Dissertations and Theses
Spring 2013
Investigation of Pulse Detonation Engines; Theory, Design and Analysis
Jeff Vizcaino Embry-Riddle Aeronautical University - Daytona Beach
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Scholarly Commons Citation Vizcaino, Jeff, "Investigation of Pulse Detonation Engines; Theory, Design and Analysis" (2013). Dissertations and Theses. 145. https://commons.erau.edu/edt/145
This Thesis - Open Access is brought to you for free and open access by Scholarly Commons. It has been accepted for inclusion in Dissertations and Theses by an authorized administrator of Scholarly Commons. For more information, please contact [email protected]. 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
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.
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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.
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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 v
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 vi
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 vii
13 APPENDIX D: RAW DATA & RESULTS...... 148
viii
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
(4) Figure 5: Soot image of detonation propagation (H2 + O2) 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
(10) Figure 17: Critical Tube diameter vs. Equivalence Ratio (Dc = 13λ) 22
Figure 18: Critical energy vs. Discharge time (11) 24
Figure 19: Critical Energy vs. Spark Gap Length (11) 23 ix
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 x
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 xi
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 xii
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
xiii
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
xiv
NOMENCLATURE
̈
Kj / mol
s-1
U(x) Uncertainty of variable x Varies
xv
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.
1
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.
2
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 a Uu/Cu 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
a Cu is the acoustic velocity in the unburned gasses. Uu/Cu is the Mach number of the wave.
3
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.
4
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
5
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
6
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
7
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.
8
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.
(4) Figure 5: Soot image of detonation propagation (H2 + O2)
9
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) 10
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.
11
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)
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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.
13
Figure 8: Cell size vs. Equivalence Ratio (14)
14
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)
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( ) 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:
16
[ ( ) ]
( ) Where √ √ and
Figure 13: Physical Steps that make up the Fickett-Jacobs Cycle (7)
17
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.
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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
19
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
20
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.
21
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 Figure 17: Critical Tube diameter vs. Equivalence (10) (10) (Tetryl: 4.2kJ/g) Ratio (Dc = 13λ) Figure above using spherical strong blast theory;
( )
22
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)
23
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
24
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.
25
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
26
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
27
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.
28
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,
29
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.
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Figure 24: Chemiluminescence Images of Toroidal Initiator (9)
Crossover Branching
Figure 25: Crossover Detonation Tube Internal Configuration
31
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.
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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.
33
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.).
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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)
35
Figure 27: Valveless PDE Design by Brophy et al. (24)
Figure 28: Valve-less PDE by Shimo & Heister (23)
Rotating Detonation Engines (RDE)
36
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.
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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.
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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
39
Setup and initialization
Table 3: Conditions for Validation Case 1 Initial Conditions (Unburned Gas)
1 atm Initial Pressure 298 K Initial Temperature 1.314 % H Mass Fraction 2 22.99 % O Mass Fraction 2 75.69 % N Mass Fraction 2 0.000 % H O Mass Fraction 2
Initial Conditions (Ignition Region)
30 atm Initial Pressure 3000 K Initial Temperature 0 H Mass Fraction 2 0 O Mass Fraction 2 0 N Mass Fraction 2 1 H O Mass Fraction 2
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
40
An
Final T = 2078.2 K; Max T = 2104.1 K Final P = 11 atm; Max P = 20.1 atm
2200
20
2000
18
1800
16
1600 Pressure
Temperature
14
1400
12
1200
10 0 0.002 0.004 0.006 0.008 0.01 0.012 0 0.002 0.004 0.006 0.008 0.01 0.012 Distance; = 0.0107 m Distance
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.
41
20
18
16
14
12
10
Pressure (atm) Pressure 8
6
4
2
0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 X Location (m)
Figure 31: Pressure Distribution for 1-D simulation
42
X Location (m) 0.195 0.196 0.197 0.198 0.199 0.2 0.201 0.202 0.203 0.204 20 2.5 Pressure Reaction
18
16 2
14
12 1.5
10
Pressure (atm) Pressure
Rate of Reaction of Rate 8 1
6
4 0.5
2
4 x 10 0 0 0.195 0.196 0.197 0.198 0.199 0.2 0.201 0.202 0.203 0.204 0.205 X Location (m)
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.
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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.
3000
2500
2000
1500
Temperature (K) Temperature
1000
500
0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 X Location (m)
Figure 33: Temperature Distribution for 1-D Simulation
44
X Location (m) 0.195 0.196 0.197 0.198 0.199 0.2 0.201 0.202 0.203 0.204 3000 2.5 Temperature Reaction
2500 2
2000
1.5
1500
Temperature (K) Temperature
Rate of Reaction of Rate 1
1000
0.5 500
4 x 10 0 0 0.195 0.196 0.197 0.198 0.199 0.2 0.201 0.202 0.203 0.204 0.205 X Location (m)
Figure 34: Peak Temperature Region for 1-D simulation
X Location (m) 0.195 0.196 0.197 0.198 0.199 0.2 0.201 0.202 0.203 0.204 20 3000 Pressure Temperature
18
2500 16
14 2000
12
10 1500
Pressure (atm) Pressure
Temperature (K) Temperature 8
1000 6
4 500
2
0 0 0.195 0.196 0.197 0.198 0.199 0.2 0.201 0.202 0.203 0.204 0.205 X Location (m)
Figure 35: Pressure vs. Temperature in Peak Region for 1-D Simulation
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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) Pvn (atm) Tvn (K) 0.2002 17.25 1695.13 1570 20.05 1212.49
0.1980 10.97 2136.61 1570 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.
46
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.
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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
48
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 % H Mass Fraction 2 22.64 % O Mass Fraction 2 74.51 % N Mass Fraction 2 0.000 % H O Mass Fraction 2
49
Initial Conditions (Ignition Region)
90 atm Initial Pressure 3500 K Initial Temperature 0 H Mass Fraction 2 0 O Mass Fraction 2 0 N Mass Fraction 2 1 H O Mass Fraction 2
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
Final T = 2920.2 K; Max T = 2947 K Final P = 14.9 atm; Max P = 27.4 atm
3000 28
2800 26
2600 24
2400
22
2200
Pressure
Temperature 20
2000
18
1800
16 1600
14 1400 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 -3 -3 Distance; = 0.00016 m x 10 Distance x 10
Figure 38: Expected ZND Profile for Case 2
50
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.
51
60
50
40
30
Pressure (atm) Pressure
20
10
0 0 0.2 0.4 0.6 0.8 1 1.2 X Location (m) Figure 40: Pressure vs. X Location for Case 2 at 50s intervals for constant Y = 0.14
4500
4000
3500
3000
2500
2000
Temperature (K) Temperature
1500
1000
500
0 0 0.2 0.4 0.6 0.8 1 1.2 X Location (m) 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 X Location Pressure Temperature (s) (m) (atm) (K)
52
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
53
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
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40
35
30
25
20
Pressure (atm) Pressure
15
10
5
0 0 0.2 0.4 0.6 0.8 1 1.2 X Location (m) Figure 43: Pressure vs. X Location for Case 2 at 50s intervals behind shock
4500
4000
3500
3000
2500
2000
Temeperature (K) Temeperature
1500
1000
500
0 0 0.2 0.4 0.6 0.8 1 1.2 X Location (m) Figure 44: Temperature vs. X Location for Case 2 at 50s intervals behind Shock
Table 13: Post Detonation Conditions behind Shock Time X Location Pressure Temperature (s) (m) (atm) (K)
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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.
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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
57
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.
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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
59
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
60
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
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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
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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
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Figure 52: High Frequency Tube Measurement Section
Figure 53: High Frequency Tube Interior Obstacle Configuration
Figure 54: Injection plate for High Frequency Tube
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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
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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
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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. 67
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.
68
Speed:(m/s) 120 1-2: 769.7 2-3: 1043.9 3-4: 952.5 Avg: 922.01 TR1 (us): 15 TR1 (us): 5 100 TR1 (us): 5 TR1 (us): 6 Max P1: 108.8 Max P2: 96.71 Max P3: 101.71 Max P4: 91.1 80
)
g
60
Pressure (PSI Pressure
40
20
0
26.7 26.8 26.9 27 27.1 27.2 27.3 27.4 27.5 27.6 Time (ms) Figure 57: Low Frequency Tube pressure traces with Ethylene gas
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Figure 58: Low Frequency Tube pressure traces with Propane gas
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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
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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.
