P1 = 256.4 psig
P2 = 262.0 psig
P3 = 239.9 psig
P4 = 289.1 psig
226
0.4312 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433-100
-50
0
50
100
150
200
250
300
V21 = 1694.3 m/s
V32 = 1955.2 m/s
V43 = 1996.8 m/sV43
comb = 1679.0 m/s
Avg. Vel. = 1882.1 m/s
DDT Time = 12.02 ms
P1 = 272.5 psig
P2 = 247.5 psig
P3 = 291.7 psig
P4 = 216.4 psig
227
0.4292 0.4294 0.4296 0.4298 0.43 0.4302 0.4304 0.4306 0.4308 0.431-50
0
50
100
150
200
250
V21 = 1745.1 m/s
V32 = 1906.3 m/s
V43 = 1982.1 m/sV43
comb = 1969.6 m/s
Avg. Vel. = 1877.8 m/s
DDT Time = 10.06 ms
P1 = 240.4 psig
P2 = 218.0 psig
P3 = 194.4 psig
P4 = 202.9 psig
228
0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404-100
-50
0
50
100
150
200
250
300
V21 = 1687.1 m/s
V32 = 1973.1 m/s
V43 = 1957.7 m/sV43
comb = 1679.5 m/s
Avg. Vel. = 1872.6 m/s
DDT Time = 19.48 ms
P1 = 287.7 psig
P2 = 176.2 psig
P3 = 196.8 psig
P4 = 268.8 psig
229
0.4406 0.4408 0.441 0.4412 0.4414 0.4416 0.4418 0.442 0.4422 0.4424-100
-50
0
50
100
150
200
250
V21 = 1780.1 m/s
V32 = 1831.7 m/s
V43 = 1945.6 m/sV43
comb = 1960.1 m/s
Avg. Vel. = 1852.5 m/s
DDT Time = 21.45 ms
P1 = 232.4 psig
P2 = 228.9 psig
P3 = 204.1 psig
P4 = 205.2 psig
230
0.4284 0.4286 0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302-100
-50
0
50
100
150
200
250
300
V21 = 1675.8 m/s
V32 = 1973.4 m/s
V43 = 2012.2 m/sV43
comb = 1738.2 m/s
Avg. Vel. = 1887.1 m/s
DDT Time = 9.36 ms
P1 = 234.1 psig
P2 = 255.1 psig
P3 = 246.5 psig
P4 = 219.6 psig
231
0.4366 0.4368 0.437 0.4372 0.4374 0.4376 0.4378 0.438 0.4382 0.4384-100
-50
0
50
100
150
200
250
300
V21 = 1672.7 m/s
V32 = 1977.8 m/s
V43 = 1949.8 m/sV43
comb = 1781.3 m/s
Avg. Vel. = 1866.8 m/s
DDT Time = 17.47 ms
P1 = 259.8 psig
P2 = 228.0 psig
P3 = 242.3 psig
P4 = 208.4 psig
232
0.4348 0.435 0.4352 0.4354 0.4356 0.4358 0.436 0.4362 0.4364 0.4366-100
-50
0
50
100
150
200
250
300
V21 = 1989.6 m/s
V32 = 1696.4 m/s
V43 = 1991.3 m/sV43
comb = -5.3 m/s
Avg. Vel. = 1892.5 m/s
DDT Time = 15.75 ms
P1 = 237.8 psig
P2 = 198.6 psig
P3 = 216.3 psig
P4 = 253.9 psig
233
0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336-100
-50
0
50
100
150
200
250
300
350
400
V21 = 1962.2 m/s
V32 = 1768.4 m/s
V43 = 1876.7 m/sV43
comb = 1966.1 m/s
Avg. Vel. = 1869.1 m/s
DDT Time = 12.74 ms
P1 = 378.2 psig
P2 = 293.9 psig
P3 = 231.9 psig
P4 = 210.8 psig
234
0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338 0.434 0.4342-100
-50
0
50
100
150
200
250
V21 = 1718.8 m/s
V32 = 1978.7 m/s
V43 = 1872.5 m/sV43
comb = 1688.1 m/s
Avg. Vel. = 1856.7 m/s
DDT Time = 13.39 ms
P1 = 209.5 psig
P2 = 187.3 psig
P3 = 162.3 psig
P4 = 202.9 psig
235
0.4384 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402-100
-50
0
50
100
150
200
250
300
V21 = 1964.4 m/s
V32 = 1817.3 m/s
V43 = 1835.1 m/sV43
