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Dissertations and Theses Spring 2012 Design and Optimization of a Deflagration to Detonation Design and Optimization of a Deflagration to Detonation Transition (DDT) Section Transition (DDT) Section Francisco X. Romo Embry-Riddle Aeronautical University - Daytona Beach Follow this and additional works at: https://commons.erau.edu/edt Part of the Aerospace Engineering Commons Scholarly Commons Citation Scholarly Commons Citation Romo, Francisco X., "Design and Optimization of a Deflagration to Detonation Transition (DDT) Section" (2012). Dissertations and Theses. 124. https://commons.erau.edu/edt/124 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].
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Page 1: Design and Optimization of a Deflagration to Detonation ...

Dissertations and Theses

Spring 2012

Design and Optimization of a Deflagration to Detonation Design and Optimization of a Deflagration to Detonation

Transition (DDT) Section Transition (DDT) Section

Francisco X. Romo Embry-Riddle Aeronautical University - Daytona Beach

Follow this and additional works at: https://commons.erau.edu/edt

Part of the Aerospace Engineering Commons

Scholarly Commons Citation Scholarly Commons Citation Romo, Francisco X., "Design and Optimization of a Deflagration to Detonation Transition (DDT) Section" (2012). Dissertations and Theses. 124. https://commons.erau.edu/edt/124

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].

Page 2: Design and Optimization of a Deflagration to Detonation ...

Design and Optimization of a Deflagration to Detonation Transition

(DDT) Section

Francisco X. Romo

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, Florida

Spring 2012

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Table of Contents  

Acknowledgements..................................................................................................................... iv

Abstract ........................................................................................................................................ v

List of Tables .............................................................................................................................. vi

List of Figures .............................................................................................................................vii

Nomenclature ............................................................................................................................. ix

1. Introduction .............................................................................................................................. 1  

1.1 Problem statement ........................................................................................................... 1  

1.2 Combustion and Detonation............................................................................................. 3  

1.3 Detonation Initiation – Direct and DDT ............................................................................ 8  

1.4 Pulsed Detonation Engine (PDE)................................................................................... 10  

1.5 Literature survey ............................................................................................................ 12  

2. Test equipment and methodology ......................................................................................... 15  

2.1 Methodology................................................................................................................... 15  

2.2 Equipment layout ........................................................................................................... 19  

2.3 Equipment description.................................................................................................... 23  

2.3.1 Electrical equipment description .................................................................................. 23  

2.3.2 Hardware description ................................................................................................... 27  

2.3.3 Control system description ........................................................................................... 31  

3. Results and analysis ............................................................................................................. 37  

3.1 Data processing methodology ....................................................................................... 37  

3.2 Numerical results ........................................................................................................... 39  

3.3 Regression model .......................................................................................................... 41  

3.4 Analysis .......................................................................................................................... 43  

3.5 Oxygen testing results.................................................................................................... 53  

3.6 Testing observations ...................................................................................................... 55  

4. Conclusions and recommendations ...................................................................................... 59  

References ..................................................................................................................................... 60

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Acknowledgements  

I would like to dedicate this work to my Wife and Family, who supported me throughout my

journey at Embry-Riddle. Without them none of this would have been possible.

 

 I would like to express my sincere gratitude to Dr. Magdy Attia. His knowledge and mentorship

skills tremendously helped me through my career at Embry-Riddle. I would like to recognize

committee members Dr. Eric Perrell and Dr. William Engblom, for their time and support with this

paper.

 

 I would also like to thank my colleagues from the Gas Turbine Lab Jeff Vizcaino and Walter

 ‘Boomer’ Olliff for their help with this project. Derek Noce also deserves recognition for his help.

  

 This work was supported by an internal student research grant provided by Embry-Riddle

 Aeronautical University.

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Abstract  

Throughout the previous century, hydrocarbon-fueled engines have used and optimized the  

‘traditional’ combustion process called deflagration (subsonic combustion). An alternative form of

combustion, detonation (supersonic combustion), can increase the thermal efficiency of the

process by anywhere from 20 - 50%. Even though several authors have studied detonation

waves since the 1890’s and a plethora of papers and books have been published, it was not until

2008 that the first detonation-powered flight took place. It lasted for 10 seconds at 100 ft. altitude.   

 Achieving detonation presents its own challenges: some fuels are not prone to detonate, severe

vibrations caused by the cyclic nature of the engine and its intense noise are some of the key

areas that need further research. Also, to directly achieve detonation either a high-energy, bulky,

ignition system is required, or the combustion chamber must be fairly long (5 ft. or more in some

cases). In the latter method, a subsonic flame front accelerates within the combustion chamber

until it reaches supersonic speeds, thus detonation is attained. This is called deflagration-to-

detonation transition (DDT).

 

 Previous papers and experiments have shown that obstacles, such as discs with an orifice,

located inside the combustion chamber can shorten the distance required to achieve detonation.

This paper describes a hands-on implementation of a DDT device. Different disc geometries

inside the chamber alter the wave characteristics at the exit of the tube. Although detonation was

reached only when using pure oxygen, testing identified an obstacle configuration for LPG and air

mixtures that increased pressure and wave speed significantly when compared to baseline or

other obstacle configurations. Mixtures of LPG and air were accelerated to Mach 0.96 in the

downstream frame of reference, which would indicate a transition to detonation was close.

Reasons for not achieving detonation may include poor fuel and oxidizer mixing, and/or the need

for a longer DDT section.

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List of Tables  

Table 1 - Cell size vs. fuel mixtures ................................................................................................. 8  

Table 2 - Tube characteristics........................................................................................................ 28  

Table 3 - Flange characteristics ..................................................................................................... 28  

Table 4 - LPG composition ............................................................................................................ 31  

Table 5 - Best performance runs ................................................................................................... 39  

Table 6 - Pressure regression model results ................................................................................. 42  

Table 7 - Ideal cartridge parameters.............................................................................................. 51

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List of Figures  

Figure 1 - Rayleigh lines and Rankine-Hugoniot curve ................................................................... 5  

Figure 2 - ZND 1D model detonation wave ..................................................................................... 7  

Figure 3 - 2D Detonation wave propagation pattern ....................................................................... 7  

Figure 4 - Shchelkin spiral .............................................................................................................. 9  

Figure 5 - Shchelkin spiral degradation after testing ...................................................................... 9  

Figure 6 - Brayton and Humphrey cycles P-V and T-s diagrams ................................................. 10  

Figure 7 - Thermal Efficiency vs. Compression Ratio ................................................................... 12  

Figure 8 - Proposed detonation test tube (not to scale)................................................................. 16  

Figure 9 - Test configurations (abbreviated) .................................................................................. 18  

Figure 10 - Injector configuration comparison ............................................................................... 20  

Figure 11 - Injection section top view............................................................................................. 20  

Figure 12 - Injection section tangential ports and spark plug ........................................................ 21  

Figure 13 - Center section with cartridge, end-view ...................................................................... 21  

Figure 14 - Equipment block diagram ............................................................................................ 22  

Figure 15 - Complete test setup..................................................................................................... 23  

Figure 16 - DAQ with quick-disconnect harness............................................................................ 25  

Figure 17 - Modified spark plug ..................................................................................................... 27  

Figure 18 - Cartridges and discs .................................................................................................... 30  

Figure 19 - Injector valves block .................................................................................................... 30  

Figure 20 - Labview graphical user interface (GUI) ....................................................................... 32  

Figure 21 - DAQ output control lines, simplified ............................................................................ 34  

Figure 22 - Labview program ......................................................................................................... 35  

Figure 23 - Labview routine flowchart ............................................................................................ 36  

Figure 24 - Matlab sample output graphs ...................................................................................... 38  

Figure 25 - Best performance plots................................................................................................ 40  

Figure 26 - Average pressure histogram ....................................................................................... 43  

Figure 27 - Average speed histogram............................................................................................ 44

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Figure 28 - Average TR histogram.................................................................................................. 45  

Figure 29 - Average pressure vs. BR vs. L .................................................................................... 46  

Figure 30 - Average pressure vs. BR vs. d .................................................................................... 47  

Figure 31 - Average pressure vs. L vs. disc spacing ..................................................................... 47  

Figure 32 - Average speed vs. BR vs. L ........................................................................................ 48  

Figure 33 - Average speed vs. BR vs. number of discs................................................................. 48  

Figure 34 - Average speed vs. L vs. disc spacing ......................................................................... 49  

Figure 35 - Rise time vs. BR vs. L ................................................................................................. 49  

Figure 36 - Rise time vs. BR vs. number of discs .......................................................................... 50  

Figure 37 - Rise time vs. L vs. disc spacing................................................................................... 50  

Figure 38 - Oxygen testing results ................................................................................................. 54  

Figure 39 - Discs after oxygen testing (bent) ................................................................................. 57

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Nomenclature     

DDT Deflagration to Detonation Transition  

PDE Pulse detonation engine

DAQ Digital acquisition system

GUI Graphical user interface

LPG Liquefied petroleum gas

d Number of discs in cartridge

s Disc spacing, inches

λ Lambda – Detonation cell height

v Specific volume

q Heat  

η Efficiency  

γ Specific heats ratio

m Mass

m Mass flux – mass flow by area

π Compression ratio  

BR Blockage ratio – blocked area by total area  

P Pressure  

T Temperature  

ρ Density  

M Mach number  

Φ Equivalence ratio  

L Inverse of Φ  

TR Signal rise time

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1. Introduction

Pulse-detonation engines (or PDE) have received increased attention in the past decade due to

their potential for higher overall thermal efficiency. A PDE has fewer moving parts than a gas

turbine or internal combustion engine, making it also attractive from a reliability and mechanical

standpoint. PDE’s operate in a similar intermittent-manner as pulse-jet engines, but with a

different combustion process: detonation. Entropy is maximized during deflagration [1] (i.e.

‘normal’ combustion), thus making it the least efficient way of burning fuel. Detonation is an

alternate, supersonic type of combustion which in addition to (chemically) releasing heat, also

increases the burning gas pressure. To date, no PDE has been put into production. Most of the

existing PDE prototypes (from Caltech, University of Texas, and USAF) focus on thrust

production.

The author previously performed testing of a privately-funded Pulse Detonation Engine prototype

at Embry-Riddle’s Gas Turbine Lab. This prototype differs because it claims to employ detonation

to spin a shaft rather than producing thrust. Almost every motor and engine, whether used for

transportation, industrial or power generation, has a rotating axle as the de-facto power transfer

mechanism. The observations and experiences learned from testing the aforementioned

prototype finally helped the development of this paper.

1.1 Problem statement

From a theoretical standpoint, detonation has been shown to be more thermally efficient than low-

speed, normal deflagration. In an oil-dependent world, it shouldn’t be a surprise to hear that

detonation is receiving renewed interest from the scientific community. Yet a practical detonation

device, industrial or commercial, seems to be a few years (if not decades) away. Previous

research has been focused on using highly detonable fuels, such as hydrogen, or pure oxygen

instead of air. These two conditions effectively limit detonation to laboratory-only situations.

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Although the first detonation models were developed over a century ago, between 1899 and 1905

by Chapman and Jouguet, detonation still remains an unpractical, theoretical concept described

in combustion books. The problem lies in achieving detonation in a practical, controlled,

consistent and repeatable manner. To achieve detonation, either direct detonation or deflagration

to detonation transition (DDT) methods have been used.

Direct detonation entails releasing sufficient energy into a combustible mixture so that a

detonation wave is directly formed. Energy levels vary up to millions of Joules, depending on the

fuel and oxidizer being used. The methods used to deliver such energy are numerous, including

plasma or corona-type electrical discharges, lasers, and perhaps the most obvious: explosives.

Any of these methods remain clearly impractical outside research facilities.

DDT on the other hand, employs a much less drastic approach. Using a conventional consumer-

grade ignition system, the resulting flame accelerates inside a chamber with obstacles until it

transitions into detonation speeds. The main drawback with this approach is that the required

distance for the wave to reach the CJ velocity (the supersonic speed at which detonation is

stable) can be substantial. Depending on the fuel and oxidizer used, this distance can vary from a

few inches to several feet.

Several authors have previously studied the effects of obstacles inside detonation tubes and their

effects on DDT length [8] [10] [11]. All studies have used specific geometries, either by using

Shchelkin spirals (coil springs) or fixed discs with a small orifice located inside the tube. Wire-

wound spirals cannot withstand the high pressures and temperatures of detonation, and previous

experiments showed they tend to disintegrate after a few cycles [8]. Most studies have been

performed using small diameter tubes (less than 2 inches) with spirals inside them. This severely

limits the mass flow through the device, thus limiting the amount of thrust and/or power generated

by detonation. Other studies [10] [11] have used highly detonable mixtures (such as hydrogen

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and pure oxygen) with discs inside the tube. However, the use of pure oxygen limits the

implementation and operation of such devices to laboratory conditions.

This paper explores the experimental results aimed to achieve detonation by DDT in a 4-inch ID,

6-foot long tube. In order to keep the experiment conditions as practical as possible, pure oxygen

will be avoided, if only used to verify theoretical results. Therefore, consumer-grade LPG and air

will be used. The selection of a 4-inch tube was made in order to allow one full detonation cell to

pass through (see the following section), and to increase mass flow which would increase thrust

and/or power on a PDE. Obstacles used inside the tube will be assembled using discs with

different size orifices, limited by the length of the tube. The ideal disc stack will achieve the fastest

flame speed within the tube.

The findings from this project will help develop easier, economical and more effective methods for

building the next Pulse Detonation Engine prototypes. It will also provide a better understanding

of detonation requirements regarding overall device dimensions as well as ignition systems.

However, in order to better understand the nature and difficulty of detonation, a quick review of

some combustion basics is warranted.

1.2 Combustion and Detonation

Combustion can be either subsonic (deflagration) or supersonic (detonation). During deflagration,

heat is released due to the chemical reaction between fuel and oxidizer: a slight expansion

lowers the final pressure of the gas (unless the reaction is carried out in a closed chamber) [2].

Gas downstream the flame front moves away from the flame. Deflagration can be modeled as an

isobaric heat addition process.

Detonation is the combustion of a fuel and oxidizer mixture, where the combustion wave travels

at supersonic speeds relative to the upstream gas mixture [2]. Unlike deflagration, detonation

compresses the gas due to the supersonic wave. During detonation, downstream gas follows the

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flame front. Although simplified, a conservative assumption is that detonation can be modeled as

an isochoric (constant volume) process.

Previous studies have shown that for unsteady combustion, total entropy gain is lower for

detonation. However, when the same analysis is applied to a steady-state process, detonation is

shown to have a greater entropy gain than deflagration. Therefore, detonation has potential when

used on pulsed, unsteady, cyclical devices [1].

Chapman and Jouguet (CJ) independently developed the basic thermodynamic model behind

detonation. The CJ model describes the interaction between Rayleigh and Rankine-Hugoniot

curves, defining the physically possible states that a thermodynamic process is bound to. The CJ

model shows that detonation reaches equilibrium speed as the combustion wave reaches the

speed of sound in the local wave frame of reference. From here, pressure and density can be

easily calculated.

By using the conservation of energy, mass, momentum, continuity and ideal gas relationships,

the Rankine-Hugoniot equation (1.1) is easily derived:

y

y - 1 (P2 v2 - Pl vl ) -

1 2

(P2 - Pl )(vl + v2 ) - q = 0 (1.1)

In equation 1.1, if the upstream flow conditions P1 and v1 are known, as well as the heat addition

term q, then the Rankine-Hugoniot equation determines the possible combinations of

downstream conditions P2 and v2 while imposing the conservation laws. This can be plotted on a

P-v diagram, as in Figure 1.

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Figure 1 - Rayleigh lines and Rankine-Hugoniot curve[15]

On the other hand, the Rayleigh line equation (1.2) results from simultaneously solving the

continuity and momentum conservation equations:

P2 - Pl

v2 - vl

= -m 2 (1.2)

The mass flux term is defined as mass flow divided by area. Once again, if upstream conditions

P1 and v1 are known, several Rayleigh lines can be plotted on a P-v diagram passing through

point A. For different mass flux values, the slope of the Rayleigh line will change. Since the mass

flux term can only be positive (or zero), the resulting line slope can only vary from zero to

negative infinity. This means no positive slope lines can exist.

When both Rayleigh and Rankine-Hugoniot are plotted together, the resulting graph is Figure 1.

Both curves have P1 and v1 (point A) as initial conditions. When solving both equations, the first

solution region is defined by the Rayleigh lines A-D and A-B. Any Rayleigh line with lower

negative slope would not intersect the Rankine-Hugoniot curve. Any line with a positive slope (i.e.

right of A-B) wouldn’t be a real process. Using the same arguments, the second region is limited

from A-C to A-E.

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This divides the Rankine-Hugoniot curve into 5 sections. To the left of point D, a subsonic ‘strong

detonation’ area is defined. From D to B, a supersonic ‘weak detonation’ area is defined. The

section B-C is not a real process. From C to E, a subsonic ‘weak deflagration’ region is defined.

Below E, a supersonic ‘strong deflagration’ zone exists. The strong detonation and strong

deflagration areas are mathematically possible, but such phenomena rarely exist [15].

Typical values for detonation wave velocities are Mach 5-10. For comparison, air-hydrocarbon

mixtures deflagrations rarely exceed 1 m/s [2] [15].

Zel’dovich, von Neumann and Doering (ZND) further developed in the early 1940’s a model for a

one-dimensional detonation wave. The ZND model suggests that a detonation wave can be

modeled as a coupled, mutually supporting normal shock wave and a thin combustion reaction

zone behind the shock. As the normal shock compresses and thus heats the gas, the chemical

reaction is initiated behind the shock. The chemically released energy drives in turn the normal

shock propagation [3]. A pressure spike can be observed right after the shock (induction zone),

called the von Neumann spike. As the wave travels further down the mixture, pressure drops and

decays to a stable value. The detonation wave speed is dependent on the fuel and oxidizer used,

as well as their initial conditions (pressure, and to a lesser extent temperature) and stoichiometric

ratio [4]. Typical detonation wave thickness is on the order of 0.1mm. A typical diagram of the

ZND 1-D wave model is shown in Figure 2.

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Figure 2 - ZND 1D model detonation wave

Experimental results have shown that the ZND model, a simplified 1D approximation, isn’t truly

capable of predicting 2D/3D waves, which are complex structures characterized by an oscillatory

motion. The leading shocks create transverse waves, and when these transverse waves collide,

localized high pressure points are formed. The reaction rate of the mixture is increased at these

points, which in turn accelerates the shock. The resulting effect is the observed fishnet pattern, as

seen in

Figure 3.

Figure 3 - 2D Detonation wave propagation pattern [1]

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An important wave parameter is the cell width, λ, seen in

Figure 3. The cell size is dependent on the fuel and oxidizer used, stoichiometric ratio, initial

pressure and temperature. To ensure detonation propagation, any detonation tube must be large

enough to accommodate at least one complete detonation cell.

Detonation cell size is also a measure of the sensitivity of the mixture to detonate [5]. Table 1

shows a comparison of select fuels and their cell size. Although mathematical models to predict

cell size exist, their poor accuracy favors values obtained experimentally.

Table 1 - Cell size vs. fuel mixtures

Fuel λ (mm)

Oxygen Air

Hydrogen 1.3 10.9

Acetylene C2H2 0.109 5.8

Methane CH4 8 280

Ethane C2H6 - 51

Propane C3H8 2.5 51.3

Kerosene 30.0 -

1.3 Detonation Initiation – Direct and DDT

The two most frequent methods to start detonation are direct initiation or DDT. Studies have

shown that direct initiation requires considerable amounts of energy. Different variations of

electric arcs (such as corona) are common methods for imparting high-energy levels. Direct

detonation energy requirements vary depending on fuel being used and its conditions

(temperature, pressure, stoichiometric ratio, oxidizer, diluents). Typical initiation energy ranges

from a few joules to millions of joules [5] [7]. To ensure direct detonation is achieved, the amount

of energy must be above that of the critical initiation energy. Due to the large amount of energy

required for direct initiation, DDT is considered an easier method to initiate detonation.

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DDT starts with a low-energy spark, which initiates deflagration in the gas mixture. As the flame

travels through the combustion chamber, heat, pressure, and turbulence accelerate the flame

until it reaches the speed of sound in the flame frame of reference, thus transitioning into a

detonation wave. Obstacles placed inside the chamber can help accelerate the flame in a shorter

distance. The Shchelkin spiral is perhaps the most common method used to partially block the

chamber and induce DDT. The most important parameter for the spiral is the blockage ratio

(BR), as shown in Figure 4. A similar definition for BR is used for obstacles such as discs with an

orifice. Previous studies have shown that the spiral can be worn down after only a few

detonations [8]: see Figure 5. For DDT to occur, the chamber (or detonation tube) must be long

enough to ensure deflagration has sufficient distance to transition into detonation.

Figure 4 - Shchelkin spiral [8]

Figure 5 - Shchelkin spiral degradation after testing [8]

An interesting study showing different regimes for flame acceleration using discs was presented

by Lee et al. in 1984 [19]. In their experiment, flame acceleration was measured in different tubes

ranging from 11 to 17 meters long. They identified four different regimes for flame acceleration:

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quenching, choking, quasi-detonation and CJ. In quenching, the flame initially accelerates and

then self-extinguishes after passing through a certain number of discs. In choking, the wall friction

and heat addition balance out, thus the flame reaches an equilibrium speed below the local sonic

conditions. The discs effectively ‘choke’ the flame speed. In quasi-detonation, detonation is the

propagation mode of the flame, but the momentum loss of the gas due to the obstacles and

friction losses prevents it from reaching the CJ conditions. It was found that in the quasi-

detonation and choking regimes, wave speed was very similar (around ~1000m/s in both cases).

Finally, when detonation is achieved and the obstacles do not interfere with the wave

propagation, CJ velocities are reached.

1.4 Pulsed Detonation Engine (PDE)

Ultimately, PDEs will use detonation and extract work from the burning gases. PDE prototypes

have an unsteady nature: after detonation takes place, burnt gases must be expelled and fresh

mixture fed to the chamber before a new detonation cycle can take place. Therefore, engine total

output power will be proportional to its operating frequency. Mechanical and flow considerations

currently limit the frequency at which prototype PDEs can operate. Let’s compare PDE efficiency

with a gas turbine engine by considering Figure 6.

Figure 6 - Brayton and Humphrey cycles P-V and T-s diagrams[3]

Traditional gas turbines operate on the Brayton cycle (0-1-4-5-0). A PDE engine can be modeled

by the Humphrey cycle (0-1-2-3-0), where combustion (1-2) is an isochoric heat addition process.