70
60
50
) 40
g
Pressure (PSI Pressure 30
20
10
0 0 20 40 60 80 100 120 140 160 180 200 Fill Percentage (%)
Figure 59: Maximum Pressure vs. Fill percentage trends for configuration I
72
70
60
50
) 40
g
Pressure (PSI Pressure 30
20
10
0 0 1 2 3 4 5 6 7 8 9 10 Frequency (Hz)
Figure 60: Maximum pressure vs. Pulsing Frequency trends for configuration I
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70 13 Discs 8 Discs
60
50
) 40
g
Pressure (PSI Pressure 30
20
10
0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Equivalence Ratio
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
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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.
1200
1000
800
600
Wave VelocityWave (m/s)
400
200
0 0 20 40 60 80 100 120 140 160 180 200 Fill Percentage (%)
Figure 62: Velocity vs. Fill Percentage trends for configuration I
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1200
1000
800
600
Wave VelocityWave (m/s)
400
200
0 0 1 2 3 4 5 6 7 8 9 10 Frequency (Hz)
Figure 63: Velcoity vs. Frequency trends for configuration I
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1200 13 Discs 8 Discs
1000
800
600
Wave VelocityWave (m/s)
400
200
0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Equivalence Ratio
Figure 64: Velocity vs. Equivalence ratio trends for configuration I
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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
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trails the pressure wave by a significant amount of time rather than coupled with it like ZND theory predicts.
120
100
80
60
40
20
0
-20
-40
-60 0.433 0.4332 0.4334 0.4336 0.4338 0.434 0.4342 0.4344 0.4346 0.4348 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.
79
300
250
200
150
100
50
0
-50
-100
-150 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404 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
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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
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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
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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.
Pressure Distribution 300
250
200
150
100 Sample Frequency Sample
50
0 34 106 178 251 323 395 467 More
Pressure (PSIg)
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.
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Velocity Distribution 250
200
150
Frequency 100
50
0 1459 1597 1734 1871 2008 2146 2283 More
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
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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.
Velocity Distribution (Pressure Sensors) 160
140
120
100
80
Frequency 60
40
20
0 1459 1597 1734 1871 2008 2146 2283 More
Figure 72: Normal distribution of measured Detonation Velocities from Pressure Transducers
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Velocity Distribution (Ion Sensors) 60
50
40
30 Frequency 20
10
0 1459 1597 1734 1871 2008 2146 2283 More
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.
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Transition Time Distribution 45
40
35
30
25
20 Frequency 15
10
5
0 0.0 5.8 11.7 17.6 23.5 29.5 35.4 More
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
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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
88
Figure 76: Thermal Imaging of Detonation Tube Transition Section
Figure 77: Thermal Imaging of Detonation Tube Measurement Section
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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
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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
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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
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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.
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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
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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.
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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.
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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
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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 98
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 99
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.
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19. Sinibaldi, Jose O., et al. Investigation of Transient Plasma Ignition for Pulse
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Laboratories, 2004.
23. Shimo, Masa and Heister, Stephen. Multicyclic Detonation Initiation Studies in
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M., Werner, LT S. and Sinibaldi, J. O. Reno : 41st Aersopace Sciences Meeting
and Exibit, 2003.
25. Numerical Investigation of Detonation in Premixed Hydrogen-Air-Mixture - Assesment
of Simplified Chemical Mechanisms. Hsu, K. and Jemcov, A. Denver : American
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26. The Influence of Chemical Kinetics on the Strucure of Hydrogen-Air Detonations.
Gamezo, Vadim N., Ogawa, Takanobu and Oran, Elaine S. Nashville : 50th
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27. Khemani, Haresh. The Stoichiometric Air-Fuel Ratio. Bright Hub. [Online]
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M9wMn.
28. Ishii, K. and Tanaka, T. A Study on Jet Initiation of Detonation Using Multiple
Tubes. Shock Waves. 2005, Vol. 14, 4.
29. Liberman, Michael. Flame, Detonation, Explosion - When Where and How They
Occur. Uppsala : Department of Physics, Uppsala University, 2003.
30. Tian, Zhang Gui, Tsann, Jiang Yi and Sin, Yip Mee. Computational Analysis of
Reduction Techniques for Shock-To-Detonation Transition. s.l. : DSO National
Laboratories.
31. Wittmers, Nicole Kays. Direct-Connect Performance Evaluation of A Valveless Pulse
Detonation Engine. Monterey : Naval Postgraduate School, 2004.
32. Jiang, Zonglin and Han, Z. -Y. Shock Waves. s.l. : Springer, 2005.
33. Development of a Compact Liquid Fueled Pulse Detonation Engien with Predetonator.
Li, Jiun-Ming, et al. Reno : 45th AIAA Aerospace Sciences Meetign and Exhibit,
2007.
34. Eckett, C. A., Quirk, J. J. and Shepherd, J. E. An analytical model for direct
initiation of gaseous detonations. Great Keppel Island : s.n., 1997.
35. Kuhl, A. L., Leyer, J. -C. and Borisov, A. A. Progress in Astronautics and
Aeronautics. Dynamic Aspects of Detonations. 1993, Vol. 153.
36. Frolov, Sergey M., et al. Enhancement of Shock-to-Detonation Tranisiton in
Channels with Regular Shaped Obstacles. Potiers : 21st ICDERS, 2007.
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37. Kailasanath, K. Research on Pulse Detonation Combustion Systems - A Status Report.
Orlando : 47th AIAA Aerospace Sciences Meeting, 2009.
38. Detonation Initiation by Controlled Triggering of Electric Discharges. Frolov, S. M.,
et al. 4, s.l. : Journal of Propulsion and Power, 2003, Vol. 19.
39. Shock Wave and Detonation Propagation Through U-bend Tubes. Frolov, S. M.,
Aksenov, V. S. and Shamshin, I. O. s.l. : Proceedings of the Combustion Institute
31, 2007.
40. Reactive Shock and Detonation Propagtion in U-Bend Tubes. Frolov, S. M., Aksenov,
V. S. and Shamshin, I. O. s.l. : Journal of Loss Prevention in the Process
Industries, 2007, Vol. 20.
41. Numerical simulations of flame propagation and DDT in obstructed channels filled
with hydrogen-air mixture. Gamezo, Vadim N, Ogawa, Takanobu and Oran,
Elaine S. 2, s.l. : S. Oran, Numerical simulations of flame propagation and DDT
in obstructed channels filled with hydrogen-air mixture, , 2007, Vol. 31.
42. Deflagration-to-Detonation Transition in Premixed H2-Air in Channels with
Obstacles. Gamezo, Vadim N., Ogawa, Takanobu and Oran, Elaine S. Reno :
45th AIAA Aerospace Sciences Meeting and Exhibit, 2007. AIAA 2007-1172.
43. Deflaration-to-Detonaiton Transtion in H2-Air Mixtures: Effect of Blockage Ratio.
Gamezo, Vadim N., Ogawa, Takanobu and Oran, Elaine S. Orlando : 47th
AIAA Aerospace Sciences Meeting, 2009. AIAA 2009-440.
44. Romo, Francisco X. Design, Construction, and Optimization of a Pulse Detonation
Engine DDT Section. Daytona Beach, FL : Embry-Riddle Aeronautical University,
2012.
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45. Explosion Dynamics Laboratory. Spectral Analysis for Cell Size Measurement.
Explosion Dynamics Laboratory. [Online] April 2, 2007.
http://www2.galcit.caltech.edu/EDL/CellImageProcessing/cellsize.html.
106
10 APPENDIX A: DETAILED EXPERIMENTAL SETUP
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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
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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. 109
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.
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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
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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.
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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
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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
2 will modify the volume by a ratio of L/Lo as governed by the equation V = R L. 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
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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.