comb = 1962.1 m/s
Avg. Vel. = 1872.3 m/s
DDT Time = 19.27 ms
P1 = 255.2 psig
P2 = 214.2 psig
P3 = 225.4 psig
P4 = 266.8 psig
236
0.4376 0.4378 0.438 0.4382 0.4384 0.4386 0.4388 0.439 0.4392 0.4394-100
-50
0
50
100
150
200
250
300
V21 = 1685.1 m/s
V32 = 1987.6 m/s
V43 = 1945.4 m/sV43
comb = 1998.9 m/s
Avg. Vel. = 1872.7 m/s
DDT Time = 18.47 ms
P1 = 206.9 psig
P2 = 252.1 psig
P3 = 193.4 psig
P4 = 293.4 psig
237
0.4344 0.4346 0.4348 0.435 0.4352 0.4354 0.4356 0.4358 0.436 0.4362-100
-50
0
50
100
150
200
250
V21 = 1959.0 m/s
V32 = 1703.8 m/s
V43 = 1950.6 m/sV43
comb = 1997.1 m/s
Avg. Vel. = 1871.1 m/s
DDT Time = 15.36 ms
P1 = 230.6 psig
P2 = 203.5 psig
P3 = 166.0 psig
P4 = 180.7 psig
238
0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404 0.4406 0.4408-100
-50
0
50
100
150
200
250
300
350
V21 = 1913.9 m/s
V32 = 1978.7 m/s
V43 = 1714.3 m/sV43
comb = 1676.2 m/s
Avg. Vel. = 1868.9 m/s
DDT Time = 19.78 ms
P1 = 199.9 psig
P2 = 306.6 psig
P3 = 204.8 psig
P4 = 207.5 psig
239
0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302 0.4304 0.4306 0.4308-100
-50
0
50
100
150
200
250
300
V21 = 1979.0 m/s
V32 = 1738.8 m/s
V43 = 2263.9 m/sV43
comb = 1821.5 m/s
Avg. Vel. = 1993.9 m/s
DDT Time = 9.94 ms
P1 = 249.5 psig
P2 = 201.4 psig
P3 = 242.5 psig
P4 = 259.6 psig
240
0.435 0.4352 0.4354 0.4356 0.4358 0.436 0.4362 0.4364 0.4366 0.4368-50
0
50
100
150
200
250
300
350
V21 = 1712.0 m/s
V32 = 1941.0 m/s
V43 = 2000.8 m/sV43
comb = 1697.3 m/s
Avg. Vel. = 1884.6 m/s
DDT Time = 15.89 ms
P1 = 247.0 psig
P2 = 186.4 psig
P3 = 237.4 psig
P4 = 328.9 psig
241
0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334-50
0
50
100
150
200
250
300
350
V21 = 1698.9 m/s
V32 = 1964.0 m/s
V43 = 1711.8 m/sV43
comb = 1971.4 m/s
Avg. Vel. = 1791.6 m/s
DDT Time = 12.45 ms
P1 = 342.0 psig
P2 = 242.6 psig
P3 = 241.8 psig
P4 = 226.2 psig
242
0.4382 0.4384 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44-50
0
50
100
150
200
250
300
350
400
450
V21 = 1720.4 m/s
V32 = 1944.1 m/s
V43 = 1994.7 m/sV43
comb = 1687.3 m/s
Avg. Vel. = 1886.4 m/s
DDT Time = 19.07 ms
P1 = 418.8 psig
P2 = 193.0 psig
P3 = 268.4 psig
P4 = 302.0 psig
243
0.4354 0.4356 0.4358 0.436 0.4362 0.4364 0.4366 0.4368 0.437 0.4372-50
0
50
100
150
200
250
300
V21 = 1977.4 m/s
V32 = 1965.8 m/s
V43 = 1978.0 m/sV43
comb = 1683.3 m/s
Avg. Vel. = 1973.7 m/s
DDT Time = 16.35 ms
P1 = 243.8 psig
P2 = 288.1 psig
P3 = 246.2 psig
P4 = 240.2 psig
244
0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338-100
0
100
200
300
400
500
600
V21 = 1708.0 m/s
V32 = 1954.0 m/s
V43 = 2044.7 m/sV43
comb = 2003.0 m/s
Avg. Vel. = 1902.2 m/s
DDT Time = 12.85 ms
P1 = 248.3 psig
P2 = 219.8 psig
P3 = 211.2 psig
P4 = 547.7 psig
245
0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404 0.4406-50