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T

T

The T-s diagram in Figure 6 shows that during detonation (1-2), final entropy is lower and

pressure is higher for the Humphrey cycle (points 2 vs. 4). Due to the additional pressure, the

expansion process (2-3) can achieve a larger temperature drop, which results in additional work

performed by the gas. It should not be surprising that cycle efficiency for a PDE could be much

higher than an equivalent engine operating on the Brayton cycle. Assuming ideal gas, the

efficiency for both cycles are given by the following equations [2]:

TO ton = 1 -

l

(1.3)

Th O

l

T2 y - 1

Tl

(1.4)

Htaph e = 1 -

l

* y

T2 - 1 Tl

Comparing equations 1.3 and 1.4, the Humphrey cycle has an additional term which is always less

than unity. The additional term makes the efficiency dependent not only on the temperature ratio

across the compression process, but also on specific heats and temperature ratio across the

combustion process. Since the additional term is less than unity, an engine based on the

Humphrey cycle will have a greater efficiency than a Brayton one, provided compression (hence

temperature) ratios are similar.

When comparing the CJ and isochoric model gas final conditions, one can observe that CJ

conditions are even higher than that of an isochoric process (Humphrey). A more accurate

thermodynamic cycle for an ideal PDE is the Fickett-Jacobs (FJ) cycle [6] [1]. The basics of FJ

are a cylinder and piston forming a closed system. The system is considered adiabatic, and the

mass inside the cylinder is also fixed. Detonation occurs within the cylinder and its contents are

brought back to initial conditions. The FJ cycle efficiency also depends on gamma, so a specific

fuel and initial conditions are needed. A more in-depth explanation of the FJ cycle is given in [1].

Figure 7 shows a comparison made between all three cycles, for stoichiometric propane-air

mixtures at 300K and 1 bar initial conditions. All calculations are assumed to be ideal cases, no

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losses, with isentropic compression and expansion. It is now clear to see the tremendous benefits

of detonation when applied to a PDE.

Perhaps the most obvious difference is that even without compression (i.e. π = 1), the efficiency

of the FJ cycle can exceed 30% where it would be zero for Brayton. As compression ratio

increases, the difference is reduced, yet still being significant.

Figure 7 - Thermal Efficiency vs. Compression Ratio

[1]

1.5 Literature survey

Detonation experiments have been well documented throughout the 20th

century. With the theory

set by the CJ model around 1900, newer ideas began to develop during the early and mid-20th

century. Due to the nature of detonation, it shouldn’t be a surprise that most developments

happened during times of war. Russians, Germans and Americans greatly contributed to what we

know about detonation today.

Against popular belief, the German V-1 missile used during World War II had a pulse jet engine

operating with deflagration, not detonation. The heavily used V-2, unlike the V-1, switched to

liquid fuels instead.

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In a similar way as with the CJ model, independently developed by Chapman and Jouguet, the

ZND model is named after Zeldovich (Russian), von Neumann (Hungarian-American) and Doring

(German), who each independently developed a one dimensional model to physically explain the

thermodynamics behind the CJ theory. They published their works in 1940, 1943 and 1960

respectively.

Earlier experiments by Kayushin [16], tried to explore the effects of wire mesh placed inside a tube

on flame speed. Although using hydrogen and oxygen –perhaps the most easily detonable

mixture– the author found, by using Schlieren devices, that immediately after the wire mesh flame

speed seemed to accelerate. Grids were characterized by a non-dimensional number, relating the

number of elements in a grid and the diameter of its elements. Kayushin also experimented with

what he called diaphragms: essentially similar to a disc with an orifice. He found that as BR

increased, the flame speed after the obstacles increased, initially exceeding CJ speeds, settling

to CJ speeds. Hydrogen and oxygen mixtures have a cell size of around 1.3mm. His experiments

were carried out in a tube only 17.5 cm long.

Perhaps the most renowned device known to obtain detonation is the Shchelkin spiral, named

after (Russian) Kirill Ivanovich Shchelkin. His earlier works (circa 1949) included studies about

wall surface roughness and its effect on the velocity of flames. He published his findings about

using a spiral as an obstacle and how it accelerated the flame velocity within the tube. The BR

parameter is again mentioned as one of the most important spiral characteristics [8].

A recent study using discs as obstacles was performed by Chapin [18]. Discs with orifices were

mounted inside a tube to help shorten the DDT length. Hydrogen-air and ethylene-air mixtures

were used in the study. Experiments were carried out in a 2” diameter, 40” long clear

polycarbonate tube and a high-speed camera. Detonation was achieved within the tube length.

Chapin concluded that BR, length of DDT section and spacing between obstacles all affected the

required distance for detonation. Consumer-grade LPG and air mixtures were not tested.

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Throughout the last decade, the University of Texas at Arlington has conducted several

experiments and published numerous papers. A description of most experiments and their results

can be found in Panicker’s Ph.D. dissertation [17]. Testing was performed using propane and

oxygen mixtures. Several setups have been tested, including 0.75” ID and 1” ID tubes, Shchelkin

spirals, rotary valves, water-cooled assemblies, converging-diverging nozzles, liquid-fuel

injectors, and also a turbocharger turbine on an attempt to extract power from the gas. Albeit

detonation was present on all setups, they didn’t achieve it in a consistent manner. In one of their

latest papers [18], they even conclude that a clean-tube configuration had the best detonation

success-rate over multiple firings.

Caltech’s Explosion Dynamics Laboratory hosts a very useful detonation database on their

website. They host data from over 130 different publications containing experimental detonation

data. The website shows the data based on different parameters such as cell size, tube diameter,

and critical energy, among others. It is interesting to note that for the proposed fuel (propane) and

air mixture, λ lies between 50 and 130mm, with the smallest size corresponding to a

stoichiometric mixture. The critical energy to achieve direct detonation lies in the 200 kJ range. If

direct detonation were to occur inside an engine at, say 20 times per second, the required

initiation energy would equal approximately 4MJ/s, which means four megawatts for the ignition

system alone. It should become clear to the reader why direct detonation methods can be

impractical, to say the least.

Throughout the published papers, it would seem that researchers have avoided the use of

LPG/propane and air, perhaps due to its relatively larger cell size. Although this mixture lies

somewhere in the low-end of detonation sensitivity, it may be the most easily obtainable fuel for a

commercial application. The experiments described in this paper are, for practicality reasons,

restricted to LPG and air mixtures.

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2. Test equipment and methodology

2.1 Methodology

This project focuses on a larger diameter (~4 inch ID) detonation tube, using readily available LPG

(liquefied petroleum gas) and air mixtures. The tube is split into three sections. The center tube

section allows the installation of a ‘cartridge’ consisting of discs with an orifice. The discs are

secured on threaded rods, allowing the cartridge to be easily installed and removed from the

tube. Testing was performed with several cartridge configurations in order to determine an

optimal geometry, where the final flame speed is maximized in the available tube length. Figure 8

shows a diagram of the detonation test tube.

In order to detect detonation, high speed pressure sensors were used. The easiest way to detect

detonation waves is by measuring their speed. Since the distance between two adjacent pressure

sensors is known, the wave speed can be calculated by measuring the time it takes for the

pressure spike(s) to travel between sensors. From CJ theory (see section 1.2), a theoretical

detonation wave velocity can be calculated and compared with the measurements.

Initial testing was ‘dry’ – i.e. without fuel. The proper operation of the gas injectors, igniter and

pressure sensors was verified. After checking for fuel and/or air leaks, the initial fuel tests were

performed. For safety reasons, the initial fuel tests were carried out progressively by filling the

tube with stoichiometric mixture from 10% up to 120% (tube total volume) in 10% increments.

This ensured early detection of any possible flaws in the mechanical and/or electro-mechanical

parts. All tests were performed by initially purging the tube with at least 80% (total volume) pure

oxidizer.

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Figure 8 - Proposed detonation test tube (not to scale)

Fuel testing was initially performed on an empty tube, to determine a baseline case. This

configuration should achieve deflagration speeds near the spark plug, with flow accelerating

towards the open-end of the tube due to heat addition (gas expansion) and friction.

Once a disc cartridge was installed, different equivalence ratios for the air/fuel mixture were

tested, ranging from lean to rich until the mixture failed to ignite using the available ignition

system. All equivalence ratios were tested with different fill rates (80%, 100% and 120%).

Cartridges with different disc spacing and BR were tested using the same procedure. Up to a

maximum of 14 discs were installed on a single cartridge, with a corresponding minimum disc

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spacing of 3 inches. Discs with a BR of 30, 45, 60 and 75 (as defined in Figure 4) with spacing of

3, 4.5 and 6 inches were tested. Full and half-cartridges (half the discs) were also tested. Figure 9

shows the different test configurations using a tree diagram; only one branch is fully expanded

with equivalence ratio (l) and fill rates due to space limitations.

L

Overall, 479 firings were recorded using LPG and air mixtures, and an additional 3 using pure

oxygen. After all data was collected, the results were analyzed and discussed.

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Figure 9 - Test configurations (abbreviated)

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2.2 Equipment layout

The DDT tube was built with a modular design in mind: it is comprised of three sections. The first

section contains the mixture injection ports together with an ignition spark plug. The use of

standard flanges between sections allows quick and easy cartridge changes inside the center

section. The third section contains sensors to measure pressure and wave speed, as shown in

Figure 8.

The initial section held the fuel and oxidizer injection pipes and spark plug. In order to minimize

injection time, pressurized LPG and oxidizer were used. This ensured the detonation tube was

purged and filled in a relatively short time, keeping losses through the tube’s open-end to a

minimum. Injection was controlled by electrically operated solenoid valves and high-pressure

check valves. The solenoids were controlled and timed by the Data Acquisition Board (DAQ).

The injector pipes were welded in a tangential pattern. This geometry helps maximize turbulence

(hence mixing of fuel and oxidizer) and maintain gas velocity inside the tube. Three different

tangential configurations were considered. In the first two cases both pipes were as close as

possible to each other (around 45° from each other) , with oxidizer being injected ahead of fuel

and vice versa. The third case had opposing, staggered pipes. From CFD analysis, it was

observed that the opposing pipes configuration maintained higher gas velocity and provided a

more homogeneous mixture. Figure 10 contains a snapshot of the analysis showing fuel mass

fraction after injection has taken place. A high pressure check valve was mounted at the end of

each injection pipe to prevent any backflow or flame travelling back into the supply lines. The

initial section also held the spark plug. The ignition system comprised an automotive-grade

ignition module and matching coil connected to the spark plug. A modified spark plug was used to

ignite the mixture in the chamber (see equipment description). The ignition system was also

controlled by the DAQ. The injector valves and ignition system were both powered by a 13.8 VDC

power supply. Figure 11 shows a top view of the injection section with check valves and spark

plug installed. Figure 12 shows the injection ports and spark plug.

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Figure 10 - Injector configuration comparison

Figure 11 - Injection section top view

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Figure 12 - Injection section tangential ports and spark plug

The center section was mounted to a stand, hence supporting the ignition and measurement

sections. The disc cartridges were mounted by sliding them into the center section, and secured

with radial bolts at the cartridge ends, Figure 13.

Figure 13 - Center section with cartridge, end-view

The last section of the tube held equally-spaced pressure sensors (<1 µs rise time) connected to

a signal conditioning unit, which ultimately sent a voltage to a digital acquisition system capable

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of sampling at 1.25 MHz. The DAQ was connected to a computer running Labview. Water cooling

adaptors for the pressure sensors were available but not required, as the tube had sufficient time

between firings to cool-down. Figure 8 shows the four sensors spaced 3.000 inches from each

other, used to measure wave speed. A block diagram of the entire setup is shown in Figure 14.

Figure 14 - Equipment block diagram

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2.3 Equipment description

Several aspects of the entire setup were considered. The most important being safety, as the tube

should be able to withstand the pressure of detonation. To evaluate the mechanical requirements

of the tube, the worst case scenario was calculated. Using NASA’s online Chemical Equilibrium

Analysis (CEA) program, the following scenario was considered: for detonation using pure oxygen

and propane from atmospheric starting conditions, the wave Mach number is 7.63. The pressure

ratio is 31.22, which translates to 459 psia. The tube, flanges, gaskets and check valves were

selected with this value (and an additional safety margin) in mind. Figure 15 shows the assembled

test stand.

Figure 15 - Complete test setup

The following is a brief description of the test setup, grouped by electrical, hardware and control

systems.

2.3.1 Electrical equipment description

Pressure sensors

The sensors used were PCB pressure transducers model 111A24. Maximum measurement

range is 2,000 psi. Maximum pressure is 10,000 psi. They can withstand flash temperatures up to

10,000 °F. Maximum continuous temperature is 275 °F . Each sensor had a NIST calibration

certificate, showing its output voltage vs. pressure trend. They have a linear relationship of 5.0

mV per psi.

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The sensors use a fairly complicated mounting scheme, requiring a custom multiple-section

mounting boss. This mount was machined and later welded to the final section of the tube. A soft-

metal (brass) sealing washer was used between the sensor and the mounting boss. The sensor

chassis is not electrically-isolated. The sensors require a constant current source, making them

insensitive to any resistance and / or voltage drop in the cables. The signal output is AC-coupled.

Signal conditioner

The signal conditioner is a PCB 482C15 unit. It supports up to 4-channels (sensors) with

individually adjustable gains. The signal conditioner provides a constant current source as

required by the sensors. The conditioner included a NIST calibration certificate. The default

current is set to 4 mA. The conditioner output is also AC-coupled.

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.

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Figure 16 - DAQ with quick-disconnect harness

Power supply

An adjustable 3-15 VDC 40 A 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 13.8 VDC), used for

testing. A digital display on the unit’s front panel shows the output voltage and instant current

draw.

Injector valves

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.

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Oscilloscope

A Tektronix DPO3032, 300MHz 2-channel oscilloscope was used to compare and verify the

DAQ-acquired data. This unit is capable of sampling up to 2.5 GS/s, with an analog bandwidth of

300 MHz. The scope-supplied 10x probes were used during testing. The unit’s trigger line was

connected to the DAQ igniter signal.

Wiring

Special care was taken to minimize electrical noise as much as possible. Grounding techniques

were in accordance with the DAQ manual, which extensively warns about ground loops. Shielded

wiring was used whenever possible, especially for the signal and control lines from and to the

DAQ. All cable shields were connected to ground on one end only. In order to avoid any

asymmetrical signal delays due to capacitance, inductance, or other wiring-induced effect, equal-

length cables were used from the DAQ to the signal conditioner and to the pressure sensors. For

safety reasons, wire length was sufficient to allow the DAQ and computer to be located in a

separate room.

The cable running from the pressure-sensors to the signal conditioner was a low noise, PCB-

brand shielded coaxial cable. The required BNC connectors were pre-installed on the cable. From

the conditioner to the DAQ, individually-shielded twisted-pair BELDEN-brand stranded cable was

used. Similar cable was used for the signal lines from the DAQ to igniter and injector driver box.

Oversized 3x10 AWG cable was used to connect the power supply to the igniter and injector

driver box. Two lines carried the required 13.8 VDC to both devices, while the third line was used

to ground the tube and its stand directly.

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

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module is of the ‘dumb’ type: i.e. coil charge time was directly controlled by the DAQ. A wire-

wound noise suppression cable was used to connect the coil to the spark plug.

Spark plug

The spark plug used for all experiments is a modified NGK JR10B unit, normally used on sport-

bike engines, Figure 17. The ground electrode was removed to maximize its gap, thus exposing a

larger amount of fuel/air mixture to the spark. This also increases the amount of energy released

to the gas, provided the coil remains capable of creating a high enough voltage for the arc to

occur. The spark plug temperature range is among the lowest manufactured by NGK. This means

that heat conduction from the spark plug tip to the spark plug body is higher compared to a

regular plug. A cooler plug prevents it from becoming an auto-ignition hotspot.

Figure 17 - Modified spark plug

2.3.2 Hardware description

Tube

The tube was of seamless construction, nominal size 4 inches, schedule 80, conforming to ASTM

A106 Grade B (material properties) and ASME B31.1 pressure piping standards. The tube

manufacturer is Zeleziarne Podbrezova (Slovak Republic - http://www.zelpo.sk). The tube

characteristics are shown in Table 2.

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Table 2 - Tube characteristics

Nom. ID, inches 4.0 Outer diameter, inches 4.500

Wall thickness, min., inches 0.295 Wall thickness, nominal, inches 0.337

Working pressure PSI (ambient T) 2,300 Yield strength, min, PSI 35,000

Burst pressure PSI (ambient T) 9,000 Tensile strength, min, PSI 60,000

Flanges

The flanges were socket-weld, class 300, conforming to ASTM A105 (material properties) and

ASME B16.5 flange and fittings standard. The strength characteristics are presented in Table 3.

Table 3 - Flange characteristics

Tensile strength, min, PSI 70,000

Yield strength, min, PSI 36,000

ASME B16.5 lists the working pressure for this flange as 740 psi at temperatures below 38°C,

dropping to 635 psi at 200°C. No burst pressures ar e specified. The flanges have the lowest

pressure rating in the whole assembly. A TIG machine was used to weld the flanges to the tube

sections with the appropriate filler rod.

Bolts and nuts

Bolts were selected in accordance with ASTM A193 standards for class 300 flanges, which

specify grade 5 bolts. Nuts were selected in accordance with the corresponding ASTM A194

standard. Flange bolts were torqued down to 257 ft-lbs, also in accordance with standard

practices.

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Flange gasket

The gasket had a stainless steel wire wound spiral with pure graphite filler construction. It’s able

to withstand up to 850 °F. The gasket outer dimensi ons allowed it to self-center once located

between two flanges.

Injection pipe and check valves

Tangentially-mounted pipes were used to inject the gas into the main tube. Each pipe was 1.25”

OD x 0.5” ID x 6” long. Material is drawn-over-mandrel C 1020 steel. Tensile and yield strengths

are 80,000 and 70,000 psi, better than the main tube and flanges. Each injection pipe had a

check valve installed. Parker valves 8M-C8L-1-B capable of withstanding 3000psi backpressure

were used. They open with only 1psi forward-pressure. The valve fluorocarbon seal is rated for

up to 400°F continuous service.

DDT cartridge

Obstacle discs were laser-cut from 1018 mild steel plate in two thicknesses (½ and ¼ inch thick)

and with blockage ratios of 30, 45, 60 and 75 as defined in Figure 4. The discs had a sliding fit

with the tube center section. The thicker discs were used at the ends of the cartridge for securing

the cartridge to the tube. Six radially-mounted ¼-inch grade 9 bolts were used on each end disc

to fasten the cartridge to the tube. The thinner discs were used to assemble the rest (center) of

the cartridge. Discs were mounted to high-strength grade B16 threaded rods using grade 8 nuts.

The one-piece disc cartridge was able to withstand the effects of combustion much better

compared to previous studies using wire-spirals.

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Figure 18 - Cartridges and discs

Injector valves block

The injector valves were mounted to a block of aluminum bolted on top of the test stand. The

aluminum block was previously machined so the proper ports required to mount the injectors

were ready. Fuel and oxidizer supply lines were connected to the valve inlet ports, Figure 19

Figure 19 - Injector valves block

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Test stand

The test stand was also fabricated for this project. Square-section tubing was cut, MIG-welded

and then prepped and painted before securing all the equipment to it.

LPG/air supply

A commercial LPG gas tank was procured for testing. Since LPG composition varies depending

on the origin, the manufacturer MSDS specifies a range of its composition. Table 4 shows the

specified gas composition. In order to control gas pressure (for both oxidizer and LPG), an

adjustable single-stage pressure regulator was used on each line feeding the injector valve block.

A flame arrestor valve was used at the exit of the LPG pressure regulator for extra safety.

Pressurized air was used from the test facility off-site compressor.

Table 4 - LPG composition

Component Percentage

Propane 87.5-100

Ethane 0-7.0

Propylene 0-5.0

Butanes 0-2.5

Ethyl Mercaptan 0-50 ppm

2.3.3 Control system description

The entire system is controlled by the DAQ. The written Labview software is a fully customizable

code allowing the user to select and/or change all experiment parameters such as L, injector duty

cycle, sampling period, pre and post injection delays, fill rate and others. The required constants

are coded in the Labview routine, but they can be easily changed if needed. Constants include

injector mass flow vs. inlet pressure vs. opening time equations, tube geometry (volume) and

density and stoichiometric ratios for fuel and oxidizer.

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Figure 20 - Labview graphical user interface (GUI)

For each run, specific parameters were selected using the program GUI. These include purge and

fill percentage, L (inverse of equivalence ratio), pre- and post-injection delays, fuel valve injection

period, igniter charge time and DAQ sampling frequency and period. Two ON/OFF buttons allow

the user to independently control either igniter, fuel valve or both for troubleshooting or to carry out

extended purge runs. Figure 20 shows the graphical interface.

When the program is executed, the DAQ triggers the different devices with the appropriate timing

to achieve the desired L, mixing delay, and sampling period. The code has three separate

subroutines; all of them run in parallel once the program starts. The first subroutine calculates the

injection parameters and triggers the injection valves accordingly. The second subroutine controls

the ignition system. The final subroutine contains the sampling code.

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The first subroutine calculates timing for the injection valves. Based on the user inputs, the code

starts by calculating the total mass of fuel and oxidizer to be injected to achieve the desired fill

rate and L. Oxidizer total mass includes purging and fuel-mixing mass. Based on the oxidizer

pressure line input, the required oxidizer mass is translated to an equivalent injection period. The

fuel mass injected per fuel injection period (a user input) is calculated as well. The total fuel mass

is divided by the mass injected per fuel injection, and the resultant is the number of pulses that

the fuel injector must be triggered for. To calculate timing between each fuel injection pulse (low-

time), the code divides the oxidizer valve time (minus purge time) by number of fuel pulses. The

resultant specifies the total time pert fuel injection cycle (including high and low-time). Finally,

timing for the initial fuel pulse is established so that both fuel and oxidizer valves close

simultaneously after total mass has been injected.

After the pre-injection delay has elapsed, the oxidizer valve is opened for the calculated amount

of time. The oxidizer valve initially purges the tube, yet remains open after purging for additional

oxidizer to be mixed with fuel. After the purge period elapses, the fuel valve is pulsed with the

previously calculated frequency and duty cycle. By closing both valves together, a lean-mixture

gas pocket close to the spark plug is avoided.

The second subroutine controls the ignition system. Once the required fuel and oxidizer mass are

injected, the DAQ waits for a specified amount of time (to promote mixing) before triggering the

ignition system. The coil is charged for a specific period (usually 10 ms) in order to saturate its

core, thus maximizing the discharge energy. Once the signal drops, the magnetic field collapses

and the stored energy is discharged into the spark plug. Figure 21 shows a simplified sequence

of the DAQ output lines, where the red line represents the oxidizer valve signal, pink the LPG

valve signal, and blue the igniter output.

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Figure 21 - DAQ output control lines, simplified

The last subroutine contains the code for sampling. The external oscilloscope and this subroutine

are triggered with the rising edge of the coil signal. Once triggered, sampling occurs for the

specified period and frequency. The computer records the data to the hard drive and plots it on

the screen. The oscilloscope also samples for the specified time, and the screen output is saved

to a graphics file for later analysis. Figure 22 shows the complete Labview program / routines.

Figure 23 shows the logic sequence that the routine follows, where the left branch shows the

injection subroutine, the center branch represents ignition, and the right branch the sampling

subroutine.