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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
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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
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Figure 88: Spark Plug Ignition Control System
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Figure 89: Mathscript Node for LabView VI
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Figure 90: Ignition Control Wiring
Figure 91: Injector Wiring
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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.
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11 APPENDIX B: CALCULATION OF FILLING PARAMETERS
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Given: Liquefied Propane Gas (LPG) + Air
Composition
Gas Formula Mass Molecular Density Stoichiometric Mass AFR
Fraction Weight (kg/m3) @ O/F @ Stoich.
(g/mol) SLS
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
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*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
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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
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12 APPENDIX C: DRAWINGS AND DIAGRAMS
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
13 APPENDIX D: RAW DATA & RESULTS
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V21 = 1683.0 m/s V32 = 1959.3 m/s V43 = 1986.5 m/s V43 = 1700.6 m/s comb Avg. Vel. = 1876.3300 m/s DDT Time = 12.46 ms
P1 = 229.2 psig P2 = 267.8 psig P3 = 226.8 psig P4 = 270.0 psig250
200
150
100
50
0
-50
-100 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334
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V21 = 1918.7 m/s V32 = 1701.5 m/s V43 = 2104.2 m/s V43 = 1867.8 m/s comb Avg. Vel. = 1908.1350 m/s DDT Time = 9.30 ms
P1 = 219.3 psig P2 = 347.8 psig P3 = 271.9 psig300 P4 = 277.4 psig
250
200
150
100
50
0
-50
-100 0.4284 0.4286 0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302
150
V21 = 1964.0 m/s V32 = 1689.7 m/s V43 = 1965.8 m/s V43 = 1931.7 m/s comb Avg. Vel. = 1873.2350 m/s DDT Time = 9.15 ms
P1 = 241.0 psig P2 = 289.6 psig P3 = 194.7 psig300 P4 = 324.3 psig
250
200
150
100
50
0
-50
-100 0.4282 0.4284 0.4286 0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43
151
V21 = 1995.2 m/s V32 = 1688.9 m/s V43 = 1959.5 m/s V43 = 1938.3 m/s comb Avg. Vel. = 1881.2350 m/s DDT Time = 19.58 ms
P1 = 250.0 psig P2 = 225.2 psig P3 = 253.8 psig300 P4 = 319.5 psig
250
200
150
100
50
0
-50
-100 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404
152
V21 = 1731.5 m/s V32 = 1899.8 m/s V43 = 1990.0 m/s V43 = 1957.8 m/s comb Avg. Vel. = 1873.8300 m/s DDT Time = 12.92 ms
P1 = 240.0 psig P2 = 261.4 psig P3 = 278.3 psig P4 = 248.6 psig250
200
150
100
50
0
-50
-100 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338
153
V21 = 1957.7 m/s V32 = 1807.6 m/s V43 = 1891.9 m/s V43 = 1919.3 m/s comb Avg. Vel. = 1885.7350 m/s DDT Time = 12.51 ms
P1 = 244.4 psig P2 = 244.0 psig P3 = 340.6 psig300 P4 = 312.7 psig
250
200
150
100
50
0
-50
-100 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334
154
V21 = 988.9 m/s V32 = 919.0 m/s V43 = 909.7 m/s V43 = 539.6 m/s comb Avg. Vel. = 939.2100 m/s DDT Time = 24.46 ms
P1 = 84.7 psig P2 = 89.1 psig P3 = 99.3 psig P4 = 90.7 psig 80
60
40
20
0
-20
-40 0.4436 0.4438 0.444 0.4442 0.4444 0.4446 0.4448 0.445 0.4452 0.4454
155
V21 = 930.7 m/s V32 = 996.1 m/s V43 = 925.3 m/s V43 = 497.8 m/s comb Avg. Vel. = 950.7120 m/s DDT Time = 27.26 ms
P1 = 87.5 psig P2 = 87.1 psig P3 = 111.9 psig P4 = 93.5 psig100
80
60
40
20
0
-20
-40 0.4464 0.4466 0.4468 0.447 0.4472 0.4474 0.4476 0.4478 0.448 0.4482
156
V21 = 1691.3 m/s V32 = 1932.7 m/s V43 = 1983.4 m/s V43 = 1960.9 m/s comb Avg. Vel. = 1869.1400 m/s DDT Time = 12.16 ms
P1 = 265.3 psig P2 = 216.3 psig P3 = 235.3 psig350 P4 = 399.1 psig
300
250
200
150
100
50
0
-50
-100 0.4312 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433
157
V21 = 1001.1 m/s V32 = 679.4 m/s V43 = 1850.0 m/s V43 = 3862.5 m/s comb Avg. Vel. = 1176.8200 m/s DDT Time = 22.25 ms
P1 = 101.1 psig P2 = 90.4 psig P3 = 104.7 psig P4 = 184.0 psig
150
100
50
0
-50
-100 0.4414 0.4416 0.4418 0.442 0.4422 0.4424 0.4426 0.4428 0.443 0.4432
158
V21 = 1686.9 m/s V32 = 1946.4 m/s V43 = 1751.5 m/s V43 = 1772.6 m/s comb Avg. Vel. = 1795.0300 m/s DDT Time = 18.57 ms
P1 = 282.1 psig P2 = 238.6 psig P3 = 230.0 psig P4 = 178.4 psig250
200
150
100
50
0
-50
-100 0.4376 0.4378 0.438 0.4382 0.4384 0.4386 0.4388 0.439 0.4392 0.4394
159
V21 = 1060.4 m/s V32 = 738.5 m/s V43 = 1827.0 m/s V43 = 822.8 m/s comb Avg. Vel. = 1208.6120 m/s DDT Time = 13.17 ms
P1 = 98.1 psig P2 = 102.4 psig P3 = 118.9 psig100 P4 = 104.1 psig
80
60
40
20
0
-20
-40
-60
-80 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338 0.434 0.4342
160
V21 = 1081.2 m/s V32 = 992.1 m/s V43 = 1055.9 m/s V43 = 5.2 m/s comb Avg. Vel. = 1043.1200 m/s DDT Time = 13.21 ms
P1 = 125.0 psig P2 = 133.8 psig P3 = 141.7 psig P4 = 158.0 psig
150
100
50
0
-50
-100 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338 0.434 0.4342
161
V21 = 1708.4 m/s V32 = 1942.3 m/s V43 = 1745.4 m/s V43 = 1912.1 m/s comb Avg. Vel. = 1798.7400 m/s DDT Time = 25.90 ms