0
50
100
150
200
250
V21 = 1682.7 m/s
V32 = 1974.3 m/s
V43 = 1702.3 m/sV43
comb = 1755.3 m/s
Avg. Vel. = 1786.4 m/s
DDT Time = 19.66 ms
P1 = 209.8 psig
P2 = 207.8 psig
P3 = 248.3 psig
P4 = 183.6 psig
246
0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334-100
-50
0
50
100
150
200
250
300
V21 = 1975.7 m/s
V32 = 1693.5 m/s
V43 = 1943.3 m/sV43
comb = 1961.1 m/s
Avg. Vel. = 1870.9 m/s
DDT Time = 12.54 ms
P1 = 214.6 psig
P2 = 190.2 psig
P3 = 191.1 psig
P4 = 259.7 psig
247
0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334-50
0
50
100
150
200
250
300
V21 = 1970.4 m/s
V32 = 1950.5 m/s
V43 = 1699.0 m/sV43
comb = 1984.4 m/s
Avg. Vel. = 1873.3 m/s
DDT Time = 12.48 ms
P1 = 192.9 psig
P2 = 193.9 psig
P3 = 252.7 psig
P4 = 264.0 psig
248
0.4284 0.4286 0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302-50
0
50
100
150
200
250
300
V21 = 1917.7 m/s
V32 = 1730.9 m/s
V43 = 1980.2 m/sV43
comb = 1958.8 m/s
Avg. Vel. = 1876.3 m/s
DDT Time = 9.27 ms
P1 = 250.7 psig
P2 = 228.3 psig
P3 = 207.3 psig
P4 = 242.8 psig
249
0.4286 0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302 0.4304-100
-50
0
50
100
150
200
250
300
V21 = 1954.0 m/s
V32 = 1756.0 m/s
V43 = 1930.7 m/sV43
comb = 1984.8 m/s
Avg. Vel. = 1880.2 m/s
DDT Time = 9.51 ms
P1 = 266.4 psig
P2 = 201.1 psig
P3 = 213.4 psig
P4 = 176.9 psig
250
0.4368 0.437 0.4372 0.4374 0.4376 0.4378 0.438 0.4382 0.4384 0.4386-50
0
50
100
150
200
250
V21 = 1931.1 m/s
V32 = 1453.8 m/s
V43 = 1972.2 m/sV43
comb = 1722.9 m/s
Avg. Vel. = 1785.7 m/s
DDT Time = 17.69 ms
P1 = 224.2 psig
P2 = 243.4 psig
P3 = 178.7 psig
P4 = 232.5 psig
251
0.4362 0.4364 0.4366 0.4368 0.437 0.4372 0.4374 0.4376 0.4378 0.438-50
0
50
100
150
200
250
300
350
400
450
V21 = 1868.3 m/s
V32 = 1615.5 m/s
V43 = 2046.2 m/sV43
comb = 1853.4 m/s
Avg. Vel. = 1843.4 m/s
DDT Time = 17.19 ms
P1 = 221.5 psig
P2 = 258.1 psig
P3 = 185.6 psig
P4 = 404.8 psig
252
0.4384 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402-100
-50
0
50
100
150
200
250
300
V21 = 1695.8 m/s
V32 = 1771.0 m/s
V43 = 1875.2 m/sV43
comb = 1705.8 m/s
Avg. Vel. = 1780.7 m/s
DDT Time = 19.29 ms
P1 = 222.1 psig
P2 = 202.6 psig
P3 = 225.0 psig
P4 = 269.9 psig
253
0.4394 0.4396 0.4398 0.44 0.4402 0.4404 0.4406 0.4408 0.441 0.4412-50
0
50
100
150
200
250
300
V21 = 1714.7 m/s
V32 = 1784.0 m/s
V43 = 1850.2 m/sV43
comb = 1718.9 m/s
Avg. Vel. = 1783.0 m/s
DDT Time = 20.24 ms
P1 = 206.7 psig
P2 = 206.3 psig
P3 = 170.3 psig
P4 = 255.4 psig
254
0.4372 0.4374 0.4376 0.4378 0.438 0.4382 0.4384 0.4386 0.4388 0.439-50
0
50
100
150
200
250
300
350
V21 = 1520.0 m/s
V32 = 1633.9 m/s
V43 = 1972.5 m/sV43
comb = 1435.6 m/s
Avg. Vel. = 1708.8 m/s
DDT Time = 18.12 ms
P1 = 348.5 psig
P2 = 309.3 psig
P3 = 276.2 psig
P4 = 321.5 psig