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Figure 22 - Labview program

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Figure 23 - Labview routine flowchart

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3. Results and analysis

3.1 Data processing methodology

The tube was fired over 600 times: 482 of them being recorded. The recorded pressure signals

represent over 280 MB of raw data. This required a significant amount of time to analyze. The last

three recordings correspond to oxygen tests, which deserve further special attention. Data was

processed using MATLAB. Two separate programs were written to analyze the data. The first

code calculates basic signal parameters and plots the data for each run. The second code

gathers all the calculated parameters from all runs and then plots overall results.

The first code uses a subroutine from National Instruments to read Labview data into Matlab. The

code then calculates the time difference between each sensor signal, the wave speed for each

sensor pair and its average, the signal rise-time, and each channel’s maximum pressure. Finally,

it plots and displays the calculated values on the figure. The appendix contains all 482 graphs.

Figure 24 shows a sample output from the first code.

Due to the nature of the ignition system, electrical noise is generated (and recorded) during the

ignition coil charge and discharge. For each recorded dataset, the initial 14 ms corresponding to

ignition system noise are deleted. The code then calculates pressure from the voltage data. The

next step is to locate the maximum pressure point for each channel. The code zooms-in to 0.5 ms

before and 1 ms after the earliest maximum pressure point. For each channel, the script then

locates the point where pressure starts to rise. The criteria for locating the rise point is to search

for either the first sample with a value of at least 25% of the channel’s maximum pressure value,

or the first sample to exceed a pre-established pressure level. The time difference between the

rise point and maximum pressure location is calculated and displayed as TR for each channel on

the graph. This indicator is closely related to the pressure spike local first derivative. It is a

numerical indicator of the pressure spike shape. To calculate wave speed, the code uses the time

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7

4

4

Pre

ssure

(p

sig

)

Pre

ssure

(p

sig

)

difference between the (previously located) rise points. A speed average is finally calculated and

displayed along with the other parameters on the graph.

100

90

Sens or 1

Sens or 2

Sens or 3

12 Speed: (m /s )

1-2: 865.2

2-3: 865.2

3-4: 924.9

Sens or 1

Sens or 2

Sens or 3

Speed: (m /s )

1-2: Inf

2-3: Inf

3-4: Inf

80 Sens or 4

70

60

50

Avg: 885.1 T

R 1(us ): 8.5

TR

2(us ): 22.

T 3(us ): 11. R

T 4(us ): 11. R

Max P1: 93.6

Max P2: 93.1

Max P3: 91.2

Max P4: 95.3

10 Sens or 4

8

6

Avg: Inf T

R 1(us ): 497.2

TR

2(us ): 565.3 T 3(us ): 747.2

R

T 4(us ): 704.5 R

Max P1: 11.1

Max P2: 11.2

Max P3: 11.1

Max P4: 10.7

40

4 30

20

2

10

0

33.4 33.6 33.8 34 34.2 34.4 34.6

Time (ms)

0

43.2 43.4 43.6 43.8 44 44.2 44.4

Time (ms)

Figure 24 - Matlab sample output graphs

Once all 482 datasets were analyzed, the second code gathered the calculated data from each

run. It then plotted distribution graphs for average maximum pressure, speed and rise time

values. It also produced 3-D contour maps for pressure, speed and rise time.

Visual inspection of the plots revealed two very distinctive groups. One group had a low rise time

showing an abrupt pressure spike (Figure 24 – left), while a second group showed high rise times

and a gradual, oscillating pressure increase (Figure 24 – right). A sharp spike can be associated

with supersonic flow, while a gradual pressure increase corresponds to a subsonic perturbation.

The base line configuration (empty tube) pressure change, if any, was too small to be detected

from the sensors background noise: a flat line was recorded by all four sensors.

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3.2 Numerical results

This initial analysis identifies those runs with the best performance: maximum speed, pressure

and lowest TR. Table 5 presents the top three samples for each category.

Table 5 - Best performance runs

Maximum speed

Cartridge config Speed avg

(m/s)

TR avg

(µs)

P avg

(psig)

d

s

BR

L

Fill %

24 904.4 12.1 94.3 14 3 45 1.4 120

24 885.1 13.5 93.3 14 3 45 1.4 120

24 875.5 11.4 86.0 14 3 45 1.4 100

Maximum pressure

Cartridge config Speed avg

(m/s)

TR avg

(µs)

P avg

(psig)

d

s

BR

L

Fill %

24 904.4 12.1 94.3 14 3 45 1.4 120

24 885.1 13.5 93.3 14 3 45 1.4 120

21 725.3 266.3 91.5 7 6 60 1.3 150

Lowest TR

Cartridge config Speed avg

(m/s)

TR avg

(µs)

P avg

(psig)

d

s

BR

L

Fill %

23 759.7 9.2 61.8 14 2 60 1.6 120

15 797.3 9.9 80.5 14 3 60 1.6 120

23 759.3 9.9 62.1 14 2 60 1.2 120

The highest speed and pressure were both obtained on the same run using cartridge 24: 14 discs

with BR of 45, spacing of 3 inches and L equal 1.4. For the best (lowest) TR, a slightly different

combination is required: 14 discs at either 2 or 3 inches spacing, but with BR of 60. Equivalence

ratio (L) does not appear to be closer to a single value, as the top two observations had L=1.6

and the third L=1.2. For pressure and speed, L=1.4 seems to be the optimum. Lean mixtures are

known to have faster flame speeds, and the experiment results match accordingly. Higher fill

volumes seem to support better performance overall. The pressure plot for best pressure and

speed is shown in Figure 25 – left. The pressure plot for best TR is in Figure 25 – right.

Page 50: Design and Optimization of a Deflagration to Detonation ...

40

)

g i s p (

e r u s s e r P

Pre

ssure

(p

sig

)

70

Sens or 1

Sens or 2

Speed: (m /s )

1-2: 745.1

2-3: 745.1

100 Sens or 1

Sens or 2

Speed: (m /s )

1-2: 894.1

2-3: 894.1

60 Sens or 3

Sens or 4

50

40

30

3-4: 788.9

Avg: 759.7 T

R 1(us ): 11.4

TR

2(us ): 8.5 T 3(us ): 8.5

R

T 4(us ): 8.5 R

Max P1: 68.7

Max P2: 58.6

Max P3: 63.3

Max P4: 56.7

Sens or 3

80 Sens or 4

60

40

3-4: 924.9

Avg: 904.4 T

R 1(us ): 5.7

TR

2(us ): 22.7 T 3(us ): 8.5

R

T 4(us ): 11.4 R

Max P1: 94.0

Max P2: 93.7

Max P3: 93.5

Max P4: 95.9

20

20

10

0 0

-10

29 29.2 29.4 29.6 29.8 30 30.2 30.4

Time (ms)

-20 32.4 32.6 32.8 33 33.2 33.4 33.6 33.8

Time (ms)

Figure 25 - Best performance plots

Using CEA and LPG composition from Table 4, the calculated pressure ratio for detonation is

18.265 (254 psig) and wave speed is 1,798 m/s. The best experimental results were able to reach

50.3% detonation speed and 37.1% detonation pressure. The flame is supersonic in the

upstream frame of reference at Mach 2.66, and high-subsonic (Mach 0.96) in the downstream

frame of reference. When compared to isentropic normal shock relations a pressure ratio of 8.04

is calculated: within 8% of the 7.4 measured ratio.

These results correspond to the fast flame regime. It is known that the flame front can transition

to detonation once the sonic downstream conditions are attained. Here, the flame reached 96%

of said conditions. Several reasons for not achieving detonation are possible and will be

discussed in the following sections.

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41

3.3 Regression model

To statistically analyze the experiment data, a multi-variable second-degree regression model

using the least-squares method was created. The model tries to explain average pressure, rise

time or wave speed using the following input variables: total discs, disc spacing, BR, L and fill

percentage. Due to the non-linear behavior of these variables, a second-degree polynomial was

assumed for all five variables. This requires extra data for the model, namely the square of each

variable input data. The resulting model is expressed by equation 3.1.

= a2 + a + c2 + c + 2 + + 2 + + F2 + kF + onct nt (3.1) Where:

y Parameter to be estimated: pressure, TR or wave speed

d Total number of discs

s Disc spacing

BR Blockage ratio

L Inverse of equivalence ratio

F Fill percentage

a,b,c,e,f,g,h,I,j,k Variable coefficients, to be determined by the regression model

Several models were created, but all of them have a low adjusted determination coefficient R2

and / or have variable coefficients that cannot reject the null hypothesis. The model with the

highest R2

is shown in

Table 6.

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42

Table 6 - Pressure regression model results

Average Pressure

Regression Statistics

Multiple R 0.765

R Square 0.586

Adjusted R

Square 0.577

Standard Error 13.280

Observations 479

ANOVA

df SS MS F Significance F

Regression 10 116625.578 11662.558 66.125 0.000

Residual 468 82541.925 176.372

Total 478 199167.503

Coefficients Standard

t Stat P-value Lower 95% Upper 95% Error

Constant -238.733 23.012 -10.374 0.000% -283.952 -193.513

d 4.157 1.195 3.479 0.055% 1.809 6.505

d2

-0.036 0.066 -0.539 59.031% -0.166 0.095

s 1.419 2.743 0.517 60.520% -3.971 6.809

s2

0.217 0.331 0.657 51.143% -0.433 0.868

BR 0.257 0.231 1.113 26.614% -0.197 0.710

BR2

0.000 0.002 -0.026 97.926% -0.005 0.004

L 230.829 29.323 7.872 0.000% 173.207 288.451

L2

-86.339 10.013 -8.622 0.000% -106.016 -66.663

F 1.170 0.258 4.537 0.001% 0.663 1.676

F2

-0.004 0.001 -3.165 0.165% -0.007 -0.002

With an adjusted R2

value of 0.577, this model can only explain 57.7% of pressure behavior.

Analyzing the p-values, the coefficients for d2, s, s

2, BR and BR

2 cannot be statistically proven

with a 95% confidence level to be different than zero. The corresponding optimum values are

either negative or simply impossible (for example, BR of 2130%). Nevertheless, some useful data

from the model can be extracted by calculating the suggested optimum values for L: 1.336 and

for F: 140.9%. The calculated L-value matches the maximums observed during testing. Although

Page 53: Design and Optimization of a Deflagration to Detonation ...

43

Perc

enta

ge o

f observ

ations

Num

ber

of

observ

ations

fill rates of 140% weren’t tested, better performance was attained at higher fill rates, which agrees

qualitatively with the regression model.

Due to the low R2

value, model predictions or extrapolations cannot be considered accurate. This

mathematical model expresses the irregularity of collected data. Even though testing conditions

were kept as constant as possible, pressure and speed values have a high degree of variability

that is unaccounted for.

3.4 Analysis

Distribution plots were obtained to get an idea of data behavior. Three plots showing a histogram

and cumulative distribution for each one of the main variables are shown in Figure 26, Figure 27

and Figure 28.

Average pressure histogram

60

40

20

0

100

0 10 20 30 40 50 60 70 80 90 100

Average pressure (psig)

Cumulative distribution

50

0 0 10 20 30 40 50 60 70 80 90 100

Average pressure (psig)

Figure 26 - Average pressure histogram

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44

Perc

enta

ge o

f observ

ations

Num

ber

of

observ

ations

The average pressure histogram shows a slightly right-skewed distribution. Mean value is 34.41

psig and median is 31.60 psig. The cumulative plot shows a smooth curve, in accordance with the

distribution histogram. Changes to the cartridge configuration will affect average pressure

gradually. As long as the cartridge configuration is near the ‘sweet spot’, slight cartridge

deviations will not change pressure significantly.

200 Average speed histogram

150

100

50

0

100

0 100 200 300 400 500 600 700 800 900

Average speed (m/s)

Cumulative distribution

50

0 0 100 200 300 400 500 600 700 800 900

Average speed (m/s)

Figure 27 - Average speed histogram

The average speed histogram shows a different pattern than the pressure histogram. Average

speed calculations are set to zero if a valid rise point cannot be detected or if they happen at the

same location. This occurred on slow deflagrations that don’t have a clear, sharp pressure spike.

Therefore, a significant number of observations (~40%) fall within the first bin of speeds between

zero and ~30 m/s. A clear gap exists between samples for which a valid average speed cannot

Page 55: Design and Optimization of a Deflagration to Detonation ...

45

Perc

enta

ge

of

observ

ations

Num

ber

of

observ

ations

be calculated and the rest. The remaining 60% show a bell-shaped distribution, with a slight right-

hand skewness. Median speed is 570.9 m/s; mean speed is 405.7 m/s. Looking at the bell-

shaped distribution section, the right skewness (as in the pressure histogram) allows some

flexibility regarding deviations from the ideal cartridge configuration.

100 Rise time histogram

50

0

100

0 200 400 600 800 1000 1200

Rise time (us)

Cumulative distribution

50

0 0 200 400 600 800 1000 1200

Rise time (us)

Figure 28 - Average TR histogram

The rise time histogram shows two groups, one centered on the origin and another around 550

µs. Mean value is 326.2 µs, and median is 315.3 µs. The (ideal) first bin has 100 observations,

while the second bin drops sharply to 30 events. The cumulative distribution show that roughly

20% of all samples fall into the first bin. The higher TR group represents slow-deflagrations.

Unlike the previous two distributions, the cartridge needs to be close to the ideal configuration in

Page 56: Design and Optimization of a Deflagration to Detonation ...

46

order to obtain a low TR value. The function becomes relatively insensitive between 100 and 400

µs, just below the point where most deflagrations start to occur.

After analyzing the histograms, contour plots can be used to determine what the optimum

configuration(s) is (are). The following figures show different relationships between the main

variables, by plotting pressure, speed or rise time vs. two other variables, holding everything else

constant.

Figure 29 - Average pressure vs. BR vs. L

Page 57: Design and Optimization of a Deflagration to Detonation ...

47

Avera

ge p

ressure

(psig

)

Figure 30 - Average pressure vs. BR vs. d

Avg pressure vs. L vs. disc spacing - All data 70

d=14 s=3

d=14 s=2

60 d=10 s=4.5 d=7 s=6

d=8 s=3

50 d=5 s=4.5

d=5 s=6

40

30

20

10 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

L

Figure 31 - Average pressure vs. L vs. disc spacing

Page 58: Design and Optimization of a Deflagration to Detonation ...

48

Figure 32 - Average speed vs. BR vs. L

Figure 33 - Average speed vs. BR vs. number of discs

Page 59: Design and Optimization of a Deflagration to Detonation ...

49

Avg

speed

(m

/s)

800

700

600

500

Avg speed vs. L vs. disc spacing - All data

d=14 s=3

d=14 s=2

d=10 s=4.5

d=7 s=6

d=8 s=3

d=5 s=4.5

d=5 s=6

400

300

200

100

0 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

L

Figure 34 - Average speed vs. L vs. disc spacing

Figure 35 - Rise time vs. BR vs. L

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50

Ris

e tim

e (

us)

Figure 36 - Rise time vs. BR vs. number of discs

900

800

700

600

500

Rise time vs. L vs. disc spacing - All data

d=14 s=3

d=14 s=2

d=10 s=4.5

d=7 s=6

d=8 s=3

d=5 s=4.5

d=5 s=6

400

300

200

100

0 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

L

Figure 37 - Rise time vs. L vs. disc spacing

Page 61: Design and Optimization of a Deflagration to Detonation ...

51

From the previous nine figures, an optimum configuration for each main variable can be obtained.

Table 7 summarizes the ideal configurations for each main variable.

Table 7 - Ideal cartridge parameters

Main variable to be optimized

Avg max pressure Avg max speed Avg TR

BR 45-60 45 45 to 70

L 1.4 1.4 1.4

s 3 3 3

Number of discs 14 14 14

For average maximum pressure, the function seems to be more sensitive to L variations than BR

(Figure 29). At the same time, gradient is higher for BR than number of discs (Figure 30). From

Figure 31, it can be observed that cartridges with a higher number of discs obtain the highest

pressure levels, and are more sensitive to variations in L than cartridges with lower disc density.

For average maximum speed, the function seems much more sensitive to L changes than BR

(Figure 32). Similar to the maximum pressure case, speed is more sensitive to number of discs

than changes in BR (Figure 33). Note that a significant change occurs when discs drop below 8 (it

should be noted that number of discs is also related to disc spacing). Looking at Figure 34, it is

observed that high disc-density cartridges (with low disc spacing) obtain the highest speeds, and

are more sensitive to L than disc spacing. Lower disc-density cartridges seem as sensitive to L as

high-density configurations, but obtain much lower speeds.

From Figure 35, TR appears to be largely insensitive to BR changes between 45 and 75

compared to L. However, it’s more sensitive to BR than number of discs, as long as 8 or more

discs are used (Figure 36). Finally, Figure 37 shows that TR seems to be most insensitive to disc

spacing; a low-disc-density cartridge (d=5 s=4.5) obtained TR’s comparable to two high-density

cartridges (d=14 s=2 and d=10 s=4.5).

Page 62: Design and Optimization of a Deflagration to Detonation ...

52

Although detonation was not achieved, there appears to be an optimum cartridge configuration

able to obtain better readings when compared to other configurations. For average pressure and

speed, the configuration can be considered the same. Rise time shows a slight variation

regarding the ideal BR, although the other three parameters L, s and number of discs are

consistent with the previous numerical results.

Overall, it can be said that in order of importance, the most significant parameter is gas mixture

composition L, followed by BR, number of discs, and finally disc spacing. As long as all

parameters are close to their optimum, small deviations in pressure, speed and rise time will

occur. If one or more parameter deviate significantly, pressure, speed and / or TR performance

will be severely degraded. For this paper, the ideal cartridge must have BR 60, using 8 or more

discs with 3-inch spacing.

Reasons for not achieving detonation can be several, including incorrect cartridge configuration,

incomplete fuel/oxidizer mixing, or a longer DDT section is required.

Analyzing the cartridge configuration, the unrestricted core diameter for a disc with the highest

BR of 75 is 47.6 mm. For propane, λ is close to 51 mm [9]. Although it’s possible that BR 70 discs

were restricting the propagation of a complete detonation cell, tests with lower BR’s showed

better speed and pressure characteristics. At BR 60, the unrestricted core diameter is 61.0 mm,

enough for detonation to propagate. The same argument is valid for discs with an even larger

core diameter (i.e. lower BR).

The second reason involves the injection procedure. In order to achieve the appropriate

equivalence ratio, fuel injection was pulsed into the tube while the oxidizer injector was held open.

This creates alternating fuel-rich and lean pockets, where gas speed and turbulence is expected

to help complete mixing. CFD-results show that with the given tube geometry and mass flow,

Page 63: Design and Optimization of a Deflagration to Detonation ...

53

mixing should not be a concern. A risky alternative would be pre-mixing. Any connection

mechanism between the main tube and pre-mixing chamber will need to be flame-proof.

The third reason is perhaps the most reasonable: the maximum obtained speed falls short of that

required to transition within the tube length and cartridge configuration. With the modular design

of the test setup, the center tube section could be easily replaced or a second DDT section added

to verify this allegation.

3.5 Oxygen testing results

After testing all cartridges with fuel/air mixtures, pure oxygen was used to verify the equipment

capabilities. Pressure levels were over 10 times higher when detonation was finally achieved,

confirmed by the corresponding wave speed. Figure 38 shows the results for oxygen testing. On

the right, the graphs correspond to a cartridge with BR 30, 6-inch disc spacing, 4 discs total.

Results for an empty tube are shown on the left. The top figures were recorded by the DAQ while

the bottom figures were recorded with an oscilloscope.

Page 64: Design and Optimization of a Deflagration to Detonation ...

54

Pre

ssure

(p

sig

)

Pre

ssure

(p

sig

)

1000 Sens or 1

Sens or 2

Sens or 3

Speed: (m /s )

1-2: 2980.3

2-3: 2980.3

3-4: 2438.4

600

500

Sens or 1

Sens or 2

Sens or 3

Speed: (m /s )

1-2: 2438.4

2-3: 1915.9

3-4: 1915.9

800 Sens or 4

600

400

Avg: 2799.6 T

R 1(us ): 2.8

TR

2(us ): 2.8 T 3(us ): 2.8

R

T 4(us ): 2.8 R

Max P1: 970.9

Max P2: 962.4

Max P3: 768.5

Max P4: 561.3

400

300

200

Sens or 4

Avg: 2090.1 T

R 1(us ): 0.0

TR

2(us ): 0.0 T 3(us ): 42.6

R

T 4(us ): 8.5 R

Max P1: 552.8

Max P2: 574.1

Max P3: 312.0

Max P4: 252.9

200

100

0

0

-200

35.6 35.8 36 36.2 36.4 36.6 36.8 37

Time (ms)

-100 41 41.2 41.4 41.6 41.8 42 42.2 42.4

Time (ms)

Figure 38 - Oxygen testing results

The use of pure oxygen resulted in much higher speeds (2799.6 m/s) compared to LPG/air

(maximum reached of 904 m/s). A pressure increase of roughly tenfold was achieved with

oxygen: a maximum of 970.9 psig was recorded vs. a peak of 98.3 psig with air.

Using CEA, LPG / pure oxygen detonation predicts a wave speed of 2,357 m/s and pressure ratio

of 36.1. For the empty-tube case (left), a wave speed of 2,799.6 m/s was recorded. Average

pressure ratio was 56.5. It’s interesting to note that the pressure region is very thin, as pressure

drops almost to zero by the time it reaches the next pressure sensor. This may indicate a

decoupled wave, as pressure downstream of the wave should remain higher than initial

conditions. Experiments from other research facilities have observed transitioning initially

Page 65: Design and Optimization of a Deflagration to Detonation ...

55

produces over-driven waves before reaching CJ conditions. An over-driven wave is not

considered to be stable, so additional equipment is required to determine its behavior. Current

equipment does not allow for additional measurements up- or downstream of the tube, which

would help determine if the wave was stabilizing towards CJ conditions.

For the obstacle case (right), wave speed (2,090 m/s) was closer to CJ conditions (2,357 m/s).

Pressure ratio was also closer at 29.77 (CJ 36.1). Deviations from CJ-values are small (11%

lower speed and 17% lower pressure ratio), which would indicate a slightly under-driven wave

was established. The variations are comparable to other detonation studies. Downstream of the

wave, pressure levels of around 100 psig were recorded. Short rise times were also present; both

are typical characteristics of detonation waves.

DAQ verification

To verify the DAQ measurement capabilities, a comparison with an oscilloscope was made. For

the empty tube case, the oscilloscope shows a time difference between channels 1 and 4 of

82.24000µs. Using this value, a speed of 2779.7 m/s is calculated. The value obtained using the

DAQ / Matlab routine is 0.7% higher. Using the same procedure for the empty tube case, the

DAQ value is found to be within 3% of the oscilloscope value. The oscilloscope has a higher

accuracy due to its sampling rate of 5 MHz per channel (vs. 352 KHz per channel for the DAQ).