P1 = 225.6 psig P2 = 207.0 psig P3 = 371.2 psig350 P4 = 267.1 psig
300
250
200
150
100
50
0
-50
-100 0.445 0.4452 0.4454 0.4456 0.4458 0.446 0.4462 0.4464 0.4466 0.4468
162
V21 = 1958.9 m/s V32 = 2344.2 m/s V43 = 1341.7 m/s V43 = 1904.0 m/s comb Avg. Vel. = 1881.6500 m/s DDT Time = 7.21 ms
P1 = 228.5 psig P2 = 297.7 psig P3 = 490.3 psig P4 = 310.3 psig
400
300
200
100
0
-100 0.4264 0.4266 0.4268 0.427 0.4272 0.4274 0.4276 0.4278 0.428 0.4282
163
V21 = 1668.6 m/s V32 = 1962.8 m/s V43 = 1835.0 m/s V43 = 1936.6 m/s comb Avg. Vel. = 1822.1500 m/s DDT Time = 12.08 ms
P1 = 299.0 psig P2 = 319.0 psig P3 = 226.0 psig P4 = 412.5 psig
400
300
200
100
0
-100 0.4312 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433
164
V21 = 1956.3 m/s V32 = 1945.7 m/s V43 = 1715.5 m/s V43 = 1690.0 m/s comb Avg. Vel. = 1872.5400 m/s DDT Time = 19.28 ms
P1 = 228.0 psig P2 = 266.4 psig P3 = 384.9 psig350 P4 = 193.2 psig
300
250
200
150
100
50
0
-50
-100 0.4384 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402
165
V21 = 1945.7 m/s V32 = 1715.6 m/s V43 = 1855.3 m/s V43 = -15030.8 m/s comb Avg. Vel. = 1838.9300 m/s DDT Time = 10.82 ms
P1 = 228.7 psig P2 = 241.8 psig P3 = 256.1 psig P4 = 213.8 psig250
200
150
100
50
0
-50
-100 0.43 0.4302 0.4304 0.4306 0.4308 0.431 0.4312 0.4314 0.4316 0.4318
166
V21 = 1693.1 m/s V32 = 1978.4 m/s V43 = 1720.9 m/s V43 = 1696.9 m/s comb Avg. Vel. = 1797.4300 m/s DDT Time = 19.73 ms
P1 = 254.8 psig P2 = 226.3 psig P3 = 206.2 psig P4 = 237.5 psig250
200
150
100
50
0
-50
-100 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404 0.4406
167
V21 = 1970.9 m/s V32 = 1692.8 m/s V43 = 2068.1 m/s V43 = 1983.1 m/s comb Avg. Vel. = 1910.6350 m/s DDT Time = 10.83 ms
P1 = 206.3 psig P2 = 317.7 psig P3 = 229.2 psig300 P4 = 308.7 psig
250
200
150
100
50
0
-50
-100 0.43 0.4302 0.4304 0.4306 0.4308 0.431 0.4312 0.4314 0.4316 0.4318
168
V21 = 1951.5 m/s V32 = 1687.6 m/s V43 = 2358.3 m/s V43 = 1958.1 m/s comb Avg. Vel. = 1999.1500 m/s DDT Time = 18.00 ms
P1 = 206.2 psig P2 = 213.6 psig P3 = 220.1 psig P4 = 446.9 psig
400
300
200
100
0
-100 0.437 0.4372 0.4374 0.4376 0.4378 0.438 0.4382 0.4384 0.4386 0.4388
169
V21 = 1705.7 m/s V32 = 1949.0 m/s V43 = 1996.3 m/s V43 = 1670.4 m/s comb Avg. Vel. = 1883.6350 m/s DDT Time = 25.89 ms
P1 = 320.0 psig P2 = 223.8 psig P3 = 266.8 psig300 P4 = 292.7 psig
250
200
150
100
50
0
-50
-100 0.445 0.4452 0.4454 0.4456 0.4458 0.446 0.4462 0.4464 0.4466 0.4468
170
V21 = 1972.3 m/s V32 = 1683.4 m/s V43 = 1693.9 m/s V43 = 1936.4 m/s comb Avg. Vel. = 1783.2400 m/s DDT Time = 19.21 ms
P1 = 219.2 psig P2 = 213.3 psig P3 = 383.7 psig350 P4 = 269.5 psig
300
250
200
150
100
50
0
-50
-100 0.4384 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402
171
V21 = 2070.2 m/s V32 = 1863.6 m/s V43 = 1763.5 m/s V43 = 1924.8 m/s comb Avg. Vel. = 1899.1500 m/s DDT Time = 27.54 ms
P1 = 482.4 psig P2 = 208.2 psig P3 = 190.2 psig P4 = 246.1 psig
400
300
200
100
0
-100 0.4466 0.4468 0.447 0.4472 0.4474 0.4476 0.4478 0.448 0.4482 0.4484
172
V21 = 1942.5 m/s V32 = 1697.4 m/s V43 = 1983.3 m/s V43 = 1967.1 m/s comb Avg. Vel. = 1874.4250 m/s DDT Time = 12.79 ms
P1 = 246.7 psig P2 = 219.0 psig P3 = 218.7 psig P4 = 207.5 psig 200
150
100
50
0
-50
-100 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338
173
V21 = 2009.3 m/s V32 = 1960.1 m/s V43 = 1732.8 m/s V43 = 1964.5 m/s comb Avg. Vel. = 1900.7400 m/s DDT Time = 16.27 ms
P1 = 368.3 psig P2 = 224.6 psig P3 = 239.6 psig P4 = 356.1 psig
300
200
100
0
-100
-200 0.4354 0.4356 0.4358 0.436 0.4362 0.4364 0.4366 0.4368 0.437 0.4372
174
V21 = 1970.3 m/s V32 = 1841.8 m/s V43 = 1807.2 m/s V43 = 1942.7 m/s comb Avg. Vel. = 1873.1300 m/s DDT Time = 19.59 ms
P1 = 271.2 psig P2 = 265.7 psig P3 = 199.2 psig250 P4 = 263.6 psig
200
150
100
50
0
-50
-100
-150 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404
175
V21 = 1695.7 m/s V32 = 1959.7 m/s V43 = 1954.7 m/s V43 = 1731.9 m/s comb Avg. Vel. = 1870.0500 m/s DDT Time = 18.92 ms
P1 = 253.7 psig P2 = 218.1 psig P3 = 243.1 psig P4 = 481.3 psig
400
300
200
100
0
-100 0.438 0.4382 0.4384 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398
176
V21 = 1671.4 m/s V32 = 1984.6 m/s V43 = 1977.2 m/s V43 = 1967.0 m/s comb Avg. Vel. = 1877.7500 m/s DDT Time = 16.60 ms
P1 = 262.1 psig P2 = 414.5 psig P3 = 252.1 psig P4 = 375.5 psig
400
300
200
100
0
-100 0.4358 0.436 0.4362 0.4364 0.4366 0.4368 0.437 0.4372 0.4374 0.4376
177
V21 = 1706.1 m/s V32 = 1949.3 m/s V43 = 1708.6 m/s V43 = 2026.3 m/s comb Avg. Vel. = 1788.0350 m/s DDT Time = 14.45 ms
P1 = 211.3 psig P2 = 181.8 psig P3 = 233.7 psig300 P4 = 309.1 psig
250
200
150
100
50
0
-50
-100 0.4336 0.4338 0.434 0.4342 0.4344 0.4346 0.4348 0.435 0.4352 0.4354
178
V21 = 1703.3 m/s V32 = 1947.5 m/s V43 = 2021.2 m/s V43 = 1963.0 m/s comb Avg. Vel. = 1890.7300 m/s DDT Time = 9.75 ms
P1 = 243.4 psig P2 = 256.4 psig P3 = 246.6 psig P4 = 225.1 psig250
200
150
100
50
0
-50
-100 0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302 0.4304 0.4306
179
V21 = 1897.3 m/s V32 = 1738.3 m/s V43 = 1902.3 m/s V43 = 1670.6 m/s comb Avg. Vel. = 1845.9250 m/s DDT Time = 11.96 ms
P1 = 207.8 psig P2 = 195.1 psig P3 = 173.5 psig P4 = 234.2 psig 200
150
100
50
0
-50
-100 0.431 0.4312 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328
180
V21 = 1786.4 m/s V32 = 1864.2 m/s V43 = 2149.4 m/s V43 = 1982.5 m/s comb Avg. Vel. = 1933.3350 m/s DDT Time = 9.06 ms
P1 = 205.6 psig P2 = 198.1 psig P3 = 197.4 psig300 P4 = 314.6 psig
250
200
150
100
50
0
-50
-100 0.4282 0.4284 0.4286 0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43
181
V21 = 1977.1 m/s V32 = 1698.3 m/s V43 = 2351.5 m/s V43 = 1945.5 m/s comb Avg. Vel. = 2009.0300 m/s DDT Time = 20.66 ms
P1 = 232.0 psig P2 = 214.1 psig P3 = 226.9 psig P4 = 266.9 psig250
200
150
100
50
0
-50
-100 0.4398 0.44 0.4402 0.4404 0.4406 0.4408 0.441 0.4412 0.4414 0.4416
182
V21 = 1887.3 m/s V32 = 1777.2 m/s V43 = 1982.6 m/s V43 = 1945.7 m/s comb Avg. Vel. = 1882.4250 m/s DDT Time = 27.22 ms
P1 = 193.8 psig P2 = 194.6 psig P3 = 210.4 psig P4 = 196.4 psig 200
150
100
50
0
-50
-100 0.4464 0.4466 0.4468 0.447 0.4472 0.4474 0.4476 0.4478 0.448 0.4482
183
V21 = 1966.3 m/s V32 = 1959.8 m/s V43 = 1695.6 m/s V43 = 1814.1 m/s comb Avg. Vel. = 1873.9250 m/s DDT Time = 17.88 ms
P1 = 202.6 psig P2 = 230.4 psig P3 = 210.3 psig P4 = 243.2 psig 200
150
100
50
0
-50
-100 0.437 0.4372 0.4374 0.4376 0.4378 0.438 0.4382 0.4384 0.4386 0.4388
184
V21 = 1694.4 m/s V32 = 2007.6 m/s V43 = 1658.8 m/s V43 = 1960.3 m/s comb Avg. Vel. = 1786.9250 m/s DDT Time = 20.39 ms
P1 = 241.7 psig P2 = 207.5 psig P3 = 191.4 psig P4 = 191.0 psig 200
150
100
50
0
-50
-100 0.4394 0.4396 0.4398 0.44 0.4402 0.4404 0.4406 0.4408 0.441 0.4412
185
V21 = 1707.3 m/s V32 = 1961.9 m/s V43 = 1723.9 m/s V43 = 1807.5 m/s comb Avg. Vel. = 1797.7300 m/s DDT Time = 17.65 ms
P1 = 295.9 psig P2 = 202.9 psig P3 = 209.3 psig P4 = 165.8 psig250
200
150
100
50
0
-50
-100 0.4368 0.437 0.4372 0.4374 0.4376 0.4378 0.438 0.4382 0.4384 0.4386
186
V21 = 2414.0 m/s V32 = 1985.8 m/s V43 = 1700.0 m/s V43 = 1690.5 m/s comb Avg. Vel. = 2033.3300 m/s DDT Time = 27.97 ms
P1 = 239.2 psig P2 = 253.6 psig P3 = 177.1 psig P4 = 218.6 psig250
200
150
100
50
0
-50
-100 0.447 0.4472 0.4474 0.4476 0.4478 0.448 0.4482 0.4484 0.4486 0.4488
187
V21 = 1673.2 m/s V32 = 1942.4 m/s V43 = 2038.4 m/s V43 = 1970.2 m/s comb Avg. Vel. = 1884.7300 m/s DDT Time = 24.94 ms
P1 = 267.2 psig P2 = 234.2 psig P3 = 237.8 psig P4 = 233.2 psig250
200
150
100
50
0
-50
-100 0.444 0.4442 0.4444 0.4446 0.4448 0.445 0.4452 0.4454 0.4456 0.4458
188
V21 = 1768.0 m/s V32 = 1846.3 m/s V43 = 1980.6 m/s V43 = 1953.9 m/s comb Avg. Vel. = 1865.0300 m/s DDT Time = 12.28 ms
P1 = 250.7 psig P2 = 222.7 psig P3 = 189.2 psig P4 = 206.7 psig250
200
150
100
50
0
-50
-100 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332
189
V21 = 1973.0 m/s V32 = 1970.4 m/s V43 = 1689.3 m/s V43 = 1935.8 m/s comb Avg. Vel. = 1877.6300 m/s DDT Time = 29.17 ms
P1 = 237.2 psig P2 = 192.8 psig P3 = 199.1 psig P4 = 281.4 psig250
200
150
100
50
0
-50
-100 0.4482 0.4484 0.4486 0.4488 0.449 0.4492 0.4494 0.4496 0.4498 0.45
190
V21 = 1984.5 m/s V32 = 1684.5 m/s V43 = 1957.7 m/s V43 = -4.9 m/s comb Avg. Vel. = 1875.6300 m/s DDT Time = 22.51 ms
P1 = 254.4 psig P2 = 201.3 psig P3 = 201.9 psig P4 = 264.8 psig250
200
150
100
50
0
-50
-100 0.4416 0.4418 0.442 0.4422 0.4424 0.4426 0.4428 0.443 0.4432 0.4434
191
V21 = 1690.3 m/s V32 = 1980.3 m/s V43 = 1958.6 m/s V43 = 1984.9 m/s comb Avg. Vel. = 1876.4250 m/s DDT Time = 23.30 ms
P1 = 232.3 psig P2 = 217.8 psig P3 = 220.9 psig P4 = 203.7 psig 200
150
100
50
0
-50
-100 0.4424 0.4426 0.4428 0.443 0.4432 0.4434 0.4436 0.4438 0.444 0.4442
192
V21 = 1926.2 m/s V32 = 1720.1 m/s V43 = 1950.4 m/s V43 = 1971.7 m/s comb Avg. Vel. = 1865.6500 m/s DDT Time = 20.82 ms
P1 = 207.4 psig P2 = 166.1 psig P3 = 229.1 psig P4 = 415.1 psig
400
300
200
100
0
-100 0.44 0.4402 0.4404 0.4406 0.4408 0.441 0.4412 0.4414 0.4416 0.4418
193
V21 = 1832.5 m/s V32 = 1813.8 m/s V43 = 1975.0 m/s V43 = 1997.2 m/s comb Avg. Vel. = 1873.8400 m/s DDT Time = 13.29 ms
P1 = 355.3 psig P2 = 175.3 psig P3 = 239.6 psig350 P4 = 212.1 psig
300
250
200
150
100
50
0
-50
-100 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338 0.434 0.4342
194
V21 = 1678.2 m/s V32 = 1986.3 m/s V43 = 1974.1 m/s V43 = 1677.2 m/s comb Avg. Vel. = 1879.5350 m/s DDT Time = 13.00 ms
P1 = 253.9 psig P2 = 293.8 psig P3 = 230.0 psig P4 = 319.1 psig300
250
200
150
100
50
0
-50 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338 0.434
195
V21 = 1726.1 m/s V32 = 1948.5 m/s V43 = 1952.4 m/s V43 = 1967.5 m/s comb Avg. Vel. = 1875.7900 m/s DDT Time = 23.84 ms
P1 = 264.8 psig P2 = 162.8 psig P3 = 225.9 psig800 P4 = 808.7 psig
700
600
500
400
300
200
100
0
-100 0.443 0.4432 0.4434 0.4436 0.4438 0.444 0.4442 0.4444 0.4446 0.4448
196
V21 = 1701.1 m/s V32 = 1981.2 m/s V43 = 1676.3 m/s V43 = 1728.4 m/s comb Avg. Vel. = 1786.2300 m/s DDT Time = 20.30 ms
P1 = 254.3 psig P2 = 199.3 psig P3 = 197.7 psig P4 = 217.7 psig250
200
150
100
50
0
-50
-100 0.4394 0.4396 0.4398 0.44 0.4402 0.4404 0.4406 0.4408 0.441 0.4412
197
V21 = 1910.2 m/s V32 = 1731.6 m/s V43 = 1936.5 m/s V43 = 1946.2 m/s comb Avg. Vel. = 1859.4250 m/s DDT Time = 26.34 ms
P1 = 236.9 psig P2 = 175.8 psig P3 = 249.9 psig P4 = 210.2 psig
200
150
100
50
0
-50 0.4454 0.4456 0.4458 0.446 0.4462 0.4464 0.4466 0.4468 0.447 0.4472
198
V21 = 1976.3 m/s V32 = 1944.9 m/s V43 = 1699.4 m/s V43 = 1942.1 m/s comb Avg. Vel. = 1873.6350 m/s DDT Time = 10.81 ms