Although the DAQ is sampling at its maximum frequency, the values obtained are very close to

those obtained by the higher-accuracy oscilloscope. Slower flames accuracy (LPG / air) shouldn’t

be a concern either.

3.6 Testing observations

Signal clipping / signal conditioner output impedance

While testing with oxygen, the signal conditioner output voltage was found to be ‘clipping’ at

roughly 5 volts (1,000 psi). Clipping means the pressure measurement reaches hardware limits.

Further testing showed the pressure sensor output presented no signs of clipping, while clipping

Page 66: Design and Optimization of a Deflagration to Detonation ...

56

existed at the signal conditioner output. Wave speed is calculated based on the time difference

between pressure rise points (and not the peak values), so speed calculation is not affected.

PCB was contacted for advice, and the conditioner was sent back for diagnosis. PCB didn’t find

any problems with the unit. They did notice the signal would clip when connected to a 50 ohm

output impedance load. Some discrepancy exists as to the proper conditioner output impedance.

The conditioner manual specifies 50-ohms output impedance, while emails from PCB suggested

a high-impedance load should be used. The issue was never fully cleared by PCB. The test setup

used a 50 ohm resistor in parallel with the DAQ (with an internal impedance greater than 1 Gohm

– i.e. negligible) to comply with the unit’s manual specs. For this application, an impedance

mismatch would result in pressure scaling being off. The recorded peak pressure values should

be considered accordingly. Another undesirable result of impedance mismatch would be the

introduction of a delay in the pressure signal. If any delay was introduced, it would be applied

equally to all channels. This would effectively cancel out any influence on wave speed calculation.

As PCB was never completely clear regarding the output impedance of the signal conditioner, a

comparison test with a known calibrated pressure sensor should be carried out. For the present

study, an off-scale pressure reading will not affect the speed calculations. However, validated

pressure data would allow verification beyond that of flame speed. A comparison of pressure ratio

and isentropic normal shock characteristics would be the prime candidate. It was noted during

testing that pressure values seemed to match normal shock characteristics.

If scaling is confirmed to be accurate without the 50-ohm impedance-matching resistor, an AC-

coupled digitizer or multiple-channel oscilloscope should be used. Since the DAQ is DC-coupled,

the resistor kept the conditioner signal not only within the DAQ voltage limits (+/- 10V), but it also

stabilized the output signal at zero volts with respect to ground. The signal conditioner output

voltage drifts considerably without a resistor.

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57

A different measurement option would be to monitor the pressure sensor output directly. This

would bypass the signal conditioner signal circuitry. The conditioner would then only operate as a

power supply for the sensors. The signal conditioner gain feature would be lost. For this scenario,

AC-coupled equipment would be a must.

Air-fuel ratio accuracy

When stoichiometric conditions were called for, the resulting mixture appeared to be ‘rich’, based

on excessive gas smell and ignitability issues. Although a gas analyzer (or oxygen sensor) was

not available during testing, troubleshooting showed that once the oxidizer injector opened, line

pressure dropped. This indicates mass flow was restricted. Attempts were made to increase or

keep pressure constant, but were unsuccessful. Bigger oxidizer lines may help with this issue, as

the off-site air compressor should be able to deliver the required mass flow. For this reason, the

mixture parameter L should be treated accordingly. Nevertheless, it remains an effective tool to

alter the actual equivalence ratio.

Oxygen cartridge deformation

Oxygen-testing showed much higher pressures than LPG / air mixtures. After obstacle-testing

with oxygen, discs were found to be bent. Discs with BR 30 were the only ones tested with

oxygen. Figure 39 shows the discs after removal. Further testing with oxygen will require thicker

discs, similar to the cartridge end-discs.

Figure 39 - Discs after oxygen testing (bent)

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58

Others

During initial fuel tests (at 10% fill volume), a blue-colored swirling flame was clearly

observed inside the tube. At higher fill levels flame magnitude and speed didn’t allow for

visual identification. Most experiments were recorded with a camera at 24 frames per second.

At such slow rate, only a single bright frame was obtained. High-speed cameras would allow

identification and measurement of flame propagation (luminescence) characteristics.

The interaction of the chemically reactive gas with the threaded rods supporting the discs is

unknown. Although testing with only 1 disc and all three rods mounted inside the tube

showed no improvement versus any other case, the effect of the rods on the combusting gas

inside the tube should be considered. CFD may be the only available tool to account for the

threaded rods effects.

No significant difference was found between installing half-cartridges at the ignition or

exhaust end. One of the studies from the University of Arlington at Texas (mentioned in

section 1.5) tested whether ignition location was significant to pressure and speed levels.

They concluded that no significant evidence was found when changing ignition location. The

equivalent effect of reversing the half-cartridge inside the tube is that of moving the ignition

within the tube. Therefore, the experiment results match those of the previous paper.

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59

4. Conclusions and recommendations

The experiments were able to achieve the fast flame regimes for LPG and air mixtures. Although

LPG and oxygen mixtures were the only ones able to achieve detonation, pure oxygen limits the

practicality of any device. Continuous efforts should be made towards achieving detonation with

ordinary-fuel and air mixtures.

It is interesting to note that for oxygen mixtures, obstacles hampered wave pressure and speed,

while for air mixtures they greatly increased pressure and speed. This can be interpreted as

supporting evidence that a DDT section depends on the gas mixture being ignited.

All three main variables: peak pressure, maximum speed, and rise time are found to be sensitive

to cartridge configuration, as long as the proper equivalence ratio mixture is supplied.

Statistical evidence suggests the ideal cartridge configuration depends on whether high pressure,

speed or the sharpest pressure spike is desired, see Table 7. A sharper spike was obtained by

using a slightly higher BR.

Future testing should include different fuels and DDT mechanisms. Extending the test section and

mixing different BR discs on a single cartridge could be tested with minimal effort.

The present work not only identifies the most favorable obstacle configuration for the test tube, but

also presents a platform upon which future testing can be performed. Other research facilities

have revealed their intent to explore different geometries such as toroidal or helical DDT sections.

Different flame acceleration devices should be explored while keeping in mind the usefulness and

practicality of them.

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60

References

1. Wintenberger, E., “Application of Steady and Unsteady Detonation Waves to Propulsion”,

California Institute of Technology, Pasadena, CA, 2004

2. Coleman, M.L., “Overview of pulse detonation propulsion technology”, Chemical Propulsion

Information Agency, The John Hopkins University, Baltimore, MD, April 2001

3. Bussing, T., Papas, G., “An introduction to Pulse Detonation Engines”, 32nd

Aerospace

Sciences Meeting and Exhibit, AIAA 94-0623

4. Ciccarelli, G., Dubocage, P., “Flame acceleration in fuel-air mixtures at elevated initial

temperatures”, 38th

AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2002

5. Lee, J., “Initiation of Gaseous Detonation”, Annual Reviews Phys. Chem. Vol. 75, 1977, pp.

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6. Wintenberger, E., Shepherd, J.E., “Thermodynamic Cycle Analysis for Propagating

Detonations”, Graduate Aeronautical Laboratories, California Institute of Technology, 2005

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9. Glossary on Explosion Dynamics”, Explosion Dynamics Laboratory, California Institute of

Technology, Pasadena, CA, URL:

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10. Silvestrini, M., Genova, B., et al. “Flame acceleration and DDT run-up distance for smooth

and obstacles filled tubes” Journal of Loss Prevention in the Process Industries 21. 2008

11. Dick Ng, H., Lee, John H.S., “Comments on explosion problems for hydrogen safety” Journal

of Loss Prevention in the Process Industries 21. 2008

12. Katta, V., Tucker, C., et al. “Initiation of Detonation in a Large Tube” 19th

International

Colloquium on the Dynamics of Explosions and reactive systems. July 2003, Japan.

13. Bellini, R., Lu, F., “Exergy Analysis of a Pulse Detonation Power Device”, Journal of

Propulsion and Power, Vol. 26, No. 4 2010

14. Scragg, R., “Detonation cycle gas turbine engine system having intermittent fuel and air

delivery”, US Patent 6,000,214, Dec 1999

15. Turns, Stephen R. “An introduction to Combustion” 2nd

edition. McGraw-Hill, 2000.

16. Kayushin, L. P. “The influence of external friction and heat exchange on the motion of an

ignition surface and a shock-discontinuity in a chemically reactive medium” Gas Dynamics

and Physics of Combustion. Translated from Russian for the National Science Foundation,

Washington D.C. Jerusalem 1962.

17. Panicker, Phillip K. “The development and testing of pulsed detonation engine ground

demonstrators” The University of Texas at Arlington. 2008

Page 72: Design and Optimization of a Deflagration to Detonation ...

62

18. Chapin, David. “A study of deflagration to detonation transition in a pulsed detonation engine”

Georgia Institute of Technology. 2005

19. Lee, J.H., Knystautas R., Chan C.K., “Turbulent flame propagation in obstacle-filled tubes”

Twentieth symposium on Combustion. 1984

20. Panicker Phillip K., Lu, Frank K., Wilson, Donald R. “Practical methods for reducing the

deflagration-to-detonation transition length for pulse detonation engines”, Aerodynamics

Research Center, University of Texas at Arlington, URL:

http://arc.uta.edu/publications/cp_files/ISAIF9-6C-2.pdf [retrieved 15 February 2011]

Page 73: Design and Optimization of a Deflagration to Detonation ...

63

Appendix

Figure 1 - 01 S3D12+2 BR75_20percL1

Figure 2 - 01 S3D12+2 BR75_40percL1

Figure 3 - 01 S3D12+2 BR75_60percL1

Figure 4 - 01 S3D12+2 BR75_80percL1

51.6 51.8 52 52.2 52.4 52.6 52.80

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psig

)

Speed: (m/s)1-2: 1072.92-3: 670.63-4: 705.9Avg: 816.4T

R 1(us): 497.2

TR 2(us): 585.2

TR 3(us): 483.0

TR 4(us): 548.3

Max P1: 50.2Max P2: 54.6Max P3: 53.1Max P4: 61.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Figure 5 - 01 S3D12+2 BR75_100percL1

Figure 6 - 01 S3D12+2 BR75_120percL1

30.8 31 31.2 31.4 31.6 31.8 32 32.20.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 329.5

TR 2(us): 497.2

TR 3(us): 622.2

TR 4(us): 886.4

Max P1: 1.5Max P2: 1.4Max P3: 1.2Max P4: 1.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.6 29.8 30 30.2 30.4 30.6 30.8-2

0

2

4

6

8

10

12

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 425.82-3: 425.83-4: 447.0Avg: 432.8T

R 1(us): 741.5

TR 2(us): 36.9

TR 3(us): 22.7

TR 4(us): 34.1

Max P1: 10.9Max P2: 11.2Max P3: 9.9Max P4: 11.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.6 37.8 38 38.2 38.4 38.6 38.8 39-5

0

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 558.82-3: 547.43-4: 536.4Avg: 547.5T

R 1(us): 14.2

TR 2(us): 22.7

TR 3(us): 34.1

TR 4(us): 19.9

Max P1: 28.7Max P2: 24.4Max P3: 27.2Max P4: 26.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

45.8 46 46.2 46.4 46.6 46.8 47-5

0

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 623.83-4: 638.6Avg: 628.7T

R 1(us): 11.4

TR 2(us): 480.1

TR 3(us): 392.0

TR 4(us): 500.0

Max P1: 33.3Max P2: 38.4Max P3: 35.9Max P4: 33.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

56.8 57 57.2 57.4 57.6 57.8 580

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1577.82-3: 1031.63-4: 812.8Avg: 1140.7T

R 1(us): 414.8

TR 2(us): 536.9

TR 3(us): 559.7

TR 4(us): 193.2

Max P1: 40.8Max P2: 41.9Max P3: 43.3Max P4: 45.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 74: Design and Optimization of a Deflagration to Detonation ...

64

Figure 7 - 02 S3D12+2 BR75_L=0.9

Figure 8 - 02 S3D12+2 BR75_L=1.1

Figure 9 - 02 S3D12+2 BR75_L=1.2

Figure 10 - 02 S3D12+2 BR75_L=1.3

Figure 11 - 02 S3D12+2 BR75_L=1.4

Figure 12 - 02 S3D12+2 BR75_L=1.5

52.8 53 53.2 53.4 53.6 53.8 54-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 670.63-4: 609.6Avg: 656.0T

R 1(us): 8.5

TR 2(us): 17.0

TR 3(us): 505.7

TR 4(us): 301.1

Max P1: 46.5Max P2: 39.3Max P3: 38.7Max P4: 36.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33 33.2 33.4 33.6 33.8 34 34.2 34.4-5

0

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 525.93-4: 536.4Avg: 544.4T

R 1(us): 11.4

TR 2(us): 17.0

TR 3(us): 31.3

TR 4(us): 14.2

Max P1: 30.1Max P2: 24.0Max P3: 23.7Max P4: 26.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.6 30.8 31 31.2 31.4 31.6 31.8 32-5

0

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 547.42-3: 525.93-4: 506.1Avg: 526.5T

R 1(us): 28.4

TR 2(us): 17.0

TR 3(us): 42.6

TR 4(us): 17.0

Max P1: 29.3Max P2: 22.9Max P3: 19.7Max P4: 25.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.4 29.6 29.8 30 30.2 30.4 30.60

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 515.82-3: 515.83-4: 506.1Avg: 512.6T

R 1(us): 22.7

TR 2(us): 17.0

TR 3(us): 22.7

TR 4(us): 22.7

Max P1: 21.2Max P2: 21.2Max P3: 18.6Max P4: 18.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.4 28.6 28.8 29 29.2 29.4 29.6-5

0

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 515.82-3: 506.13-4: 496.7Avg: 506.2T

R 1(us): 22.7

TR 2(us): 19.9

TR 3(us): 45.5

TR 4(us): 14.2

Max P1: 21.3Max P2: 20.4Max P3: 17.1Max P4: 17.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30 30.2 30.4 30.6 30.8 31 31.2-2

0

2

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 439.72-3: 454.63-4: 462.5Avg: 452.3T

R 1(us): 167.6

TR 2(us): 31.3

TR 3(us): 48.3

TR 4(us): 36.9

Max P1: 12.0Max P2: 12.5Max P3: 11.2Max P4: 12.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 75: Design and Optimization of a Deflagration to Detonation ...

65

Figure 13 - 02 S3D12+2 BR75_L=1.6

Figure 14 - 02 S3D12+2 BR75_L=1.7

Figure 15 - 02 S3D12+2 BR75_L=1.8

Figure 16 - 02 S3D12+2 BR75_L=1

Figure 17 - 02 S3D12+2 BR75_L=2

Figure 18 - 03 S3D6+2 BR75_60percL=0.9

29.6 29.8 30 30.2 30.4 30.6 30.8-4

-2

0

2

4

6

8

10

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 865.22-3: 412.73-4: 419.1Avg: 565.7T

R 1(us): 1224.4

TR 2(us): 593.8

TR 3(us): 548.3

TR 4(us): 42.6

Max P1: 8.3Max P2: 7.8Max P3: 7.8Max P4: 8.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30 30.2 30.4 30.6 30.8 31 31.2 31.40

1

2

3

4

5

6

7

8

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1676.43-4: 425.8Avg: InfT

R 1(us): 812.5

TR 2(us): 497.2

TR 3(us): 1377.8

TR 4(us): 863.6

Max P1: 6.8Max P2: 6.6Max P3: 7.1Max P4: 6.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31 31.2 31.4 31.6 31.8 32 32.2 32.40

0.5

1

1.5

2

2.5

3

3.5

4

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 8940.83-4: 454.6Avg: InfT

R 1(us): 1161.9

TR 2(us): 1241.5

TR 3(us): 1474.4

TR 4(us): 321.0

Max P1: 2.9Max P2: 3.3Max P3: 3.5Max P4: 3.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41.2 41.4 41.6 41.8 42 42.2 42.4 42.6-5

0

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 547.43-4: 547.4Avg: 559.3T

R 1(us): 19.9

TR 2(us): 19.9

TR 3(us): 36.9

TR 4(us): 14.2

Max P1: 30.4Max P2: 26.2Max P3: 28.1Max P4: 29.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.2 34.4 34.6 34.8 35 35.2 35.4 35.6-1

-0.5

0

0.5

1

1.5

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1031.62-3: -1031.63-4: InfAvg: InfT

R 1(us): 323.9

TR 2(us): 423.3

TR 3(us): 761.4

TR 4(us): 59.7

Max P1: 1.0Max P2: 1.5Max P3: 1.1Max P4: 0.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

51 51.2 51.4 51.6 51.8 52 52.20

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 1315.3

TR 2(us): 909.1

TR 3(us): 497.2

TR 4(us): 554.0

Max P1: 18.0Max P2: 21.2Max P3: 17.9Max P4: 15.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 76: Design and Optimization of a Deflagration to Detonation ...

66

Figure 19 - 03 S3D6+2 BR75_60percL=1.2

Figure 20 - 03 S3D6+2 BR75_60percL=1.4

Figure 21 - 03 S3D6+2 BR75_60percL=1.6

Figure 22 - 03 S3D6+2 BR75_60percL=1

Figure 23 - 03 S3D6+2 BR75_80percL=1.2

Figure 24 - 03 S3D6+2 BR75_80percL=1

29.8 30 30.2 30.4 30.6 30.8 31 31.2-5

0

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 558.83-4: 583.1Avg: 570.9T

R 1(us): 17.0

TR 2(us): 19.9

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 29.7Max P2: 24.2Max P3: 24.2Max P4: 22.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.6 32.8 33 33.2 33.4 33.6 33.8 34-5

0

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 525.92-3: 525.93-4: 536.4Avg: 529.4T

R 1(us): 28.4

TR 2(us): 28.4

TR 3(us): 22.7

TR 4(us): 25.6

Max P1: 22.3Max P2: 19.4Max P3: 19.9Max P4: 18.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

40.6 40.8 41 41.2 41.4 41.6 41.8-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 766.43-4: 766.4Avg: 752.5T

R 1(us): 306.8

TR 2(us): 252.8

TR 3(us): 275.6

TR 4(us): 451.7

Max P1: 54.4Max P2: 57.6Max P3: 66.2Max P4: 67.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33 33.2 33.4 33.6 33.8 34 34.2 34.4-5

0

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 596.13-4: 583.1Avg: 591.7T

R 1(us): 17.0

TR 2(us): 14.2

TR 3(us): 17.0

TR 4(us): 17.0

Max P1: 27.0Max P2: 26.4Max P3: 23.1Max P4: 25.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.4 30.6 30.8 31 31.2 31.4 31.6 31.8-5

0

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 596.13-4: 623.8Avg: 614.5T

R 1(us): 19.9

TR 2(us): 19.9

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 36.1Max P2: 31.5Max P3: 31.7Max P4: 29.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

47.8 48 48.2 48.4 48.6 48.8 49-5

0

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 514.2

TR 2(us): 497.2

TR 3(us): 551.1

TR 4(us): 593.8

Max P1: 42.7Max P2: 39.1Max P3: 41.1Max P4: 43.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 77: Design and Optimization of a Deflagration to Detonation ...

67

Figure 25 - 04 S45D8+2 BR75_80percL=0.9

Figure 26 - 04 S45D8+2 BR75_80percL=1.2

Figure 27 - 04 S45D8+2 BR75_80percL=1.4

Figure 28 - 04 S45D8+2 BR75_80percL=1

Figure 29 - 05 baseline tube - empty_80percL=0.9

Figure 30 - 05 baseline tube - empty_80percL=1.2

73 73.2 73.4 73.6 73.8 74 74.2 74.40

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1490.12-3: 1788.23-4: 432.6Avg: 1237.0T

R 1(us): 514.2

TR 2(us): 613.6

TR 3(us): 610.8

TR 4(us): 193.2

Max P1: 33.4Max P2: 33.7Max P3: 30.8Max P4: 41.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.4 34.6 34.8 35 35.2 35.4 35.6 35.8-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 623.83-4: 705.9Avg: 651.1T

R 1(us): 8.5

TR 2(us): 28.4

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 39.7Max P2: 44.8Max P3: 49.5Max P4: 45.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32 32.2 32.4 32.6 32.8 33 33.2-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 583.13-4: 623.8Avg: 596.7T

R 1(us): 261.4

TR 2(us): 31.3

TR 3(us): 14.2

TR 4(us): 11.4

Max P1: 48.5Max P2: 39.7Max P3: 37.2Max P4: 42.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

43.8 44 44.2 44.4 44.6 44.8 45 45.2-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 638.63-4: 745.1Avg: 679.3T

R 1(us): 309.7

TR 2(us): 434.7

TR 3(us): 14.2

TR 4(us): 11.4

Max P1: 53.4Max P2: 43.7Max P3: 59.7Max P4: 48.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

127.8 128 128.2 128.4 128.6 128.8 129 129.2

0.7

0.8

0.9

1

1.1

1.2

1.3

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 815.3

TR 3(us): 642.0

TR 4(us): 1289.8

Max P1: 1.1Max P2: 0.9Max P3: 0.8Max P4: 0.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

14 14.2 14.4 14.6 14.8 15 15.2 15.40.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 76.7

TR 2(us): 105.1

TR 3(us): 414.8

TR 4(us): 17.0

Max P1: 0.4Max P2: 0.2Max P3: 0.2Max P4: 0.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 78: Design and Optimization of a Deflagration to Detonation ...

68

Figure 31 - 05 baseline tube - empty_80percL=1

Figure 32 - 05 baseline tube - empty_100percL=0.9

Figure 33 - 05 baseline tube - empty_100percL=1.2

Figure 34 - 05 baseline tube - empty_100percL=1

Figure 35 - 06 S45D4+1 BR75_60percL=1.2

Figure 36 - 06 S45D4+1 BR75_60percL=1.4

94.2 94.4 94.6 94.8 95 95.2 95.40.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 233.0

TR 3(us): 1358.0

TR 4(us): 1329.5

Max P1: 1.1Max P2: 0.9Max P3: 0.9Max P4: 0.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

141.8 142 142.2 142.4 142.6 142.8 143 143.20.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 897.7

TR 2(us): 1323.9

TR 3(us): 1207.4

TR 4(us): 497.2

Max P1: 0.8Max P2: 1.0Max P3: 0.9Max P4: 1.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

14 14.2 14.4 14.6 14.8 15 15.2 15.40.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 17.0

TR 2(us): 187.5

TR 3(us): 440.3

TR 4(us): 411.9

Max P1: 0.4Max P2: 0.2Max P3: 0.2Max P4: 0.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

120.4 120.6 120.8 121 121.2 121.4 121.60

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 673.3

TR 3(us): 1392.0

TR 4(us): 1304.0

Max P1: 1.1Max P2: 1.1Max P3: 1.0Max P4: 0.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30 30.2 30.4 30.6 30.8 31 31.20

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 623.83-4: 654.2Avg: 633.9T

R 1(us): 14.2

TR 2(us): 19.9

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 37.1Max P2: 37.9Max P3: 44.0Max P4: 42.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

27.8 28 28.2 28.4 28.6 28.8 29 29.20

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 536.42-3: 536.43-4: 570.7Avg: 547.9T

R 1(us): 423.3

TR 2(us): 42.6

TR 3(us): 22.7

TR 4(us): 17.0

Max P1: 25.7Max P2: 25.9Max P3: 26.5Max P4: 25.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 79: Design and Optimization of a Deflagration to Detonation ...