P1 = 212.6 psig P2 = 162.1 psig P3 = 320.2 psig300 P4 = 193.2 psig
250
200
150
100
50
0
-50
-100 0.43 0.4302 0.4304 0.4306 0.4308 0.431 0.4312 0.4314 0.4316 0.4318
199
V21 = 1937.6 m/s V32 = 1730.4 m/s V43 = 1908.8 m/s V43 = 1996.6 m/s comb Avg. Vel. = 1858.9300 m/s DDT Time = 24.05 ms
P1 = 173.8 psig P2 = 188.3 psig P3 = 183.8 psig P4 = 261.1 psig250
200
150
100
50
0
-50
-100 0.4432 0.4434 0.4436 0.4438 0.444 0.4442 0.4444 0.4446 0.4448 0.445
200
V21 = 1937.6 m/s V32 = 1730.4 m/s V43 = 1908.8 m/s V43 = 1996.6 m/s comb Avg. Vel. = 1858.9300 m/s DDT Time = 24.05 ms
P1 = 173.8 psig P2 = 188.3 psig P3 = 183.8 psig P4 = 261.1 psig250
200
150
100
50
0
-50
-100 0.4432 0.4434 0.4436 0.4438 0.444 0.4442 0.4444 0.4446 0.4448 0.445
201
V21 = 1955.3 m/s V32 = 1949.7 m/s V43 = 1704.3 m/s V43 = 1684.3 m/s comb Avg. Vel. = 1869.7300 m/s DDT Time = 14.60 ms
P1 = 210.2 psig P2 = 187.6 psig P3 = 273.8 psig P4 = 258.3 psig250
200
150
100
50
0
-50
-100 0.4338 0.434 0.4342 0.4344 0.4346 0.4348 0.435 0.4352 0.4354 0.4356
202
V21 = 1698.8 m/s V32 = 2009.0 m/s V43 = 1947.7 m/s V43 = 1701.3 m/s comb Avg. Vel. = 1885.2350 m/s DDT Time = 13.64 ms
P1 = 238.3 psig P2 = 304.1 psig P3 = 208.8 psig300 P4 = 197.0 psig
250
200
150
100
50
0
-50
-100 0.4328 0.433 0.4332 0.4334 0.4336 0.4338 0.434 0.4342 0.4344 0.4346
203
V21 = 1644.2 m/s V32 = 1708.5 m/s V43 = 1778.1 m/s V43 = 2512.7 m/s comb Avg. Vel. = 1710.3250 m/s DDT Time = 24.54 ms
P1 = 232.4 psig P2 = 229.9 psig P3 = 206.9 psig P4 = 249.1 psig 200
150
100
50
0
-50
-100 0.4436 0.4438 0.444 0.4442 0.4444 0.4446 0.4448 0.445 0.4452 0.4454
204
V21 = 1684.2 m/s V32 = 1980.3 m/s V43 = 1795.3 m/s V43 = 1697.7 m/s comb Avg. Vel. = 1820.0400 m/s DDT Time = 12.79 ms
P1 = 219.2 psig P2 = 344.2 psig P3 = 222.6 psig P4 = 274.7 psig300
200
100
0
-100
-200
-300
-400 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336
205
V21 = 1963.3 m/s V32 = 1687.6 m/s V43 = 1950.6 m/s V43 = -5.3 m/s comb Avg. Vel. = 1867.2400 m/s DDT Time = 12.45 ms
P1 = 255.7 psig P2 = 229.0 psig P3 = 252.9 psig P4 = 328.2 psig 300
200
100
0
-100
-200
-300 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334
206
V21 = 1760.6 m/s V32 = 2006.8 m/s V43 = 1926.3 m/s V43 = 1679.9 m/s comb Avg. Vel. = 1897.9300 m/s DDT Time = 9.86 ms
P1 = 221.3 psig P2 = 257.2 psig P3 = 174.9 psig250 P4 = 228.7 psig
200
150
100
50
0
-50
-100
-150 0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302 0.4304 0.4306 0.4308
207
V21 = 1806.7 m/s V32 = 1967.0 m/s V43 = 1697.6 m/s V43 = 1676.7 m/s comb Avg. Vel. = 1823.8300 m/s DDT Time = 19.40 ms
P1 = 293.1 psig P2 = 251.7 psig P3 = 242.9 psig P4 = 232.7 psig250
200
150
100
50
0
-50
-100 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404
208
V21 = 1963.3 m/s V32 = 1851.4 m/s V43 = 1849.3 m/s V43 = 1988.5 m/s comb Avg. Vel. = 1888.0400 m/s DDT Time = 22.24 ms
P1 = 252.2 psig P2 = 259.4 psig P3 = 233.5 psig350 P4 = 372.0 psig
300
250
200
150
100
50
0
-50
-100 0.4414 0.4416 0.4418 0.442 0.4422 0.4424 0.4426 0.4428 0.443 0.4432
209
V21 = 1923.8 m/s V32 = 1826.1 m/s V43 = 2165.6 m/s V43 = 1925.4 m/s comb Avg. Vel. = 1971.8400 m/s DDT Time = 12.54 ms
P1 = 242.6 psig P2 = 392.3 psig P3 = 217.2 psig350 P4 = 308.7 psig
300
250
200
150
100
50
0
-50
-100 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334
210
V21 = 1963.0 m/s V32 = 1955.4 m/s V43 = 1774.7 m/s V43 = 1938.0 m/s comb Avg. Vel. = 1897.7400 m/s DDT Time = 20.99 ms
P1 = 235.2 psig P2 = 255.5 psig P3 = 224.4 psig P4 = 310.9 psig
300
200
100
0
-100
-200 0.4402 0.4404 0.4406 0.4408 0.441 0.4412 0.4414 0.4416 0.4418 0.442
211
V21 = 1745.7 m/s V32 = 2234.7 m/s V43 = 1713.1 m/s V43 = 1989.7 m/s comb Avg. Vel. = 1897.8300 m/s DDT Time = 15.79 ms
P1 = 230.5 psig P2 = 224.1 psig P3 = 266.7 psig P4 = 235.4 psig250
200
150
100
50
0
-50
-100 0.4348 0.435 0.4352 0.4354 0.4356 0.4358 0.436 0.4362 0.4364 0.4366
212
V21 = 1955.5 m/s V32 = 1936.2 m/s V43 = 1726.7 m/s V43 = 1956.6 m/s comb Avg. Vel. = 1872.8350 m/s DDT Time = 16.16 ms
P1 = 242.2 psig P2 = 309.6 psig P3 = 229.8 psig300 P4 = 219.8 psig
250
200
150
100
50
0
-50
-100 0.4352 0.4354 0.4356 0.4358 0.436 0.4362 0.4364 0.4366 0.4368 0.437
213
V21 = 1986.6 m/s V32 = 1670.1 m/s V43 = 1968.4 m/s V43 = 1963.4 m/s comb Avg. Vel. = 1875.1350 m/s DDT Time = 11.94 ms
P1 = 243.3 psig P2 = 178.4 psig P3 = 268.4 psig300 P4 = 319.6 psig
250
200
150
100
50
0
-50
-100 0.431 0.4312 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328
214
V21 = 1981.5 m/s V32 = 1969.3 m/s V43 = 1683.9 m/s V43 = 1937.3 m/s comb Avg. Vel. = 1878.2300 m/s DDT Time = 12.26 ms
P1 = 277.9 psig P2 = 204.7 psig P3 = 296.3 psig P4 = 249.5 psig250
200
150
100
50
0
-50
-100 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332
215
V21 = 1926.6 m/s V32 = 1963.6 m/s V43 = 1704.7 m/s V43 = 1676.9 m/s comb Avg. Vel. = 1864.9250 m/s DDT Time = 16.48 ms
P1 = 231.7 psig P2 = 201.3 psig P3 = 236.2 psig P4 = 223.7 psig 200
150
100
50
0
-50
-100 0.4356 0.4358 0.436 0.4362 0.4364 0.4366 0.4368 0.437 0.4372 0.4374
216
V21 = 1688.8 m/s V32 = 1959.3 m/s V43 = 1713.2 m/s V43 = 1705.1 m/s comb Avg. Vel. = 1787.1350 m/s DDT Time = 28.72 ms
P1 = 301.8 psig P2 = 319.6 psig P3 = 267.8 psig300 P4 = 197.6 psig
250
200
150
100
50
0
-50
-100 0.4478 0.448 0.4482 0.4484 0.4486 0.4488 0.449 0.4492 0.4494 0.4496