69

Figure 37 - 06 S45D4+1 BR75_60percL=1.6

Figure 38 - 06 S45D4+1 BR75_60percL=1.8

Figure 39 - 06 S45D4+1 BR75_60percL=1

Figure 40 - 06 S45D4+1 BR75_80percL=1.2

Figure 4106 S45D4+1 BR75_80percL=1.3 delay 1.0 -

Figure 42 - 06 S45D4+1 BR75_80percL=1.4

29.6 29.8 30 30.2 30.4 30.6 30.8 310

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 487.72-3: 515.83-4: 525.9Avg: 509.8T

R 1(us): 454.5

TR 2(us): 485.8

TR 3(us): 31.3

TR 4(us): 25.6

Max P1: 19.5Max P2: 18.5Max P3: 20.9Max P4: 20.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35 35.2 35.4 35.6 35.8 36 36.24

5

6

7

8

9

10

11

12

13

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 639.2

TR 3(us): 798.3

TR 4(us): 892.0

Max P1: 13.5Max P2: 13.3Max P3: 13.5Max P4: 12.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.2 37.4 37.6 37.8 38 38.2 38.40

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 638.63-4: 654.2Avg: 643.8T

R 1(us): 304.0

TR 2(us): 19.9

TR 3(us): 19.9

TR 4(us): 14.2

Max P1: 36.7Max P2: 36.7Max P3: 36.3Max P4: 34.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.4 30.6 30.8 31 31.2 31.4 31.60

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 623.83-4: 670.6Avg: 625.8T

R 1(us): 485.8

TR 2(us): 281.3

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 48.1Max P2: 40.2Max P3: 45.4Max P4: 46.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39 39.2 39.4 39.6 39.8 40 40.2 40.4-5

0

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 596.13-4: 623.8Avg: 601.0T

R 1(us): 360.8

TR 2(us): 19.9

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 35.7Max P2: 36.8Max P3: 35.7Max P4: 35.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.2 28.4 28.6 28.8 29 29.2 29.4-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 654.23-4: 670.6Avg: 649.5T

R 1(us): 318.2

TR 2(us): 17.0

TR 3(us): 17.0

TR 4(us): 11.4

Max P1: 41.0Max P2: 46.5Max P3: 44.4Max P4: 44.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 80: Design and Optimization of a Deflagration to Detonation ...

70

Figure 43 - 06 S45D4+1 BR75_80percL=1.6

Figure 44 - 06 S45D4+1 BR75_80percL=1.8

Figure 45 - 06 S45D4+1 BR75_80percL=2

Figure 46 - 06 S45D4+1 BR75_120percL=1.2

Figure 47 - 06 S45D4+1 BR75_120percL=1.3

Figure 48 - 06 S45D4+1 BR75_120percL=1.4

29 29.2 29.4 29.6 29.8 30 30.20

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 558.82-3: 583.13-4: 596.1Avg: 579.3T

R 1(us): 338.1

TR 2(us): 17.0

TR 3(us): 19.9

TR 4(us): 22.7

Max P1: 32.8Max P2: 31.3Max P3: 29.7Max P4: 30.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.4 29.6 29.8 30 30.2 30.4 30.6 30.80

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 496.72-3: 506.13-4: 547.4Avg: 516.7T

R 1(us): 585.2

TR 2(us): 352.3

TR 3(us): 31.3

TR 4(us): 31.3

Max P1: 22.5Max P2: 22.4Max P3: 22.9Max P4: 23.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.4 33.6 33.8 34 34.2 34.4 34.62

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1219.23-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 596.6

TR 3(us): 863.6

TR 4(us): 798.3

Max P1: 16.6Max P2: 15.9Max P3: 16.5Max P4: 15.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.6 33.8 34 34.2 34.4 34.6 34.80

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 623.83-4: 654.2Avg: 629.2T

R 1(us): 286.9

TR 2(us): 400.6

TR 3(us): 352.3

TR 4(us): 309.7

Max P1: 63.8Max P2: 53.7Max P3: 49.8Max P4: 46.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

43 43.2 43.4 43.6 43.8 44 44.2 44.4-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 558.82-3: 609.63-4: 638.6Avg: 602.3T

R 1(us): 329.5

TR 2(us): 122.2

TR 3(us): 19.9

TR 4(us): 14.2

Max P1: 44.4Max P2: 40.3Max P3: 47.0Max P4: 41.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.6 28.8 29 29.2 29.4 29.6 29.8 30-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 654.23-4: 687.8Avg: 665.4T

R 1(us): 460.2

TR 2(us): 14.2

TR 3(us): 17.0

TR 4(us): 11.4

Max P1: 53.8Max P2: 43.2Max P3: 55.1Max P4: 50.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 81: Design and Optimization of a Deflagration to Detonation ...

71

Figure 49 - 06 S45D4+1 BR75_120percL=1.6

Figure 50 - 06 S45D4+1 BR75_120percL=1.8

Figure 51 - 07 S45D4+2 BR75_60percL=1.0

Figure 52 - 07 S45D4+2 BR75_60percL=1.2

Figure 53 - 07 S45D4+2 BR75_60percL=1.4

Figure 54 - 07 S45D4+2 BR75_60percL=1.6

27.8 28 28.2 28.4 28.6 28.8 29 29.2-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 638.63-4: 687.8Avg: 650.1T

R 1(us): 19.9

TR 2(us): 11.4

TR 3(us): 14.2

TR 4(us): 11.4

Max P1: 43.1Max P2: 42.6Max P3: 46.3Max P4: 45.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.8 30 30.2 30.4 30.6 30.8 310

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 558.82-3: 558.83-4: 609.6Avg: 575.7T

R 1(us): 380.7

TR 2(us): 340.9

TR 3(us): 19.9

TR 4(us): 22.7

Max P1: 35.3Max P2: 33.4Max P3: 34.2Max P4: 35.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.4 39.6 39.8 40 40.2 40.4 40.6 40.8-5

0

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 623.83-4: 623.8Avg: 628.7T

R 1(us): 14.2

TR 2(us): 11.4

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 37.3Max P2: 30.4Max P3: 25.6Max P4: 23.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29 29.2 29.4 29.6 29.8 30 30.2 30.4-5

0

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 570.73-4: 596.1Avg: 587.6T

R 1(us): 19.9

TR 2(us): 22.7

TR 3(us): 19.9

TR 4(us): 14.2

Max P1: 34.0Max P2: 28.6Max P3: 29.5Max P4: 27.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.8 29 29.2 29.4 29.6 29.8 30-5

0

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 536.42-3: 536.43-4: 547.4Avg: 540.1T

R 1(us): 19.9

TR 2(us): 31.3

TR 3(us): 39.8

TR 4(us): 17.0

Max P1: 24.6Max P2: 21.9Max P3: 22.4Max P4: 21.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.6 28.8 29 29.2 29.4 29.6 29.8 30-2

0

2

4

6

8

10

12

14

16

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 454.62-3: 487.73-4: 496.7Avg: 479.7T

R 1(us): 39.8

TR 2(us): 36.9

TR 3(us): 45.5

TR 4(us): 11.4

Max P1: 13.6Max P2: 15.4Max P3: 15.6Max P4: 15.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 82: Design and Optimization of a Deflagration to Detonation ...

72

Figure 55 - 07 S45D4+2 BR75_80percL=1.0

Figure 56 - 07 S45D4+2 BR75_80percL=1.2

Figure 57 - 07 S45D4+2 BR75_80percL=1.4

Figure 58 - 07 S45D4+2 BR75_80percL=1.6

Figure 59 - 07 S45D4+2 BR75_120percL=1.2

Figure 60 - 07 S45D4+2 BR75_120percL=1.4

56.8 57 57.2 57.4 57.6 57.8 58-4

-2

0

2

4

6

8

10

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: -2063.32-3: Inf3-4: InfAvg: InfT

R 1(us): 704.5

TR 2(us): 497.2

TR 3(us): 653.4

TR 4(us): 497.2

Max P1: 9.2Max P2: 6.8Max P3: 7.5Max P4: 7.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.8 31 31.2 31.4 31.6 31.8 32-5

0

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 558.83-4: 583.1Avg: 570.9T

R 1(us): 19.9

TR 2(us): 31.3

TR 3(us): 31.3

TR 4(us): 14.2

Max P1: 29.0Max P2: 27.4Max P3: 28.8Max P4: 27.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.6 28.8 29 29.2 29.4 29.6 29.8-5

0

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 583.13-4: 596.1Avg: 591.7T

R 1(us): 19.9

TR 2(us): 14.2

TR 3(us): 19.9

TR 4(us): 14.2

Max P1: 35.2Max P2: 32.7Max P3: 29.9Max P4: 29.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.6 28.8 29 29.2 29.4 29.6 29.8-5

0

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 547.43-4: 558.8Avg: 559.0T

R 1(us): 17.0

TR 2(us): 19.9

TR 3(us): 22.7

TR 4(us): 11.4

Max P1: 29.6Max P2: 24.8Max P3: 24.8Max P4: 24.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.8 36 36.2 36.4 36.6 36.8 37 37.2-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 2980.33-4: -3352.8Avg: InfT

R 1(us): 579.5

TR 2(us): 497.2

TR 3(us): 562.5

TR 4(us): 642.0

Max P1: 45.0Max P2: 45.1Max P3: 61.4Max P4: 41.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.6 29.8 30 30.2 30.4 30.6 30.8 310

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: -5364.52-3: 13411.23-4: 2682.2Avg: 3576.3T

R 1(us): 625.0

TR 2(us): 647.7

TR 3(us): 491.5

TR 4(us): 511.4

Max P1: 41.5Max P2: 39.5Max P3: 44.4Max P4: 48.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 83: Design and Optimization of a Deflagration to Detonation ...

73

Figure 61 - 07 S45D4+2 BR75_120percL=1.6

Figure 62 - 07 S45D4+2 BR75_120percL=1.8

Figure 63 - 08 S45D4+2 BR75 INV_80percL=1.2

Figure 64 - 08 S45D4+2 BR75 INV_80percL=1.4

Figure 65 - 08 S45D4+2 BR75 INV_100percL=1.0

Figure 66 - 08 S45D4+2 BR75 INV_100percL=1.2

29 29.2 29.4 29.6 29.8 30 30.20

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: -1411.72-3: Inf3-4: 1915.9Avg: InfT

R 1(us): 443.2

TR 2(us): 809.7

TR 3(us): 698.9

TR 4(us): 698.9

Max P1: 39.1Max P2: 33.5Max P3: 38.3Max P4: 45.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.4 31.6 31.8 32 32.2 32.4 32.6-5

0

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: -2682.22-3: Inf3-4: InfAvg: InfT

R 1(us): 639.2

TR 2(us): 497.2

TR 3(us): 670.5

TR 4(us): 730.1

Max P1: 26.5Max P2: 27.2Max P3: 25.2Max P4: 29.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.8 37 37.2 37.4 37.6 37.8 38 38.2-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 924.92-3: 766.43-4: 766.4Avg: 819.2T

R 1(us): 2.8

TR 2(us): 2.8

TR 3(us): 292.6

TR 4(us): 292.6

Max P1: 63.7Max P2: 47.6Max P3: 45.6Max P4: 47.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.8 35 35.2 35.4 35.6 35.8 36-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 766.42-3: 812.83-4: 745.1Avg: 774.7T

R 1(us): 11.4

TR 2(us): 11.4

TR 3(us): 2.8

TR 4(us): 340.9

Max P1: 45.7Max P2: 41.4Max P3: 37.7Max P4: 31.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

65.6 65.8 66 66.2 66.4 66.6 66.8-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 2235.22-3: 2438.43-4: 547.4Avg: 1740.3T

R 1(us): 329.5

TR 2(us): 213.1

TR 3(us): 358.0

TR 4(us): 625.0

Max P1: 50.3Max P2: 44.2Max P3: 47.4Max P4: 52.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.4 39.6 39.8 40 40.2 40.4 40.6-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 865.22-3: 865.23-4: 838.2Avg: 856.2T

R 1(us): 8.5

TR 2(us): 11.4

TR 3(us): 281.3

TR 4(us): 113.6

Max P1: 50.7Max P2: 59.0Max P3: 65.5Max P4: 62.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 84: Design and Optimization of a Deflagration to Detonation ...

74

Figure 67 - 08 S45D4+2 BR75 INV_100percL=1.4

Figure 68 - 08 S45D4+2 BR75 INV_120percL=1.3

Figure 69 - 08 S45D4+2 BR75 INV_120percL=1.5

Figure 70 - 08 S45D4+2 BR75 INV_120percL=1.6

Figure 71 - 08 S45D4+2 BR75 INV_120percL=1.8

Figure 72 - 08 S45D4+2 BR75 INV_120percL1.2=

32.2 32.4 32.6 32.8 33 33.2 33.4-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 812.82-3: 812.83-4: 812.8Avg: 812.8T

R 1(us): 11.4

TR 2(us): 11.4

TR 3(us): 369.3

TR 4(us): 150.6

Max P1: 52.8Max P2: 57.0Max P3: 52.3Max P4: 55.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35 35.2 35.4 35.6 35.8 36 36.2-10

0

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 812.82-3: 838.23-4: 705.9Avg: 785.6T

R 1(us): 295.5

TR 2(us): 159.1

TR 3(us): 264.2

TR 4(us): 71.0

Max P1: 54.6Max P2: 54.2Max P3: 73.1Max P4: 68.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.2 33.4 33.6 33.8 34 34.2 34.4-10

0

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 894.12-3: 865.23-4: 766.4Avg: 841.9T

R 1(us): 5.7

TR 2(us): 96.6

TR 3(us): 286.9

TR 4(us): 156.3

Max P1: 73.7Max P2: 72.3Max P3: 67.2Max P4: 71.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.4 31.6 31.8 32 32.2 32.4 32.6 32.8-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 838.22-3: 766.43-4: 766.4Avg: 790.3T

R 1(us): 11.4

TR 2(us): 76.7

TR 3(us): 156.3

TR 4(us): 14.2

Max P1: 44.4Max P2: 55.9Max P3: 52.5Max P4: 56.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.2 32.4 32.6 32.8 33 33.2 33.4 33.6-5

0

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 812.83-4: 670.6Avg: InfT

R 1(us): 511.4

TR 2(us): 758.5

TR 3(us): 403.4

TR 4(us): 579.5

Max P1: 37.5Max P2: 30.6Max P3: 32.9Max P4: 34.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

40.6 40.8 41 41.2 41.4 41.6 41.8-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 812.82-3: 766.43-4: 724.9Avg: 768.0T

R 1(us): 397.7

TR 2(us): 602.3

TR 3(us): 511.4

TR 4(us): 275.6

Max P1: 51.1Max P2: 52.5Max P3: 61.6Max P4: 63.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 85: Design and Optimization of a Deflagration to Detonation ...

75

Figure 73 - 08 S45D4+2 BR75 INV_120percL1.4=

Figure 74 - 09 S6D6+2 BR75_80percL=1.0

Figure 75 - 09 S6D6+2 BR75_80percL=1.2

Figure 76 - 09 S6D6+2 BR75_80percL=1.4

Figure 77 - 09 S6D6+2 BR75_80percL=1.6

Figure 78 - 09 S6D6+2 BR75_100percL=1.0

33.6 33.8 34 34.2 34.4 34.6 34.8-10

0

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 812.82-3: 838.23-4: 812.8Avg: 821.3T

R 1(us): 343.8

TR 2(us): 76.7

TR 3(us): 233.0

TR 4(us): 85.2

Max P1: 62.0Max P2: 73.6Max P3: 63.7Max P4: 72.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.6 39.8 40 40.2 40.4 40.6 40.8 410

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 670.63-4: 638.6Avg: 654.5T

R 1(us): 8.5

TR 2(us): 19.9

TR 3(us): 403.4

TR 4(us): 14.2

Max P1: 43.4Max P2: 38.8Max P3: 45.8Max P4: 47.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.4 31.6 31.8 32 32.2 32.4 32.6 32.8-5

0

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 583.13-4: 623.8Avg: 601.0T

R 1(us): 14.2

TR 2(us): 19.9

TR 3(us): 474.4

TR 4(us): 14.2

Max P1: 39.3Max P2: 35.9Max P3: 39.1Max P4: 33.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.2 29.4 29.6 29.8 30 30.2 30.4 30.6-5

0

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 536.42-3: 536.43-4: 536.4Avg: 536.4T

R 1(us): 133.5

TR 2(us): 19.9

TR 3(us): 31.3

TR 4(us): 31.3

Max P1: 29.8Max P2: 26.3Max P3: 30.4Max P4: 29.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.2 30.4 30.6 30.8 31 31.2 31.4-5

0

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 525.92-3: 515.83-4: 536.4Avg: 526.1T

R 1(us): 22.7

TR 2(us): 39.8

TR 3(us): 22.7

TR 4(us): 31.3

Max P1: 26.1Max P2: 22.6Max P3: 24.4Max P4: 27.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

52.2 52.4 52.6 52.8 53 53.2 53.4 53.6-10

0

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 924.92-3: 745.13-4: 705.9Avg: 791.9T

R 1(us): 622.2

TR 2(us): 394.9

TR 3(us): 571.0

TR 4(us): 235.8

Max P1: 49.3Max P2: 51.5Max P3: 71.9Max P4: 52.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 86: Design and Optimization of a Deflagration to Detonation ...

76

Figure 79 - 09 S6D6+2 BR75_100percL=1.2

Figure 80 - 09 S6D6+2 BR75_100percL=1.4

Figure 81 - 09 S6D6+2 BR75_100percL=1.6

Figure 82 - 09 S6D6+2 BR75_120percL=1 delay 1.0

Figure 83 - 09 S6D6+2 BR75_120percL=1.2

Figure 84 - 09 S6D6+2 BR75_120percL=1.4

34.8 35 35.2 35.4 35.6 35.8 36-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 623.83-4: 654.2Avg: 633.9T

R 1(us): 11.4

TR 2(us): 102.3

TR 3(us): 363.6

TR 4(us): 11.4

Max P1: 44.0Max P2: 46.5Max P3: 51.5Max P4: 55.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.2 28.4 28.6 28.8 29 29.2 29.4 29.6-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 570.73-4: 654.2Avg: 607.0T

R 1(us): 338.1

TR 2(us): 42.6

TR 3(us): 11.4

TR 4(us): 14.2

Max P1: 46.8Max P2: 39.4Max P3: 43.2Max P4: 43.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.4 29.6 29.8 30 30.2 30.4 30.6-5

0

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 583.13-4: 623.8Avg: 592.5T

R 1(us): 19.9

TR 2(us): 19.9

TR 3(us): 14.2

TR 4(us): 247.2

Max P1: 36.7Max P2: 34.3Max P3: 35.8Max P4: 31.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

80.2 80.4 80.6 80.8 81 81.2 81.40

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 2063.32-3: -2235.23-4: 5364.5Avg: 1730.8T

R 1(us): 764.2

TR 2(us): 460.2

TR 3(us): 721.6

TR 4(us): 619.3

Max P1: 35.5Max P2: 27.9Max P3: 30.1Max P4: 33.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.8 34 34.2 34.4 34.6 34.8 35 35.2-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 654.23-4: 654.2Avg: 644.1T

R 1(us): 375.0

TR 2(us): 190.3

TR 3(us): 184.7

TR 4(us): 11.4

Max P1: 50.2Max P2: 55.1Max P3: 50.2Max P4: 59.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.2 30.4 30.6 30.8 31 31.2 31.4 31.6-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 638.63-4: 654.2Avg: 638.9T

R 1(us): 150.6

TR 2(us): 93.8

TR 3(us): 14.2

TR 4(us): 14.2

Max P1: 61.9Max P2: 61.4Max P3: 45.3Max P4: 55.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 87: Design and Optimization of a Deflagration to Detonation ...

77

Figure 85 - 09 S6D6+2 BR75_120percL=1.6

Figure 86 - 09 S6D6+2 BR75_120percL=1.8

Figure 87 - 10 S_D1 BR75_100percL=1.0

Figure 88 - 10 S_D1 BR75_100percL=1.2

Figure 89 - 10 S_D1 BR75_100percL=1.4

Figure 90 - 10 S_D1 BR75_100percL=1.6

28 28.2 28.4 28.6 28.8 29 29.2-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 609.63-4: 623.8Avg: 614.3T

R 1(us): 159.1

TR 2(us): 93.8

TR 3(us): 233.0

TR 4(us): 14.2

Max P1: 46.6Max P2: 45.5Max P3: 50.4Max P4: 51.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.4 29.6 29.8 30 30.2 30.4 30.6 30.8-5

0

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 583.13-4: 623.8Avg: 592.5T

R 1(us): 323.9

TR 2(us): 22.7

TR 3(us): 14.2

TR 4(us): 11.4

Max P1: 33.0Max P2: 37.4Max P3: 35.8Max P4: 41.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

74.2 74.4 74.6 74.8 75 75.2 75.4 75.6-4

-2

0

2

4

6

8

10

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 786.9

TR 2(us): 758.5

TR 3(us): 727.3

TR 4(us): 497.2

Max P1: 8.2Max P2: 7.5Max P3: 6.8Max P4: 6.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

53.6 53.8 54 54.2 54.4 54.6 54.8-4

-2

0

2

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 590.9

TR 3(us): 608.0

TR 4(us): 644.9

Max P1: 12.6Max P2: 12.1Max P3: 11.9Max P4: 12.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

48.2 48.4 48.6 48.8 49 49.2 49.4 49.6-4

-2

0

2

4

6

8

10

12

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 610.8

TR 2(us): 497.2

TR 3(us): 548.3

TR 4(us): 656.3

Max P1: 10.7Max P2: 10.4Max P3: 9.2Max P4: 8.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

51 51.2 51.4 51.6 51.8 52 52.2-1

0

1

2

3

4

5

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 690.3

TR 2(us): 522.7

TR 3(us): 497.2

TR 4(us): 536.9

Max P1: 4.7Max P2: 4.5Max P3: 4.0Max P4: 4.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 88: Design and Optimization of a Deflagration to Detonation ...