217
V21 = 1804.0 m/s V32 = 1845.3 m/s V43 = 2381.6 m/s V43 = 1965.7 m/s comb Avg. Vel. = 2010.3350 m/s DDT Time = 22.97 ms
P1 = 271.8 psig P2 = 277.8 psig P3 = 261.1 psig300 P4 = 319.2 psig
250
200
150
100
50
0
-50
-100 0.442 0.4422 0.4424 0.4426 0.4428 0.443 0.4432 0.4434 0.4436 0.4438
218
V21 = 1693.9 m/s V32 = 1937.3 m/s V43 = 2067.8 m/s V43 = 1772.6 m/s comb Avg. Vel. = 1899.7400 m/s DDT Time = 24.08 ms
P1 = 232.4 psig P2 = 220.1 psig P3 = 222.9 psig350 P4 = 364.9 psig
300
250
200
150
100
50
0
-50
-100 0.4432 0.4434 0.4436 0.4438 0.444 0.4442 0.4444 0.4446 0.4448 0.445
219
V21 = 1966.3 m/s V32 = 1693.8 m/s V43 = 1937.8 m/s V43 = 1976.3 m/s comb Avg. Vel. = 1866.0300 m/s DDT Time = 12.12 ms
P1 = 259.6 psig P2 = 189.9 psig P3 = 232.6 psig P4 = 195.9 psig250
200
150
100
50
0
-50
-100 0.4312 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433
220
V21 = 1966.5 m/s V32 = 1756.6 m/s V43 = 2232.8 m/s V43 = -5.2 m/s comb Avg. Vel. = 1985.3300 m/s DDT Time = 20.61 ms
P1 = 229.9 psig P2 = 196.5 psig P3 = 267.7 psig P4 = 235.2 psig250
200
150
100
50
0
-50
-100 0.4398 0.44 0.4402 0.4404 0.4406 0.4408 0.441 0.4412 0.4414 0.4416
221
V21 = 1977.0 m/s V32 = 1710.7 m/s V43 = 1810.2 m/s V43 = 1970.6 m/s comb Avg. Vel. = 1832.7500 m/s DDT Time = 7.21 ms
P1 = 415.9 psig P2 = 194.7 psig P3 = 209.4 psig P4 = 225.7 psig
400
300
200
100
0
-100 0.4264 0.4266 0.4268 0.427 0.4272 0.4274 0.4276 0.4278 0.428 0.4282
222
V21 = 1907.4 m/s V32 = 1702.5 m/s V43 = 1956.5 m/s V43 = 1963.5 m/s comb Avg. Vel. = 1855.5250 m/s DDT Time = 12.53 ms
P1 = 241.0 psig P2 = 212.2 psig P3 = 243.1 psig P4 = 210.7 psig 200
150
100
50
0
-50
-100 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334
223
V21 = 1705.4 m/s V32 = 1996.4 m/s V43 = 1687.5 m/s V43 = 1688.8 m/s comb Avg. Vel. = 1796.4300 m/s DDT Time = 12.88 ms
P1 = 296.0 psig P2 = 278.5 psig P3 = 212.8 psig P4 = 268.6 psig250
200
150
100
50
0
-50
-100 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338
224
V21 = 1909.8 m/s V32 = 1757.3 m/s V43 = 2261.8 m/s V43 = 1981.5 m/s comb Avg. Vel. = 1976.3300 m/s DDT Time = 22.22 ms
P1 = 256.4 psig P2 = 262.0 psig P3 = 239.9 psig P4 = 289.1 psig250
200
150
100
50
0
-50
-100 0.4414 0.4416 0.4418 0.442 0.4422 0.4424 0.4426 0.4428 0.443 0.4432
225
V21 = 1694.3 m/s V32 = 1955.2 m/s V43 = 1996.8 m/s V43 = 1679.0 m/s comb Avg. Vel. = 1882.1300 m/s DDT Time = 12.02 ms
P1 = 272.5 psig P2 = 247.5 psig P3 = 291.7 psig P4 = 216.4 psig250
200
150
100
50
0
-50
-100 0.4312 0.4314 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433
226
V21 = 1745.1 m/s V32 = 1906.3 m/s V43 = 1982.1 m/s V43 = 1969.6 m/s comb Avg. Vel. = 1877.8250 m/s DDT Time = 10.06 ms
P1 = 240.4 psig P2 = 218.0 psig P3 = 194.4 psig P4 = 202.9 psig
200
150
100
50
0
-50 0.4292 0.4294 0.4296 0.4298 0.43 0.4302 0.4304 0.4306 0.4308 0.431
227
V21 = 1687.1 m/s V32 = 1973.1 m/s V43 = 1957.7 m/s V43 = 1679.5 m/s comb Avg. Vel. = 1872.6300 m/s DDT Time = 19.48 ms
P1 = 287.7 psig P2 = 176.2 psig P3 = 196.8 psig P4 = 268.8 psig250
200
150
100
50
0
-50
-100 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404
228
V21 = 1780.1 m/s V32 = 1831.7 m/s V43 = 1945.6 m/s V43 = 1960.1 m/s comb Avg. Vel. = 1852.5250 m/s DDT Time = 21.45 ms
P1 = 232.4 psig P2 = 228.9 psig P3 = 204.1 psig P4 = 205.2 psig 200
150
100
50
0
-50
-100 0.4406 0.4408 0.441 0.4412 0.4414 0.4416 0.4418 0.442 0.4422 0.4424
229
V21 = 1675.8 m/s V32 = 1973.4 m/s V43 = 2012.2 m/s V43 = 1738.2 m/s comb Avg. Vel. = 1887.1300 m/s DDT Time = 9.36 ms
P1 = 234.1 psig P2 = 255.1 psig P3 = 246.5 psig P4 = 219.6 psig250
200
150
100
50
0
-50
-100 0.4284 0.4286 0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302
230
V21 = 1672.7 m/s V32 = 1977.8 m/s V43 = 1949.8 m/s V43 = 1781.3 m/s comb Avg. Vel. = 1866.8300 m/s DDT Time = 17.47 ms
P1 = 259.8 psig P2 = 228.0 psig P3 = 242.3 psig P4 = 208.4 psig250
200
150
100
50
0
-50
-100 0.4366 0.4368 0.437 0.4372 0.4374 0.4376 0.4378 0.438 0.4382 0.4384
231
V21 = 1989.6 m/s V32 = 1696.4 m/s V43 = 1991.3 m/s V43 = -5.3 m/s comb Avg. Vel. = 1892.5300 m/s DDT Time = 15.75 ms
P1 = 237.8 psig P2 = 198.6 psig P3 = 216.3 psig P4 = 253.9 psig250
200
150
100
50
0
-50
-100 0.4348 0.435 0.4352 0.4354 0.4356 0.4358 0.436 0.4362 0.4364 0.4366
232
V21 = 1962.2 m/s V32 = 1768.4 m/s V43 = 1876.7 m/s V43 = 1966.1 m/s comb Avg. Vel. = 1869.1400 m/s DDT Time = 12.74 ms
P1 = 378.2 psig P2 = 293.9 psig P3 = 231.9 psig350 P4 = 210.8 psig
300
250
200
150
100
50
0
-50
-100 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336
233
V21 = 1718.8 m/s V32 = 1978.7 m/s V43 = 1872.5 m/s V43 = 1688.1 m/s comb Avg. Vel. = 1856.7250 m/s DDT Time = 13.39 ms
P1 = 209.5 psig P2 = 187.3 psig P3 = 162.3 psig P4 = 202.9 psig 200
150
100
50
0
-50
-100 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338 0.434 0.4342
234
V21 = 1964.4 m/s V32 = 1817.3 m/s V43 = 1835.1 m/s V43 = 1962.1 m/s comb Avg. Vel. = 1872.3300 m/s DDT Time = 19.27 ms
P1 = 255.2 psig P2 = 214.2 psig P3 = 225.4 psig P4 = 266.8 psig250
200
150
100
50
0
-50
-100 0.4384 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402
235
V21 = 1685.1 m/s V32 = 1987.6 m/s V43 = 1945.4 m/s V43 = 1998.9 m/s comb Avg. Vel. = 1872.7300 m/s DDT Time = 18.47 ms