78

Figure 91 - 10 S_D1 BR75_150percL=1.2

Figure 92 - 11 S6D3+2 BR75_80percL=1.0

Figure 93 - 11 S6D3+2 BR75_80percL=1.2

Figure 94 - 11 S6D3+2 BR75_80percL=1.4

Figure 95 - 11 S6D3+2 BR75_80percL=1.6

Figure 96 - 11 S6D3+2 BR75_100percL=1.0

56.6 56.8 57 57.2 57.4 57.6 57.8-6

-4

-2

0

2

4

6

8

10

12

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 633.5

TR 2(us): 738.6

TR 3(us): 724.4

TR 4(us): 497.2

Max P1: 11.0Max P2: 10.4Max P3: 9.9Max P4: 9.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

50.2 50.4 50.6 50.8 51 51.2 51.40

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: -425.82-3: -3831.83-4: -13411.2Avg: -5889.6T

R 1(us): 278.4

TR 2(us): 792.6

TR 3(us): 920.5

TR 4(us): 596.6

Max P1: 41.3Max P2: 34.2Max P3: 34.5Max P4: 32.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.6 29.8 30 30.2 30.4 30.6 30.8-5

0

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 558.82-3: 558.83-4: 570.7Avg: 562.8T

R 1(us): 22.7

TR 2(us): 17.0

TR 3(us): 34.1

TR 4(us): 14.2

Max P1: 29.8Max P2: 25.9Max P3: 27.6Max P4: 24.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.4 29.6 29.8 30 30.2 30.4 30.6-5

0

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 596.13-4: 596.1Avg: 596.1T

R 1(us): 19.9

TR 2(us): 19.9

TR 3(us): 17.0

TR 4(us): 17.0

Max P1: 33.6Max P2: 33.8Max P3: 30.5Max P4: 29.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.2 28.4 28.6 28.8 29 29.2 29.4-5

0

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 525.92-3: 515.83-4: 536.4Avg: 526.1T

R 1(us): 19.9

TR 2(us): 31.3

TR 3(us): 31.3

TR 4(us): 34.1

Max P1: 22.9Max P2: 20.2Max P3: 21.9Max P4: 20.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

57.4 57.6 57.8 58 58.2 58.4 58.6 58.8-6

-4

-2

0

2

4

6

8

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: -724.92-3: Inf3-4: 1788.2Avg: InfT

R 1(us): 451.7

TR 2(us): 1406.3

TR 3(us): 1193.2

TR 4(us): 454.5

Max P1: 4.5Max P2: 6.7Max P3: 6.2Max P4: 5.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 89: Design and Optimization of a Deflagration to Detonation ...

79

Figure 97 - 11 S6D3+2 BR75_100percL=1.2

Figure 98 - 11 S6D3+2 BR75_100percL=1.4

Figure 99 - 11 S6D3+2 BR75_100percL=1.6

Figure 100 - 11 S6D3+2 BR75_120percL=1.0

Figure 101 - 11 S6D3+2 BR75_120percL=1.2

Figure 102 - 11 S6D3+2 BR75_120percL=1.4

33 33.2 33.4 33.6 33.8 34 34.20

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 3831.83-4: -3831.8Avg: InfT

R 1(us): 497.2

TR 2(us): 627.8

TR 3(us): 849.4

TR 4(us): 681.8

Max P1: 29.2Max P2: 33.9Max P3: 34.4Max P4: 30.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.8 30 30.2 30.4 30.6 30.8 31 31.2-5

0

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 583.13-4: 596.1Avg: 587.4T

R 1(us): 19.9

TR 2(us): 19.9

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 36.5Max P2: 32.2Max P3: 31.9Max P4: 28.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.4 28.6 28.8 29 29.2 29.4 29.6-5

0

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 547.42-3: 536.43-4: 558.8Avg: 547.5T

R 1(us): 22.7

TR 2(us): 34.1

TR 3(us): 22.7

TR 4(us): 22.7

Max P1: 28.3Max P2: 26.1Max P3: 26.4Max P4: 24.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

73.8 74 74.2 74.4 74.6 74.8 75 75.2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1788.22-3: 957.93-4: -339.5Avg: 802.2T

R 1(us): 392.0

TR 2(us): 1088.1

TR 3(us): 531.3

TR 4(us): 860.8

Max P1: 1.8Max P2: 1.6Max P3: 1.2Max P4: 1.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.6 33.8 34 34.2 34.4 34.6 34.8 35-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 2235.22-3: -2235.23-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 519.9

TR 3(us): 619.3

TR 4(us): 673.3

Max P1: 42.6Max P2: 57.6Max P3: 39.6Max P4: 42.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.4 31.6 31.8 32 32.2 32.4 32.60

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: -6705.63-4: -3831.8Avg: InfT

R 1(us): 494.3

TR 2(us): 565.3

TR 3(us): 730.1

TR 4(us): 497.2

Max P1: 44.5Max P2: 37.6Max P3: 44.0Max P4: 47.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 90: Design and Optimization of a Deflagration to Detonation ...

80

Figure 103 -11 S6D3+2 BR75_120percL=1.6

Figure 104 - 12 S3D6+1 BR60_80percL=1.0

Figure 105 -12 S3D6+1 BR60_80percL=1.2

Figure 106 - 12 S3D6+1 BR60_80percL=1.4

Figure 107 - 12 S3D6+1 BR60_80percL=1.6

Figure 108 - 12 S3D6+1 BR60_80percL=1.8

28.2 28.4 28.6 28.8 29 29.2 29.4 29.6-5

0

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 558.82-3: 583.13-4: 583.1Avg: 575.0T

R 1(us): 31.3

TR 2(us): 17.0

TR 3(us): 22.7

TR 4(us): 14.2

Max P1: 34.2Max P2: 31.4Max P3: 29.2Max P4: 28.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

43.2 43.4 43.6 43.8 44 44.2 44.4 44.64

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 656.3

TR 3(us): 650.6

TR 4(us): 852.3

Max P1: 17.7Max P2: 18.0Max P3: 19.1Max P4: 18.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.4 32.6 32.8 33 33.2 33.4 33.6 33.80

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 670.63-4: 654.2Avg: 649.5T

R 1(us): 19.9

TR 2(us): 14.2

TR 3(us): 17.0

TR 4(us): 14.2

Max P1: 40.6Max P2: 43.7Max P3: 41.9Max P4: 41.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.8 29 29.2 29.4 29.6 29.8 30 30.2-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 670.63-4: 687.8Avg: 665.6T

R 1(us): 14.2

TR 2(us): 14.2

TR 3(us): 14.2

TR 4(us): 11.4

Max P1: 43.4Max P2: 44.3Max P3: 47.1Max P4: 45.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.6 28.8 29 29.2 29.4 29.6 29.8 300

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 623.83-4: 654.2Avg: 629.2T

R 1(us): 19.9

TR 2(us): 19.9

TR 3(us): 14.2

TR 4(us): 14.2

Max P1: 34.2Max P2: 38.0Max P3: 38.5Max P4: 37.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.2 30.4 30.6 30.8 31 31.2 31.40

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1411.72-3: 496.73-4: 506.1Avg: 804.8T

R 1(us): 488.6

TR 2(us): 511.4

TR 3(us): 664.8

TR 4(us): 156.3

Max P1: 21.1Max P2: 20.4Max P3: 21.4Max P4: 19.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 91: Design and Optimization of a Deflagration to Detonation ...

81

Figure 109 - 12 S3D6+1 BR60_80percL=1

Figure 110 - 12 S3D6+1 BR60_100percL=1.0

Figure 111 - 12 S3D6+1 BR60_100percL=1.2

Figure 112 - 12 S3D6+1 BR60_100percL=1.4

Figure 113 - 12 S3D6+1 BR60_100percL=1.6

Figure 114 - 12 S3D6+1 BR60_100percL=1.8

43.2 43.4 43.6 43.8 44 44.2 44.4 44.64

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 656.3

TR 3(us): 650.6

TR 4(us): 852.3

Max P1: 17.7Max P2: 18.0Max P3: 19.1Max P4: 18.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

77.6 77.8 78 78.2 78.4 78.6 78.80.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 1275.6

TR 2(us): 497.2

TR 3(us): 440.3

TR 4(us): 215.9

Max P1: 0.3Max P2: 0.3Max P3: 0.2Max P4: 0.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.4 38.6 38.8 39 39.2 39.4 39.6 39.80

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 479.03-4: 525.9Avg: 542.9T

R 1(us): 468.8

TR 2(us): 108.0

TR 3(us): 62.5

TR 4(us): 22.7

Max P1: 36.4Max P2: 32.0Max P3: 33.1Max P4: 34.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31 31.2 31.4 31.6 31.8 32 32.2-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 705.93-4: 687.8Avg: 688.1T

R 1(us): 17.0

TR 2(us): 11.4

TR 3(us): 14.2

TR 4(us): 11.4

Max P1: 48.0Max P2: 50.3Max P3: 48.1Max P4: 47.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29 29.2 29.4 29.6 29.8 30 30.20

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 687.83-4: 687.8Avg: 676.6T

R 1(us): 11.4

TR 2(us): 17.0

TR 3(us): 14.2

TR 4(us): 11.4

Max P1: 45.7Max P2: 51.3Max P3: 48.2Max P4: 46.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.6 29.8 30 30.2 30.4 30.6 30.8 310

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 536.42-3: 570.73-4: 623.8Avg: 577.0T

R 1(us): 423.3

TR 2(us): 31.3

TR 3(us): 19.9

TR 4(us): 17.0

Max P1: 30.0Max P2: 29.0Max P3: 33.2Max P4: 32.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 92: Design and Optimization of a Deflagration to Detonation ...

82

Figure 115 - 12 S3D6+1 BR60_120percL=1.0

Figure 116 - 12 S3D6+1 BR60_120percL=1.2

Figure 117 - 12 S3D6+1 BR60_120percL=1.4

Figure 118 - 12 S3D6+1 BR60_120percL=1.6

Figure 119 - 12 S3D6+1 BR60_120percL=1.8

Figure 120 - 12 S3D6+1 BR60_120percL=1

102 102.2 102.4 102.6 102.8 103 103.20.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 264.2

TR 3(us): 556.8

TR 4(us): 772.7

Max P1: 0.2Max P2: 0.2Max P3: 0.2Max P4: 0.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.8 39 39.2 39.4 39.6 39.8 400

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 547.43-4: 558.8Avg: 563.1T

R 1(us): 397.7

TR 2(us): 480.1

TR 3(us): 437.5

TR 4(us): 360.8

Max P1: 30.6Max P2: 28.6Max P3: 31.9Max P4: 29.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.6 30.8 31 31.2 31.4 31.6 31.80

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 654.23-4: 670.6Avg: 659.7T

R 1(us): 14.2

TR 2(us): 19.9

TR 3(us): 14.2

TR 4(us): 11.4

Max P1: 43.9Max P2: 42.5Max P3: 47.2Max P4: 44.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28 28.2 28.4 28.6 28.8 29 29.20

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 705.93-4: 687.8Avg: 682.6T

R 1(us): 11.4

TR 2(us): 14.2

TR 3(us): 14.2

TR 4(us): 14.2

Max P1: 45.0Max P2: 54.6Max P3: 50.9Max P4: 51.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.2 29.4 29.6 29.8 30 30.2 30.4 30.60

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 609.63-4: 638.6Avg: 606.3T

R 1(us): 25.6

TR 2(us): 19.9

TR 3(us): 14.2

TR 4(us): 14.2

Max P1: 31.4Max P2: 35.3Max P3: 36.4Max P4: 35.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

102 102.2 102.4 102.6 102.8 103 103.20.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 264.2

TR 3(us): 556.8

TR 4(us): 772.7

Max P1: 0.2Max P2: 0.2Max P3: 0.2Max P4: 0.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 93: Design and Optimization of a Deflagration to Detonation ...

83

Figure 121 - 13 S3D6+2 BR60_80percL=1.2

Figure 122 - 13 S3D6+2 BR60_80percL=1.4

Figure 123 - 13 S3D6+2 BR60_80percL=1.6

Figure 124 - 13 S3D6+2 BR60_80percL=1.8

Figure 125 - 13 S3D6+2 BR60_100percL=1.2

Figure 126 - 13 S3D6+2 BR60_100percL=1.4

36.2 36.4 36.6 36.8 37 37.2 37.4 37.60

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 506.13-4: 609.6Avg: 613.5T

R 1(us): 1269.9

TR 2(us): 45.5

TR 3(us): 17.0

TR 4(us): 17.0

Max P1: 30.4Max P2: 27.0Max P3: 29.5Max P4: 28.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.6 30.8 31 31.2 31.4 31.6 31.8 32-5

0

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 638.63-4: 638.6Avg: 629.0T

R 1(us): 31.3

TR 2(us): 17.0

TR 3(us): 17.0

TR 4(us): 11.4

Max P1: 38.7Max P2: 42.5Max P3: 35.9Max P4: 38.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.8 30 30.2 30.4 30.6 30.8 31-5

0

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 623.83-4: 609.6Avg: 609.8T

R 1(us): 31.3

TR 2(us): 19.9

TR 3(us): 19.9

TR 4(us): 8.5

Max P1: 35.7Max P2: 39.1Max P3: 33.6Max P4: 33.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.4 29.6 29.8 30 30.2 30.4 30.6 30.8-5

0

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 525.92-3: 558.83-4: 570.7Avg: 551.8T

R 1(us): 34.1

TR 2(us): 19.9

TR 3(us): 22.7

TR 4(us): 17.0

Max P1: 26.0Max P2: 25.7Max P3: 25.1Max P4: 24.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37 37.2 37.4 37.6 37.8 38 38.20

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 508.5

TR 2(us): 497.2

TR 3(us): 548.3

TR 4(us): 684.7

Max P1: 37.6Max P2: 44.4Max P3: 43.1Max P4: 52.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29 29.2 29.4 29.6 29.8 30 30.2 30.4-5

0

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 654.23-4: 623.8Avg: 633.9T

R 1(us): 34.1

TR 2(us): 17.0

TR 3(us): 17.0

TR 4(us): 11.4

Max P1: 37.9Max P2: 44.3Max P3: 36.1Max P4: 39.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 94: Design and Optimization of a Deflagration to Detonation ...

84

Figure 127 - 13 S3D6+2 BR60_100percL=1.6

Figure 128 - 13 S3D6+2 BR60_100percL=1.8

Figure 129 - 13 S3D6+2 BR60_120percL=1.2

Figure 130 - 13 S3D6+2 BR60_120percL=1.4

Figure 131 - 13 S3D6+2 BR60_120percL=1.6

Figure 132 - 13 S3D6+2 BR60_120percL=1.8

28.8 29 29.2 29.4 29.6 29.8 30 30.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 609.63-4: 609.6Avg: 600.8T

R 1(us): 31.3

TR 2(us): 19.9

TR 3(us): 19.9

TR 4(us): 14.2

Max P1: 33.1Max P2: 36.7Max P3: 32.2Max P4: 35.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.8 30 30.2 30.4 30.6 30.8 31-5

0

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 638.63-4: 623.8Avg: 619.5T

R 1(us): 34.1

TR 2(us): 17.0

TR 3(us): 19.9

TR 4(us): 14.2

Max P1: 36.6Max P2: 41.0Max P3: 34.9Max P4: 37.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.6 33.8 34 34.2 34.4 34.6 34.8 350

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 511.4

TR 2(us): 778.4

TR 3(us): 497.2

TR 4(us): 548.3

Max P1: 45.2Max P2: 43.9Max P3: 55.6Max P4: 59.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41.2 41.4 41.6 41.8 42 42.2 42.4 42.60

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 2438.4Avg: InfT

R 1(us): 497.2

TR 2(us): 906.3

TR 3(us): 929.0

TR 4(us): 758.5

Max P1: 38.9Max P2: 40.8Max P3: 44.4Max P4: 44.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.4 34.6 34.8 35 35.2 35.4 35.6-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 638.63-4: 638.6Avg: 633.7T

R 1(us): 454.5

TR 2(us): 19.9

TR 3(us): 866.5

TR 4(us): 17.0

Max P1: 42.6Max P2: 41.5Max P3: 48.0Max P4: 36.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.2 31.4 31.6 31.8 32 32.2 32.4 32.60

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 638.63-4: 623.8Avg: 628.7T

R 1(us): 34.1

TR 2(us): 19.9

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 38.1Max P2: 42.5Max P3: 37.0Max P4: 39.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 95: Design and Optimization of a Deflagration to Detonation ...

85

Figure 133 - 14 S3D6+1 BR60 INV_80percL=1.2

Figure 134 - 14 S3D6+1 BR60 INV_80percL=1.4

Figure 135 - 14 S3D6+1 BR60 INV_80percL=1.6

Figure 136 - 14 S3D6+1 BR60 INV_100percL=1.2

Figure 137 - 14 S3D6+1 BR60 INV_100percL=1.4

Figure 138 - 14 S3D6+1 BR60 INV_100percL=1.6

38.4 38.6 38.8 39 39.2 39.4 39.6-5

0

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 654.23-4: 583.1Avg: InfT

R 1(us): 517.0

TR 2(us): 497.2

TR 3(us): 536.9

TR 4(us): 360.8

Max P1: 29.6Max P2: 33.6Max P3: 36.3Max P4: 37.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.2 39.4 39.6 39.8 40 40.2 40.40

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 812.83-4: 570.7Avg: InfT

R 1(us): 559.7

TR 2(us): 497.2

TR 3(us): 599.4

TR 4(us): 627.8

Max P1: 26.1Max P2: 28.2Max P3: 28.0Max P4: 29.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41.4 41.6 41.8 42 42.2 42.4 42.60

2

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 571.0

TR 2(us): 497.2

TR 3(us): 522.7

TR 4(us): 588.1

Max P1: 13.2Max P2: 13.5Max P3: 13.1Max P4: 12.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.2 39.4 39.6 39.8 40 40.2 40.4 40.60

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 1166.23-4: 638.6Avg: 825.1T

R 1(us): 738.6

TR 2(us): 417.6

TR 3(us): 318.2

TR 4(us): 321.0

Max P1: 34.6Max P2: 37.7Max P3: 41.7Max P4: 43.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39 39.2 39.4 39.6 39.8 40 40.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 3352.83-4: 558.8Avg: InfT

R 1(us): 528.4

TR 2(us): 497.2

TR 3(us): 483.0

TR 4(us): 681.8

Max P1: 30.2Max P2: 33.9Max P3: 37.7Max P4: 39.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

40.2 40.4 40.6 40.8 41 41.2 41.4 41.60

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1277.33-4: -3831.8Avg: InfT

R 1(us): 497.2

TR 2(us): 511.4

TR 3(us): 514.2

TR 4(us): 860.8

Max P1: 22.7Max P2: 23.4Max P3: 24.4Max P4: 25.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 96: Design and Optimization of a Deflagration to Detonation ...

86

Figure 139 - 14 S3D6+1 BR60 INV_100percL=1.8

Figure 140 - 14 S3D6+1 BR60 INV_120percL=1.2

Figure 141 - 14 S3D6+1 BR60 INV_120percL=1.4

Figure 142 - 14 S3D6+1 BR60 INV_120percL=1.6

Figure 143 - 14 S3D6+1 BR60 INV_120percL=1.8

Figure 144 - 15 S3D12+2 BR60_80percL=1.2

44.2 44.4 44.6 44.8 45 45.2 45.4 45.60

2

4

6

8

10

12

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 630.7

TR 2(us): 681.8

TR 3(us): 497.2

TR 4(us): 897.7

Max P1: 11.9Max P2: 11.6Max P3: 11.0Max P4: 11.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.6 39.8 40 40.2 40.4 40.6 40.8 41-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 26822.42-3: 623.83-4: 558.8Avg: 9335.0T

R 1(us): 664.8

TR 2(us): 471.6

TR 3(us): 389.2

TR 4(us): 281.3

Max P1: 45.3Max P2: 48.3Max P3: 56.2Max P4: 68.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.2 38.4 38.6 38.8 39 39.2 39.4 39.60

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 2235.22-3: 2438.43-4: 558.8Avg: 1744.1T

R 1(us): 477.3

TR 2(us): 460.2

TR 3(us): 525.6

TR 4(us): 423.3

Max P1: 33.4Max P2: 35.7Max P3: 38.5Max P4: 40.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

40.4 40.6 40.8 41 41.2 41.4 41.60

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1915.93-4: 654.2Avg: InfT

R 1(us): 497.2

TR 2(us): 823.9

TR 3(us): 812.5

TR 4(us): 755.7

Max P1: 27.1Max P2: 27.4Max P3: 27.3Max P4: 29.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

42.4 42.6 42.8 43 43.2 43.4 43.60

2

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 525.6

TR 2(us): 497.2

TR 3(us): 579.5

TR 4(us): 710.2

Max P1: 13.4Max P2: 13.2Max P3: 12.8Max P4: 12.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

52.2 52.4 52.6 52.8 53 53.2 53.4 53.6-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 654.23-4: 705.9Avg: 688.6T

R 1(us): 11.4

TR 2(us): 34.1

TR 3(us): 14.2

TR 4(us): 8.5

Max P1: 63.7Max P2: 54.6Max P3: 60.9Max P4: 56.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 97: Design and Optimization of a Deflagration to Detonation ...

87

Figure 145 - 15 S3D12+2 BR60_80percL=1.4

Figure 146 - 15 S3D12+2 BR60_80percL=1.6

Figure 147 - 15 S3D12+2 BR60_80percL=1.8

Figure 148 - 15 S3D12+2 BR60_100percL=1.4

Figure 149 - 15 S3D12+2 BR60_100percL=1.6

Figure 150 - 15 S3D12+2 BR60_100percL=1.8

35.6 35.8 36 36.2 36.4 36.6 36.8-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 654.23-4: 724.9Avg: 683.2T

R 1(us): 11.4

TR 2(us): 31.3

TR 3(us): 8.5

TR 4(us): 14.2

Max P1: 51.7Max P2: 46.8Max P3: 55.7Max P4: 57.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.6 33.8 34 34.2 34.4 34.6 34.8 35-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 623.83-4: 705.9Avg: 661.3T

R 1(us): 85.2

TR 2(us): 34.1

TR 3(us): 11.4

TR 4(us): 14.2

Max P1: 48.4Max P2: 41.6Max P3: 55.9Max P4: 44.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30 30.2 30.4 30.6 30.8 31 31.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 596.13-4: 583.1Avg: 596.2T

R 1(us): 102.3

TR 2(us): 22.7

TR 3(us): 34.1

TR 4(us): 11.4

Max P1: 34.7Max P2: 34.2Max P3: 37.3Max P4: 37.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

48.2 48.4 48.6 48.8 49 49.2 49.4-10

0

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 745.13-4: 766.4Avg: 739.1T

R 1(us): 59.7

TR 2(us): 14.2

TR 3(us): 11.4

TR 4(us): 8.5

Max P1: 68.0Max P2: 80.8Max P3: 70.5Max P4: 70.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.2 35.4 35.6 35.8 36 36.2 36.4 36.6-10

0

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 766.43-4: 766.4Avg: 746.2T

R 1(us): 48.3

TR 2(us): 8.5

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 59.3Max P2: 82.9Max P3: 63.0Max P4: 73.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.8 31 31.2 31.4 31.6 31.8 32-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 687.83-4: 724.9Avg: 700.1T

R 1(us): 11.4

TR 2(us): 28.4

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 54.7Max P2: 51.1Max P3: 58.8Max P4: 60.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 98: Design and Optimization of a Deflagration to Detonation ...