P1 = 206.9 psig P2 = 252.1 psig P3 = 193.4 psig P4 = 293.4 psig250
200
150
100
50
0
-50
-100 0.4376 0.4378 0.438 0.4382 0.4384 0.4386 0.4388 0.439 0.4392 0.4394
236
V21 = 1959.0 m/s V32 = 1703.8 m/s V43 = 1950.6 m/s V43 = 1997.1 m/s comb Avg. Vel. = 1871.1250 m/s DDT Time = 15.36 ms
P1 = 230.6 psig P2 = 203.5 psig P3 = 166.0 psig P4 = 180.7 psig 200
150
100
50
0
-50
-100 0.4344 0.4346 0.4348 0.435 0.4352 0.4354 0.4356 0.4358 0.436 0.4362
237
V21 = 1913.9 m/s V32 = 1978.7 m/s V43 = 1714.3 m/s V43 = 1676.2 m/s comb Avg. Vel. = 1868.9350 m/s DDT Time = 19.78 ms
P1 = 199.9 psig P2 = 306.6 psig P3 = 204.8 psig300 P4 = 207.5 psig
250
200
150
100
50
0
-50
-100 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404 0.4406 0.4408
238
V21 = 1979.0 m/s V32 = 1738.8 m/s V43 = 2263.9 m/s V43 = 1821.5 m/s comb Avg. Vel. = 1993.9300 m/s DDT Time = 9.94 ms
P1 = 249.5 psig P2 = 201.4 psig P3 = 242.5 psig P4 = 259.6 psig250
200
150
100
50
0
-50
-100 0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302 0.4304 0.4306 0.4308
239
V21 = 1712.0 m/s V32 = 1941.0 m/s V43 = 2000.8 m/s V43 = 1697.3 m/s comb Avg. Vel. = 1884.6350 m/s DDT Time = 15.89 ms
P1 = 247.0 psig P2 = 186.4 psig P3 = 237.4 psig P4 = 328.9 psig300
250
200
150
100
50
0
-50 0.435 0.4352 0.4354 0.4356 0.4358 0.436 0.4362 0.4364 0.4366 0.4368
240
V21 = 1698.9 m/s V32 = 1964.0 m/s V43 = 1711.8 m/s V43 = 1971.4 m/s comb Avg. Vel. = 1791.6350 m/s DDT Time = 12.45 ms
P1 = 342.0 psig P2 = 242.6 psig P3 = 241.8 psig P4 = 226.2 psig300
250
200
150
100
50
0
-50 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334
241
V21 = 1720.4 m/s V32 = 1944.1 m/s V43 = 1994.7 m/s V43 = 1687.3 m/s comb Avg. Vel. = 1886.4450 m/s DDT Time = 19.07 ms
P1 = 418.8 psig P2 = 193.0 psig P3 = 268.4 psig400 P4 = 302.0 psig
350
300
250
200
150
100
50
0
-50 0.4382 0.4384 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44
242
V21 = 1977.4 m/s V32 = 1965.8 m/s V43 = 1978.0 m/s V43 = 1683.3 m/s comb Avg. Vel. = 1973.7300 m/s DDT Time = 16.35 ms
P1 = 243.8 psig P2 = 288.1 psig P3 = 246.2 psig P4 = 240.2 psig 250
200
150
100
50
0
-50 0.4354 0.4356 0.4358 0.436 0.4362 0.4364 0.4366 0.4368 0.437 0.4372
243
V21 = 1708.0 m/s V32 = 1954.0 m/s V43 = 2044.7 m/s V43 = 2003.0 m/s comb Avg. Vel. = 1902.2600 m/s DDT Time = 12.85 ms
P1 = 248.3 psig P2 = 219.8 psig P3 = 211.2 psig P4 = 547.7 psig 500
400
300
200
100
0
-100 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334 0.4336 0.4338
244
V21 = 1682.7 m/s V32 = 1974.3 m/s V43 = 1702.3 m/s V43 = 1755.3 m/s comb Avg. Vel. = 1786.4250 m/s DDT Time = 19.66 ms
P1 = 209.8 psig P2 = 207.8 psig P3 = 248.3 psig P4 = 183.6 psig
200
150
100
50
0
-50 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402 0.4404 0.4406
245
V21 = 1975.7 m/s V32 = 1693.5 m/s V43 = 1943.3 m/s V43 = 1961.1 m/s comb Avg. Vel. = 1870.9300 m/s DDT Time = 12.54 ms
P1 = 214.6 psig P2 = 190.2 psig P3 = 191.1 psig P4 = 259.7 psig250
200
150
100
50
0
-50
-100 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334
246
V21 = 1970.4 m/s V32 = 1950.5 m/s V43 = 1699.0 m/s V43 = 1984.4 m/s comb Avg. Vel. = 1873.3300 m/s DDT Time = 12.48 ms
P1 = 192.9 psig P2 = 193.9 psig P3 = 252.7 psig P4 = 264.0 psig 250
200
150
100
50
0
-50 0.4316 0.4318 0.432 0.4322 0.4324 0.4326 0.4328 0.433 0.4332 0.4334
247
V21 = 1917.7 m/s V32 = 1730.9 m/s V43 = 1980.2 m/s V43 = 1958.8 m/s comb Avg. Vel. = 1876.3300 m/s DDT Time = 9.27 ms
P1 = 250.7 psig P2 = 228.3 psig P3 = 207.3 psig P4 = 242.8 psig 250
200
150
100
50
0
-50 0.4284 0.4286 0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302
248
V21 = 1954.0 m/s V32 = 1756.0 m/s V43 = 1930.7 m/s V43 = 1984.8 m/s comb Avg. Vel. = 1880.2300 m/s DDT Time = 9.51 ms
P1 = 266.4 psig P2 = 201.1 psig P3 = 213.4 psig P4 = 176.9 psig250
200
150
100
50
0
-50
-100 0.4286 0.4288 0.429 0.4292 0.4294 0.4296 0.4298 0.43 0.4302 0.4304
249
V21 = 1931.1 m/s V32 = 1453.8 m/s V43 = 1972.2 m/s V43 = 1722.9 m/s comb Avg. Vel. = 1785.7250 m/s DDT Time = 17.69 ms
P1 = 224.2 psig P2 = 243.4 psig P3 = 178.7 psig P4 = 232.5 psig
200
150
100
50
0
-50 0.4368 0.437 0.4372 0.4374 0.4376 0.4378 0.438 0.4382 0.4384 0.4386
250
V21 = 1868.3 m/s V32 = 1615.5 m/s V43 = 2046.2 m/s V43 = 1853.4 m/s comb Avg. Vel. = 1843.4450 m/s DDT Time = 17.19 ms
P1 = 221.5 psig P2 = 258.1 psig P3 = 185.6 psig400 P4 = 404.8 psig
350
300
250
200
150
100
50
0
-50 0.4362 0.4364 0.4366 0.4368 0.437 0.4372 0.4374 0.4376 0.4378 0.438
251
V21 = 1695.8 m/s V32 = 1771.0 m/s V43 = 1875.2 m/s V43 = 1705.8 m/s comb Avg. Vel. = 1780.7300 m/s DDT Time = 19.29 ms
P1 = 222.1 psig P2 = 202.6 psig P3 = 225.0 psig P4 = 269.9 psig250
200
150
100
50
0
-50
-100 0.4384 0.4386 0.4388 0.439 0.4392 0.4394 0.4396 0.4398 0.44 0.4402
252
V21 = 1714.7 m/s V32 = 1784.0 m/s V43 = 1850.2 m/s V43 = 1718.9 m/s comb Avg. Vel. = 1783.0300 m/s DDT Time = 20.24 ms
P1 = 206.7 psig P2 = 206.3 psig P3 = 170.3 psig P4 = 255.4 psig 250
200
150
100
50
0
-50 0.4394 0.4396 0.4398 0.44 0.4402 0.4404 0.4406 0.4408 0.441 0.4412
253
V21 = 1520.0 m/s V32 = 1633.9 m/s V43 = 1972.5 m/s V43 = 1435.6 m/s comb Avg. Vel. = 1708.8350 m/s DDT Time = 18.12 ms
P1 = 348.5 psig P2 = 309.3 psig P3 = 276.2 psig P4 = 321.5 psig300
250
200
150
100
50
0
-50 0.4372 0.4374 0.4376 0.4378 0.438 0.4382 0.4384 0.4386 0.4388 0.439
254