88

Figure 151 - 15 S3D12+2 BR60_120percL=1.3

Figure 152 - 15 S3D12+2 BR60_120percL=1.4

Figure 153 - 15 S3D12+2 BR60_120percL=1.4v2

Figure 154 - 15 S3D12+2 BR60_120percL=1.4v3

Figure 155 - 15 S3D12+2 BR60_120percL=1.6

Figure 156 - 15 S3D12+2 BR60_120percL=1.6v2

30.2 30.4 30.6 30.8 31 31.2 31.4 31.6-20

0

20

40

60

80

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 766.42-3: 924.93-4: 812.8Avg: 834.7T

R 1(us): 48.3

TR 2(us): 2.8

TR 3(us): 11.4

TR 4(us): 8.5

Max P1: 98.1Max P2: 97.9Max P3: 75.6Max P4: 80.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

43.8 44 44.2 44.4 44.6 44.8 45-10

0

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 745.12-3: 838.23-4: 838.2Avg: 807.2T

R 1(us): 11.4

TR 2(us): 11.4

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 71.0Max P2: 87.5Max P3: 84.0Max P4: 79.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.2 34.4 34.6 34.8 35 35.2 35.4-20

0

20

40

60

80

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 766.42-3: 894.13-4: 838.2Avg: 832.9T

R 1(us): 56.8

TR 2(us): 5.7

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 98.2Max P2: 96.3Max P3: 81.0Max P4: 82.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.6 30.8 31 31.2 31.4 31.6 31.8 32-20

0

20

40

60

80

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 766.42-3: 894.13-4: 812.8Avg: 824.4T

R 1(us): 48.3

TR 2(us): 11.4

TR 3(us): 11.4

TR 4(us): 8.5

Max P1: 78.1Max P2: 98.3Max P3: 76.4Max P4: 82.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.6 28.8 29 29.2 29.4 29.6 29.8 30-20

0

20

40

60

80

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 766.42-3: 812.83-4: 812.8Avg: 797.3T

R 1(us): 8.5

TR 2(us): 11.4

TR 3(us): 8.5

TR 4(us): 11.4

Max P1: 70.4Max P2: 93.7Max P3: 70.9Max P4: 86.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.8 29 29.2 29.4 29.6 29.8 30-20

0

20

40

60

80

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 865.23-4: 788.9Avg: 793.0T

R 1(us): 375.0

TR 2(us): 11.4

TR 3(us): 11.4

TR 4(us): 8.5

Max P1: 70.9Max P2: 98.1Max P3: 71.4Max P4: 78.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 99: Design and Optimization of a Deflagration to Detonation ...

89

Figure 157 - 15 S3D12+2 BR60_120percL=1.8

Figure 158 - 15 S3D12+2 BR60_120percL=2.0

Figure 159 - 16 S45D8+2 BR60_80percL=1.2

Figure 160 - 16 S45D8+2 BR60_80percL=1.4

Figure 161 - 16 S45D8+2 BR60_80percL=1.6

Figure 162 - 16 S45D8+2 BR60_80percL=1.8

29 29.2 29.4 29.6 29.8 30 30.2-10

0

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 724.93-4: 766.4Avg: 732.4T

R 1(us): 59.7

TR 2(us): 19.9

TR 3(us): 11.4

TR 4(us): 14.2

Max P1: 77.4Max P2: 76.9Max P3: 67.7Max P4: 62.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.8 32 32.2 32.4 32.6 32.8 33 33.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 536.42-3: 583.13-4: 623.8Avg: 581.1T

R 1(us): 304.0

TR 2(us): 247.2

TR 3(us): 338.1

TR 4(us): 298.3

Max P1: 32.7Max P2: 37.0Max P3: 37.5Max P4: 36.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

49.6 49.8 50 50.2 50.4 50.6 50.80

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 654.23-4: 687.8Avg: 670.8T

R 1(us): 440.3

TR 2(us): 14.2

TR 3(us): 147.7

TR 4(us): 14.2

Max P1: 38.3Max P2: 40.0Max P3: 43.8Max P4: 38.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

40.6 40.8 41 41.2 41.4 41.6 41.8 42-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 687.83-4: 687.8Avg: 693.8T

R 1(us): 8.5

TR 2(us): 102.3

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 52.7Max P2: 59.4Max P3: 50.8Max P4: 49.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.8 31 31.2 31.4 31.6 31.8 32-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 638.63-4: 638.6Avg: 633.7T

R 1(us): 142.0

TR 2(us): 11.4

TR 3(us): 31.3

TR 4(us): 14.2

Max P1: 47.9Max P2: 42.0Max P3: 38.7Max P4: 43.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.2 31.4 31.6 31.8 32 32.2 32.4 32.60

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 623.83-4: 623.8Avg: 619.1T

R 1(us): 28.4

TR 2(us): 11.4

TR 3(us): 17.0

TR 4(us): 14.2

Max P1: 39.2Max P2: 36.4Max P3: 36.2Max P4: 31.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 100: Design and Optimization of a Deflagration to Detonation ...

90

Figure 163 - 16 S45D8+2 BR60_100percL=1.2

Figure 164 - 16 S45D8+2 BR60_100percL=1.4

Figure 165 - 16 S45D8+2 BR60_100percL=1.6

Figure 166 - 16 S45D8+2 BR60_100percL=1.8

Figure 167 - 16 S45D8+2 BR60_120percL=1.2

Figure 168 - 16 S45D8+2 BR60_120percL=1.4

67 67.2 67.4 67.6 67.8 68 68.20

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1219.22-3: 766.43-4: 687.8Avg: 891.1T

R 1(us): 446.0

TR 2(us): 366.5

TR 3(us): 332.4

TR 4(us): 363.6

Max P1: 42.3Max P2: 40.6Max P3: 48.8Max P4: 53.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.6 39.8 40 40.2 40.4 40.6 40.8-10

0

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 745.12-3: 724.93-4: 788.9Avg: 753.0T

R 1(us): 90.9

TR 2(us): 62.5

TR 3(us): 19.9

TR 4(us): 8.5

Max P1: 83.8Max P2: 84.9Max P3: 79.7Max P4: 75.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.4 36.6 36.8 37 37.2 37.4 37.6 37.8-10

0

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 687.83-4: 766.4Avg: 720.0T

R 1(us): 102.3

TR 2(us): 73.9

TR 3(us): 28.4

TR 4(us): 8.5

Max P1: 64.2Max P2: 61.0Max P3: 71.1Max P4: 72.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.8 31 31.2 31.4 31.6 31.8 32 32.2-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 654.23-4: 705.9Avg: 676.9T

R 1(us): 119.3

TR 2(us): 90.9

TR 3(us): 8.5

TR 4(us): 11.4

Max P1: 68.7Max P2: 51.3Max P3: 50.8Max P4: 49.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

48.2 48.4 48.6 48.8 49 49.2 49.4 49.60

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1166.22-3: 6705.63-4: 432.6Avg: 2768.1T

R 1(us): 551.1

TR 2(us): 431.8

TR 3(us): 528.4

TR 4(us): 306.8

Max P1: 50.1Max P2: 50.0Max P3: 49.1Max P4: 76.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34 34.2 34.4 34.6 34.8 35 35.2-20

0

20

40

60

80

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 724.93-4: 838.2Avg: 762.7T

R 1(us): 93.8

TR 2(us): 19.9

TR 3(us): 11.4

TR 4(us): 8.5

Max P1: 94.1Max P2: 67.8Max P3: 91.6Max P4: 81.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 101: Design and Optimization of a Deflagration to Detonation ...

91

Figure 169 - 16 S45D8+2 BR60_120percL=1.6

Figure 170 - 16 S45D8+2 BR60_120percL=1.8

Figure 171 - 17 S45D4+1 BR60_80percL=1.2

Figure 172 - 17 S45D4+1 BR60_80percL=1.4

Figure 173 - 17 S45D4+1 BR60_80percL=1.6

Figure 174 - 17 S45D4+1 BR60_80percL=1.8

34.4 34.6 34.8 35 35.2 35.4 35.6-10

0

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 745.13-4: 788.9Avg: 753.0T

R 1(us): 88.1

TR 2(us): 14.2

TR 3(us): 25.6

TR 4(us): 8.5

Max P1: 70.1Max P2: 78.4Max P3: 75.2Max P4: 79.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31 31.2 31.4 31.6 31.8 32 32.2-10

0

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 654.23-4: 766.4Avg: 708.8T

R 1(us): 213.1

TR 2(us): 73.9

TR 3(us): 14.2

TR 4(us): 11.4

Max P1: 83.7Max P2: 70.1Max P3: 71.7Max P4: 72.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39 39.2 39.4 39.6 39.8 40 40.20

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 570.73-4: 654.2Avg: 616.2T

R 1(us): 477.3

TR 2(us): 335.2

TR 3(us): 22.7

TR 4(us): 14.2

Max P1: 41.7Max P2: 37.1Max P3: 37.5Max P4: 36.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.4 30.6 30.8 31 31.2 31.4 31.60

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 654.23-4: 654.2Avg: 634.8T

R 1(us): 366.5

TR 2(us): 17.0

TR 3(us): 14.2

TR 4(us): 11.4

Max P1: 42.3Max P2: 42.5Max P3: 42.2Max P4: 40.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.6 29.8 30 30.2 30.4 30.6 30.8 310

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 638.63-4: 638.6Avg: 620.1T

R 1(us): 28.4

TR 2(us): 14.2

TR 3(us): 14.2

TR 4(us): 8.5

Max P1: 38.1Max P2: 39.8Max P3: 40.8Max P4: 40.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.6 29.8 30 30.2 30.4 30.6 30.80

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 525.92-3: 515.83-4: 583.1Avg: 541.6T

R 1(us): 667.6

TR 2(us): 613.6

TR 3(us): 25.6

TR 4(us): 22.7

Max P1: 25.2Max P2: 25.5Max P3: 32.7Max P4: 31.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 102: Design and Optimization of a Deflagration to Detonation ...

92

Figure 175 - 17 S45D4+1 BR60_100percL=1.2

Figure 176 - 17 S45D4+1 BR60_100percL=1.4

Figure 177 - 17 S45D4+1 BR60_100percL=1.6

Figure 178 - 17 S45D4+1 BR60_100percL=1.8

Figure 179 - 17 S45D4+1 BR60_120percL=1.2

Figure 180 - 17 S45D4+1 BR60_120percL=1.4

34.6 34.8 35 35.2 35.4 35.6 35.80

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 623.83-4: 654.2Avg: 620.4T

R 1(us): 360.8

TR 2(us): 457.4

TR 3(us): 386.4

TR 4(us): 14.2

Max P1: 46.0Max P2: 45.3Max P3: 42.8Max P4: 43.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.2 29.4 29.6 29.8 30 30.2 30.4-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 670.63-4: 670.6Avg: 665.1T

R 1(us): 14.2

TR 2(us): 14.2

TR 3(us): 14.2

TR 4(us): 11.4

Max P1: 46.6Max P2: 47.1Max P3: 44.5Max P4: 47.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.4 29.6 29.8 30 30.2 30.4 30.6 30.80

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 609.63-4: 638.6Avg: 606.3T

R 1(us): 338.1

TR 2(us): 19.9

TR 3(us): 14.2

TR 4(us): 17.0

Max P1: 32.7Max P2: 37.3Max P3: 36.6Max P4: 38.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.4 29.6 29.8 30 30.2 30.4 30.6 30.80

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 496.72-3: 506.13-4: 506.1Avg: 503.0T

R 1(us): 448.9

TR 2(us): 386.4

TR 3(us): 329.5

TR 4(us): 42.6

Max P1: 27.1Max P2: 26.2Max P3: 25.8Max P4: 25.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39 39.2 39.4 39.6 39.8 40 40.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 3831.82-3: 525.93-4: 496.7Avg: 1618.1T

R 1(us): 400.6

TR 2(us): 733.0

TR 3(us): 519.9

TR 4(us): 440.3

Max P1: 36.6Max P2: 33.9Max P3: 32.2Max P4: 29.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.2 29.4 29.6 29.8 30 30.2 30.4-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 670.63-4: 687.8Avg: 665.6T

R 1(us): 19.9

TR 2(us): 11.4

TR 3(us): 14.2

TR 4(us): 14.2

Max P1: 47.3Max P2: 47.3Max P3: 48.6Max P4: 46.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 103: Design and Optimization of a Deflagration to Detonation ...

93

Figure 181 - 17 S45D4+1 BR60_120percL=1.6

Figure 182 - 17 S45D4+1 BR60_120percL=1.8

Figure 183 - 18 S45D4+1 BR60_80percL=1.2

Figure 184 - 18 S45D4+1 BR60_80percL=1.4

Figure 185 - 18 S45D4+1 BR60_80percL=1.6

Figure 186 - 18 S45D4+1 BR60_80percL=1.8

28.6 28.8 29 29.2 29.4 29.6 29.8-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 654.23-4: 687.8Avg: 655.2T

R 1(us): 19.9

TR 2(us): 14.2

TR 3(us): 14.2

TR 4(us): 14.2

Max P1: 42.2Max P2: 45.0Max P3: 45.8Max P4: 45.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30 30.2 30.4 30.6 30.8 31 31.20

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 654.23-4: 654.2Avg: 626.4T

R 1(us): 377.8

TR 2(us): 14.2

TR 3(us): 17.0

TR 4(us): 14.2

Max P1: 37.7Max P2: 41.5Max P3: 41.5Max P4: 41.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.4 37.6 37.8 38 38.2 38.4 38.6 38.8-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 596.13-4: 654.2Avg: 629.6T

R 1(us): 471.6

TR 2(us): 500.0

TR 3(us): 397.7

TR 4(us): 403.4

Max P1: 35.4Max P2: 34.8Max P3: 41.8Max P4: 46.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

40.2 40.4 40.6 40.8 41 41.2 41.40

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 6705.62-3: 654.23-4: 570.7Avg: 2643.5T

R 1(us): 661.9

TR 2(us): 485.8

TR 3(us): 576.7

TR 4(us): 377.8

Max P1: 21.8Max P2: 24.4Max P3: 25.8Max P4: 26.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41.8 42 42.2 42.4 42.6 42.8 43 43.22

4

6

8

10

12

14

16

18

20

22

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 1072.9Avg: InfT

R 1(us): 497.2

TR 2(us): 554.0

TR 3(us): 539.8

TR 4(us): 502.8

Max P1: 17.9Max P2: 19.4Max P3: 18.6Max P4: 20.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

48.6 48.8 49 49.2 49.4 49.6 49.8 501

1.5

2

2.5

3

3.5

4

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 1051.1

TR 2(us): 872.2

TR 3(us): 650.6

TR 4(us): 497.2

Max P1: 3.8Max P2: 3.7Max P3: 3.9Max P4: 3.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 104: Design and Optimization of a Deflagration to Detonation ...

94

Figure 187 - 18 S45D4+1 BR60_100percL=1.2

Figure 188 - 18 S45D4+1 BR60_100percL=1.4

Figure 189 - 18 S45D4+1 BR60_100percL=1.6

Figure 190 - 18 S45D4+1 BR60_100percL=1.8

Figure 191 - 18 S45D4+1 BR60_120percL=1.2

Figure 192 - 18 S45D4+1 BR60_120percL=1.4

40 40.2 40.4 40.6 40.8 41 41.2 41.4-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 1072.93-4: 536.4Avg: 765.7T

R 1(us): 363.6

TR 2(us): 397.7

TR 3(us): 474.4

TR 4(us): 377.8

Max P1: 38.6Max P2: 39.8Max P3: 43.5Max P4: 54.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.6 38.8 39 39.2 39.4 39.6 39.8 40-5

0

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1411.72-3: 654.23-4: 623.8Avg: 896.6T

R 1(us): 497.2

TR 2(us): 485.8

TR 3(us): 477.3

TR 4(us): 278.4

Max P1: 34.1Max P2: 39.9Max P3: 42.3Max P4: 40.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.4 39.6 39.8 40 40.2 40.4 40.6 40.80

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 596.13-4: 583.1Avg: InfT

R 1(us): 497.2

TR 2(us): 741.5

TR 3(us): 485.8

TR 4(us): 627.8

Max P1: 24.7Max P2: 26.5Max P3: 30.9Max P4: 31.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

44.8 45 45.2 45.4 45.6 45.8 46 46.20

2

4

6

8

10

12

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 585.2

TR 2(us): 568.2

TR 3(us): 497.2

TR 4(us): 576.7

Max P1: 11.7Max P2: 11.8Max P3: 11.7Max P4: 11.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

42.4 42.6 42.8 43 43.2 43.4 43.60

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1031.63-4: 583.1Avg: InfT

R 1(us): 613.6

TR 2(us): 497.2

TR 3(us): 536.9

TR 4(us): 360.8

Max P1: 35.9Max P2: 36.0Max P3: 38.1Max P4: 42.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.2 37.4 37.6 37.8 38 38.2 38.4 38.6-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 924.92-3: 609.63-4: 570.7Avg: 701.7T

R 1(us): 497.2

TR 2(us): 571.0

TR 3(us): 431.8

TR 4(us): 332.4

Max P1: 37.8Max P2: 43.9Max P3: 42.7Max P4: 49.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 105: Design and Optimization of a Deflagration to Detonation ...

95

Figure 193 - 18 S45D4+1 BR60_120percL=1.6

Figure 194 - 18 S45D4+1 BR60_120percL=1.8

Figure 195 - 19 S6D3+1 BR60_80percL=1.2

Figure 196 - 19 S6D3+1 BR60_80percL=1.4

Figure 197 - 19 S6D3+1 BR60_80percL=1.6

Figure 198 - 19 S6D3+1 BR60_80percL=1.8

38.6 38.8 39 39.2 39.4 39.6 39.8 400

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 4470.42-3: 583.13-4: 547.4Avg: 1867.0T

R 1(us): 491.5

TR 2(us): 784.1

TR 3(us): 667.6

TR 4(us): 397.7

Max P1: 28.8Max P2: 32.0Max P3: 31.6Max P4: 35.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

44.4 44.6 44.8 45 45.2 45.4 45.60

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 4470.4Avg: InfT

R 1(us): 605.1

TR 2(us): 497.2

TR 3(us): 534.1

TR 4(us): 519.9

Max P1: 19.4Max P2: 19.3Max P3: 19.6Max P4: 21.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41.8 42 42.2 42.4 42.6 42.8 430

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 547.42-3: 547.43-4: 583.1Avg: 559.3T

R 1(us): 369.3

TR 2(us): 463.1

TR 3(us): 423.3

TR 4(us): 363.6

Max P1: 33.1Max P2: 32.4Max P3: 32.9Max P4: 30.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33 33.2 33.4 33.6 33.8 34 34.2 34.4-5

0

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 654.23-4: 654.2Avg: 649.0T

R 1(us): 108.0

TR 2(us): 17.0

TR 3(us): 17.0

TR 4(us): 19.9

Max P1: 40.6Max P2: 42.1Max P3: 39.5Max P4: 41.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.6 31.8 32 32.2 32.4 32.6 32.80

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 609.63-4: 638.6Avg: 619.3T

R 1(us): 19.9

TR 2(us): 19.9

TR 3(us): 14.2

TR 4(us): 17.0

Max P1: 32.3Max P2: 35.3Max P3: 34.5Max P4: 32.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.2 30.4 30.6 30.8 31 31.2 31.4 31.60

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 547.42-3: 558.83-4: 596.1Avg: 567.4T

R 1(us): 483.0

TR 2(us): 125.0

TR 3(us): 96.6

TR 4(us): 28.4

Max P1: 24.4Max P2: 25.0Max P3: 26.0Max P4: 25.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 106: Design and Optimization of a Deflagration to Detonation ...

96

Figure 199 - 19 S6D3+1 BR60_100percL=1.2

Figure 200 - 19 S6D3+1 BR60_100percL=1.4

Figure 201 - 19 S6D3+1 BR60_100percL=1.6

Figure 202 - 19 S6D3+1 BR60_100percL=1.8

Figure 203 - 19 S6D3+1 BR60_120percL=1.2

Figure 204 - 19 S6D3+1 BR60_120percL=1.4

48.8 49 49.2 49.4 49.6 49.8 500

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 506.12-3: 547.43-4: 570.7Avg: 541.4T

R 1(us): 468.8

TR 2(us): 372.2

TR 3(us): 437.5

TR 4(us): 261.4

Max P1: 27.4Max P2: 27.8Max P3: 26.9Max P4: 23.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.6 35.8 36 36.2 36.4 36.6 36.8 370

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 623.83-4: 638.6Avg: 619.5T

R 1(us): 375.0

TR 2(us): 329.5

TR 3(us): 19.9

TR 4(us): 17.0

Max P1: 41.0Max P2: 43.0Max P3: 38.5Max P4: 42.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.2 33.4 33.6 33.8 34 34.2 34.4 34.6-5

0

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 654.23-4: 654.2Avg: 644.1T

R 1(us): 565.3

TR 2(us): 17.0

TR 3(us): 17.0

TR 4(us): 14.2

Max P1: 38.2Max P2: 41.9Max P3: 43.0Max P4: 39.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.2 29.4 29.6 29.8 30 30.2 30.4 30.60

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 596.13-4: 609.6Avg: 600.6T

R 1(us): 19.9

TR 2(us): 22.7

TR 3(us): 22.7

TR 4(us): 17.0

Max P1: 30.1Max P2: 29.3Max P3: 31.7Max P4: 30.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

44.4 44.6 44.8 45 45.2 45.4 45.60

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 515.83-4: 609.6Avg: 565.4T

R 1(us): 366.5

TR 2(us): 318.2

TR 3(us): 264.2

TR 4(us): 360.8

Max P1: 32.6Max P2: 29.6Max P3: 29.7Max P4: 26.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.2 34.4 34.6 34.8 35 35.2 35.4 35.60

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 638.63-4: 638.6Avg: 629.0T

R 1(us): 389.2

TR 2(us): 340.9

TR 3(us): 17.0

TR 4(us): 11.4

Max P1: 42.8Max P2: 41.3Max P3: 39.6Max P4: 41.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 107: Design and Optimization of a Deflagration to Detonation ...

97

Figure 205 - 19 S6D3+1 BR60_120percL=1.6

Figure 206 - 19 S6D3+1 BR60_120percL=1.8

Figure 207 - 20 S6D3+1 BR60 INV_80percL=1.2

Figure 208 - 20 S6D3+1 BR60 INV_80percL=1.4

Figure 209 - 20 S6D3+1 BR60 INV_80percL=1.6

Figure 210 - 20 S6D3+1 BR60 INV_80percL=1.8

29.6 29.8 30 30.2 30.4 30.6 30.8-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 638.63-4: 670.6Avg: 649.3T

R 1(us): 355.1

TR 2(us): 19.9

TR 3(us): 14.2

TR 4(us): 11.4

Max P1: 41.4Max P2: 46.4Max P3: 43.3Max P4: 41.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30 30.2 30.4 30.6 30.8 31 31.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 609.63-4: 638.6Avg: 619.3T

R 1(us): 369.3

TR 2(us): 19.9

TR 3(us): 17.0

TR 4(us): 17.0

Max P1: 33.7Max P2: 36.9Max P3: 35.7Max P4: 34.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

50.8 51 51.2 51.4 51.6 51.8 52 52.20

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 2235.22-3: 558.83-4: 596.1Avg: 1130.0T

R 1(us): 497.2

TR 2(us): 855.1

TR 3(us): 585.2

TR 4(us): 295.5

Max P1: 29.0Max P2: 31.3Max P3: 32.7Max P4: 33.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

43.8 44 44.2 44.4 44.6 44.8 45-5

0

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 570.73-4: 623.8Avg: 601.4T

R 1(us): 497.2

TR 2(us): 536.9

TR 3(us): 429.0

TR 4(us): 642.0

Max P1: 28.1Max P2: 31.6Max P3: 32.5Max P4: 31.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41.2 41.4 41.6 41.8 42 42.2 42.4 42.60

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 924.93-4: 570.7Avg: InfT

R 1(us): 556.8

TR 2(us): 497.2

TR 3(us): 497.2

TR 4(us): 519.9

Max P1: 25.2Max P2: 21.4Max P3: 24.7Max P4: 23.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

44.8 45 45.2 45.4 45.6 45.8 46 46.21

2

3

4

5

6

7

8

9

10

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 778.4

TR 2(us): 556.8

TR 3(us): 497.2

TR 4(us): 849.4

Max P1: 9.0Max P2: 8.3Max P3: 8.0Max P4: 8.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 108: Design and Optimization of a Deflagration to Detonation ...

98

Figure 211 - 20 S6D3+1 BR60 INV_100percL=1.2

Figure 212 - 20 S6D3+1 BR60 INV_100percL=1.4

Figure 213 - 20 S6D3+1 BR60 INV_100percL=1.6

Figure 214 - 20 S6D3+1 BR60 INV_100percL=1.8

Figure 215 - 20 S6D3+1 BR60 INV_120percL=1.2

Figure 216 - 20 S6D3+1 BR60 INV_120percL=1.4

56 56.2 56.4 56.6 56.8 57 57.2 57.40

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 957.93-4: 525.9Avg: InfT

R 1(us): 750.0

TR 2(us): 505.7

TR 3(us): 417.6

TR 4(us): 315.3

Max P1: 24.6Max P2: 26.1Max P3: 27.3Max P4: 31.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

43 43.2 43.4 43.6 43.8 44 44.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 6705.62-3: 609.63-4: 609.6Avg: 2641.6T

R 1(us): 528.4

TR 2(us): 485.8

TR 3(us): 502.8

TR 4(us): 275.6

Max P1: 30.4Max P2: 33.1Max P3: 35.6Max P4: 36.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

44.6 44.8 45 45.2 45.4 45.6 45.8 460

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 596.13-4: 570.7Avg: 612.4T

R 1(us): 650.6

TR 2(us): 383.5

TR 3(us): 545.5

TR 4(us): 471.6

Max P1: 27.1Max P2: 30.1Max P3: 34.4Max P4: 34.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

43 43.2 43.4 43.6 43.8 44 44.20

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 957.93-4: 583.1Avg: InfT

R 1(us): 497.2

TR 2(us): 590.9

TR 3(us): 556.8

TR 4(us): 571.0

Max P1: 21.3Max P2: 22.9Max P3: 23.2Max P4: 25.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

71.4 71.6 71.8 72 72.2 72.4 72.6-2

0

2

4

6

8

10

12

14

16

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 1219.2Avg: InfT

R 1(us): 497.2

TR 2(us): 542.6

TR 3(us): 571.0

TR 4(us): 539.8

Max P1: 13.5Max P2: 14.5Max P3: 14.7Max P4: 15.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

42.6 42.8 43 43.2 43.4 43.6 43.8 440

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 894.12-3: 687.83-4: 638.6Avg: 740.2T

R 1(us): 497.2

TR 2(us): 480.1

TR 3(us): 355.1

TR 4(us): 400.6

Max P1: 40.2Max P2: 39.6Max P3: 43.6Max P4: 47.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 109: Design and Optimization of a Deflagration to Detonation ...

99

Figure 217 - 20 S6D3+1 BR60 INV_120percL=1.6

Figure 218 - 20 S6D3+1 BR60 INV_120percL=1.8

Figure 219 - 21 S6D6+1 BR60_80percL=1.2

Figure 220 - 21 S6D6+1 BR60_80percL=1.4

Figure 221 - 21 S6D6+1 BR60_80percL=1.6

Figure 222 - 21 S6D6+1 BR60_80percL=1.8

41.4 41.6 41.8 42 42.2 42.4 42.6 42.8-5

0

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 957.92-3: 596.13-4: 583.1Avg: 712.4T

R 1(us): 565.3

TR 2(us): 417.6

TR 3(us): 411.9

TR 4(us): 514.2

Max P1: 33.9Max P2: 39.0Max P3: 42.3Max P4: 43.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41 41.2 41.4 41.6 41.8 42 42.20

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 788.92-3: 570.73-4: 570.7Avg: 643.4T

R 1(us): 497.2

TR 2(us): 582.4

TR 3(us): 400.6

TR 4(us): 411.9

Max P1: 27.8Max P2: 28.4Max P3: 29.2Max P4: 29.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36 36.2 36.4 36.6 36.8 37 37.2 37.4-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 687.83-4: 687.8Avg: 693.8T

R 1(us): 14.2

TR 2(us): 210.2

TR 3(us): 170.5

TR 4(us): 133.5

Max P1: 58.6Max P2: 53.0Max P3: 65.5Max P4: 56.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.8 32 32.2 32.4 32.6 32.8 33 33.20

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 654.23-4: 638.6Avg: 643.8T

R 1(us): 176.1

TR 2(us): 17.0

TR 3(us): 227.3

TR 4(us): 11.4

Max P1: 37.2Max P2: 40.2Max P3: 39.3Max P4: 37.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34 34.2 34.4 34.6 34.8 35 35.2 35.40

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 547.42-3: 525.93-4: 570.7Avg: 548.0T

R 1(us): 747.2

TR 2(us): 554.0

TR 3(us): 34.1

TR 4(us): 11.4

Max P1: 25.2Max P2: 24.5Max P3: 26.3Max P4: 24.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

40.4 40.6 40.8 41 41.2 41.4 41.63

4

5

6

7

8

9

10

11

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 1250.0

TR 3(us): 954.5

TR 4(us): 838.1

Max P1: 10.0Max P2: 9.8Max P3: 8.9Max P4: 9.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 110: Design and Optimization of a Deflagration to Detonation ...

100

Figure 223 - 21 S6D6+1 BR60_100percL=1.2

Figure 224 - 21 S6D6+1 BR60_100percL=1.4

Figure 225 - 21 S6D6+1 BR60_100percL=1.6

Figure 226 - 21 S6D6+1 BR60_100percL=1.8

Figure 227 - 21 S6D6+1 BR60_120percL=1.2

Figure 228 - 21 S6D6+1 BR60_120percL=1.3

35 35.2 35.4 35.6 35.8 36 36.2-10

0

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 670.63-4: 745.1Avg: 701.1T

R 1(us): 241.5

TR 2(us): 193.2

TR 3(us): 127.8

TR 4(us): 11.4

Max P1: 61.9Max P2: 78.4Max P3: 72.2Max P4: 63.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33 33.2 33.4 33.6 33.8 34 34.2 34.4-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 705.93-4: 687.8Avg: 693.8T

R 1(us): 14.2

TR 2(us): 210.2

TR 3(us): 164.8

TR 4(us): 11.4

Max P1: 55.6Max P2: 50.3Max P3: 50.9Max P4: 51.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.4 32.6 32.8 33 33.2 33.4 33.6 33.80

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 638.63-4: 654.2Avg: 638.9T

R 1(us): 284.1

TR 2(us): 230.1

TR 3(us): 187.5

TR 4(us): 142.0

Max P1: 42.2Max P2: 48.8Max P3: 49.8Max P4: 44.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.4 36.6 36.8 37 37.2 37.4 37.6 37.80

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 2980.32-3: 506.13-4: 558.8Avg: 1348.4T

R 1(us): 556.8

TR 2(us): 471.6

TR 3(us): 366.5

TR 4(us): 292.6

Max P1: 28.7Max P2: 26.5Max P3: 30.5Max P4: 27.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

52.2 52.4 52.6 52.8 53 53.2 53.4 53.60

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 724.93-4: 638.6Avg: 696.2T

R 1(us): 676.1

TR 2(us): 392.0

TR 3(us): 329.5

TR 4(us): 329.5

Max P1: 50.0Max P2: 62.3Max P3: 64.4Max P4: 53.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.8 39 39.2 39.4 39.6 39.8 400

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 670.63-4: 724.9Avg: 688.7T

R 1(us): 360.8

TR 2(us): 306.8

TR 3(us): 122.2

TR 4(us): 11.4

Max P1: 60.6Max P2: 70.4Max P3: 64.5Max P4: 61.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 111: Design and Optimization of a Deflagration to Detonation ...

101

Figure 229 - 21 S6D6+1 BR60_120percL=1.4

Figure 230 - 21 S6D6+1 BR60_120percL=1.5

Figure 231 - 21 S6D6+1 BR60_120percL=1.6

Figure 232 - 21 S6D6+1 BR60_120percL=1.8

Figure 233 - 21 S6D6+1 BR60_150percL=1.3

Figure 234 - 21 S6D6+1 BR60_150percL=1.4

39.4 39.6 39.8 40 40.2 40.4 40.60

10

20

30

40

50

60

70

80

90

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 687.83-4: 670.6Avg: 688.1T

R 1(us): 244.3

TR 2(us): 184.7

TR 3(us): 136.4

TR 4(us): 213.1

Max P1: 68.3Max P2: 74.8Max P3: 96.0Max P4: 80.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.4 33.6 33.8 34 34.2 34.4 34.60

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 670.63-4: 724.9Avg: 688.7T

R 1(us): 252.8

TR 2(us): 335.2

TR 3(us): 286.9

TR 4(us): 11.4

Max P1: 51.9Max P2: 54.0Max P3: 69.3Max P4: 59.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.2 35.4 35.6 35.8 36 36.2 36.4 36.6-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 705.93-4: 705.9Avg: 705.9T

R 1(us): 252.8

TR 2(us): 207.4

TR 3(us): 161.9

TR 4(us): 17.0

Max P1: 58.8Max P2: 67.9Max P3: 60.0Max P4: 48.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.6 34.8 35 35.2 35.4 35.6 35.8 360

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 638.63-4: 638.6Avg: 638.6T

R 1(us): 284.1

TR 2(us): 423.3

TR 3(us): 343.8

TR 4(us): 19.9

Max P1: 41.1Max P2: 46.0Max P3: 41.2Max P4: 40.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.4 32.6 32.8 33 33.2 33.4 33.6 33.8-20

0

20

40

60

80

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 705.93-4: 745.1Avg: 725.3T

R 1(us): 329.5

TR 2(us): 179.0

TR 3(us): 125.0

TR 4(us): 431.8

Max P1: 96.7Max P2: 95.8Max P3: 96.2Max P4: 77.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.4 31.6 31.8 32 32.2 32.4 32.6-10

0

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 687.83-4: 705.9Avg: 706.2T

R 1(us): 545.5

TR 2(us): 193.2

TR 3(us): 133.5

TR 4(us): 238.6

Max P1: 66.9Max P2: 71.6Max P3: 80.5Max P4: 69.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 112: Design and Optimization of a Deflagration to Detonation ...

102

Figure 235 - 21 S6D6+1 BR60_150percL=1.5

Figure 236 - 21 S6D6+1 BR60_1500percL=1.4

Figure 237 - 22 S2D12+2 BR 60_80percL=1.2

Figure 238 - 22 S2D12+2 BR 60_80percL=1.4

Figure 239 - 22 S2D12+2 BR 60_80percL=1.6

Figure 240 - 22 S2D12+2 BR 60_80percL=1.8

33.2 33.4 33.6 33.8 34 34.2 34.4 34.6-10

0

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 745.12-3: 705.93-4: 705.9Avg: 718.9T

R 1(us): 11.4

TR 2(us): 196.0

TR 3(us): 142.0

TR 4(us): 8.5

Max P1: 63.3Max P2: 64.0Max P3: 71.3Max P4: 58.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.4 31.6 31.8 32 32.2 32.4 32.6-10

0

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 687.83-4: 705.9Avg: 706.2T

R 1(us): 545.5

TR 2(us): 193.2

TR 3(us): 133.5

TR 4(us): 238.6

Max P1: 66.9Max P2: 71.6Max P3: 80.5Max P4: 69.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.8 37 37.2 37.4 37.6 37.8 38 38.2-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 670.63-4: 687.8Avg: 682.0T

R 1(us): 8.5

TR 2(us): 568.2

TR 3(us): 491.5

TR 4(us): 11.4

Max P1: 42.5Max P2: 43.5Max P3: 49.4Max P4: 50.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.4 37.6 37.8 38 38.2 38.4 38.60

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 539.8

TR 3(us): 548.3

TR 4(us): 568.2

Max P1: 20.7Max P2: 21.8Max P3: 23.5Max P4: 25.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41.4 41.6 41.8 42 42.2 42.4 42.6 42.83

4

5

6

7

8

9

10

11

12

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 525.6

TR 2(us): 616.5

TR 3(us): 497.2

TR 4(us): 764.2

Max P1: 11.3Max P2: 10.7Max P3: 10.2Max P4: 9.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

45.6 45.8 46 46.2 46.4 46.6 46.8 47-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 852.3

TR 3(us): 1346.6

TR 4(us): 443.2

Max P1: 1.3Max P2: 1.5Max P3: 1.3Max P4: 1.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 113: Design and Optimization of a Deflagration to Detonation ...

103

Figure 241 - 22 S2D12+2 BR 60_100percL=1.0

Figure 242 - 22 S2D12+2 BR 60_100percL=1.2

Figure 243 - 22 S2D12+2 BR 60_100percL=1.4

Figure 244 - 22 S2D12+2 BR 60_100percL=1.6

Figure 245 - 22 S2D12+2 BR 60_100percL=1.8

Figure 246 - 22 S2D12+2 BR 60_120percL=1.2

42.8 43 43.2 43.4 43.6 43.8 44 44.20

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 2980.33-4: 654.2Avg: InfT

R 1(us): 559.7

TR 2(us): 497.2

TR 3(us): 545.5

TR 4(us): 409.1

Max P1: 38.7Max P2: 42.8Max P3: 43.3Max P4: 47.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.4 34.6 34.8 35 35.2 35.4 35.6-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 724.93-4: 812.8Avg: 736.1T

R 1(us): 423.3

TR 2(us): 187.5

TR 3(us): 8.5

TR 4(us): 11.4

Max P1: 45.9Max P2: 49.1Max P3: 62.4Max P4: 60.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.6 35.8 36 36.2 36.4 36.6 36.8 37-10

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 4470.42-3: 638.63-4: 623.8Avg: 1910.9T

R 1(us): 485.8

TR 2(us): 576.7

TR 3(us): 491.5

TR 4(us): 437.5

Max P1: 41.0Max P2: 46.1Max P3: 42.2Max P4: 39.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.6 37.8 38 38.2 38.4 38.6 38.84

6

8

10

12

14

16

18

20

22

24

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 1277.3Avg: InfT

R 1(us): 818.2

TR 2(us): 497.2

TR 3(us): 826.7

TR 4(us): 730.1

Max P1: 20.0Max P2: 20.5Max P3: 20.9Max P4: 22.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

43.8 44 44.2 44.4 44.6 44.8 451

2

3

4

5

6

7

8

9

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 548.3

TR 3(us): 934.7

TR 4(us): 647.7

Max P1: 8.1Max P2: 7.7Max P3: 7.6Max P4: 7.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.8 37 37.2 37.4 37.6 37.8 38 38.2-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 638.63-4: 788.9Avg: 683.8T

R 1(us): 454.5

TR 2(us): 363.6

TR 3(us): 258.5

TR 4(us): 11.4

Max P1: 54.4Max P2: 55.9Max P3: 56.4Max P4: 69.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 114: Design and Optimization of a Deflagration to Detonation ...

104

Figure 247 - 22 S2D12+2 BR 60_120percL=1.4

Figure 248 - 22 S2D12+2 BR 60_120percL=1.6

Figure 249 - 22 S2D12+2 BR 60_120percL=1.8

Figure 250 - 23 S2D12+2 BR60 INV_80percL=1.2

Figure 251 - 23 S2D12+2 BR60 INV_80percL=1.4

Figure 252 - 23 S2D12+2 BR60 INV_80percL=1.6

35.6 35.8 36 36.2 36.4 36.6 36.8 37-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 687.83-4: 724.9Avg: 694.4T

R 1(us): 721.6

TR 2(us): 389.2

TR 3(us): 332.4

TR 4(us): 8.5

Max P1: 41.2Max P2: 43.7Max P3: 58.8Max P4: 59.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.2 37.4 37.6 37.8 38 38.2 38.4 38.60

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 3831.8Avg: InfT

R 1(us): 497.2

TR 2(us): 531.3

TR 3(us): 715.9

TR 4(us): 602.3

Max P1: 25.0Max P2: 28.2Max P3: 27.2Max P4: 30.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41.8 42 42.2 42.4 42.6 42.8 43 43.20

5

10

15

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 571.0

TR 2(us): 585.2

TR 3(us): 582.4

TR 4(us): 497.2

Max P1: 14.1Max P2: 13.5Max P3: 13.1Max P4: 12.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.4 32.6 32.8 33 33.2 33.4 33.6-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 766.42-3: 788.93-4: 812.8Avg: 789.3T

R 1(us): 11.4

TR 2(us): 8.5

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 66.4Max P2: 63.4Max P3: 68.3Max P4: 60.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29 29.2 29.4 29.6 29.8 30 30.2-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 766.42-3: 745.13-4: 766.4Avg: 759.3T

R 1(us): 11.4

TR 2(us): 19.9

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 69.2Max P2: 58.0Max P3: 58.8Max P4: 53.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.2 29.4 29.6 29.8 30 30.2 30.4-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 724.93-4: 724.9Avg: 718.6T

R 1(us): 11.4

TR 2(us): 11.4

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 55.6Max P2: 50.7Max P3: 47.2Max P4: 46.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 115: Design and Optimization of a Deflagration to Detonation ...

105

Figure 253 - 23 S2D12+2 BR60 INV_80percL=1.8

Figure 254 - 23 S2D12+2 BR60 INV_100percL=1.2

Figure 255 - 23 S2D12+2 BR60 INV_100percL=1.4

Figure 256 - 23 S2D12+2 BR60 INV_100percL=1.6

Figure 257 - 23 S2D12+2 BR60 INV_100percL=1.8

Figure 258 - 23 S2D12+2 BR60 INV_120percL=1.2

29 29.2 29.4 29.6 29.8 30 30.2 30.40

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 558.82-3: 558.83-4: 547.4Avg: 555.0T

R 1(us): 497.2

TR 2(us): 136.4

TR 3(us): 116.5

TR 4(us): 511.4

Max P1: 26.0Max P2: 26.4Max P3: 27.4Max P4: 24.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.2 33.4 33.6 33.8 34 34.2 34.4 34.6-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 745.12-3: 766.43-4: 766.4Avg: 759.3T

R 1(us): 11.4

TR 2(us): 11.4

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 59.3Max P2: 58.9Max P3: 60.9Max P4: 61.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.2 29.4 29.6 29.8 30 30.2 30.4-10

0

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 812.82-3: 766.43-4: 788.9Avg: 789.3T

R 1(us): 8.5

TR 2(us): 11.4

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 78.0Max P2: 64.4Max P3: 61.7Max P4: 59.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.6 28.8 29 29.2 29.4 29.6 29.8 30-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 745.12-3: 724.93-4: 766.4Avg: 745.5T

R 1(us): 11.4

TR 2(us): 14.2

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 61.1Max P2: 56.0Max P3: 60.2Max P4: 59.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.6 29.8 30 30.2 30.4 30.6 30.80

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 547.42-3: 623.83-4: 638.6Avg: 603.3T

R 1(us): 125.0

TR 2(us): 19.9

TR 3(us): 34.1

TR 4(us): 11.4

Max P1: 36.6Max P2: 38.9Max P3: 41.9Max P4: 45.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.6 31.8 32 32.2 32.4 32.6 32.8-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 766.42-3: 745.13-4: 766.4Avg: 759.3T

R 1(us): 8.5

TR 2(us): 11.4

TR 3(us): 11.4

TR 4(us): 8.5

Max P1: 66.4Max P2: 59.8Max P3: 63.4Max P4: 58.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 116: Design and Optimization of a Deflagration to Detonation ...

106

Figure 259 - 23 S2D12+2 BR60 INV_120percL=1.4

Figure 260 -23 S2D12+2 BR60 INV_120percL=1.6

Figure 261 - 23 S2D12+2 BR60 INV_120percL=1.8

Figure 262 - 24 S3D12+2 BR45_80percL=1.2

Figure 263 - 24 S3D12+2 BR45_80percL=1.4

Figure 264 - 24 S3D12+2 BR45_80percL=1.6

28.6 28.8 29 29.2 29.4 29.6 29.8 30-10

0

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 812.82-3: 766.43-4: 788.9Avg: 789.3T

R 1(us): 8.5

TR 2(us): 11.4

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 77.7Max P2: 63.8Max P3: 66.9Max P4: 56.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29 29.2 29.4 29.6 29.8 30 30.2 30.4-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 745.12-3: 745.13-4: 788.9Avg: 759.7T

R 1(us): 11.4

TR 2(us): 8.5

TR 3(us): 8.5

TR 4(us): 8.5

Max P1: 68.7Max P2: 58.6Max P3: 63.3Max P4: 56.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.6 29.8 30 30.2 30.4 30.6 30.8 310

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 654.23-4: 687.8Avg: 641.7T

R 1(us): 289.8

TR 2(us): 19.9

TR 3(us): 14.2

TR 4(us): 8.5

Max P1: 36.9Max P2: 46.0Max P3: 45.6Max P4: 45.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

45.4 45.6 45.8 46 46.2 46.4 46.6 46.8-10

0

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 788.92-3: 812.83-4: 838.2Avg: 813.3T

R 1(us): 31.3

TR 2(us): 11.4

TR 3(us): 14.2

TR 4(us): 8.5

Max P1: 75.6Max P2: 66.7Max P3: 79.4Max P4: 72.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.6 33.8 34 34.2 34.4 34.6 34.80

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 788.92-3: 812.83-4: 788.9Avg: 796.9T

R 1(us): 28.4

TR 2(us): 8.5

TR 3(us): 28.4

TR 4(us): 8.5

Max P1: 75.0Max P2: 68.0Max P3: 65.1Max P4: 70.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.6 30.8 31 31.2 31.4 31.6 31.8 320

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 745.13-4: 745.1Avg: 738.4T

R 1(us): 17.0

TR 2(us): 14.2

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 53.5Max P2: 63.5Max P3: 52.2Max P4: 66.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 117: Design and Optimization of a Deflagration to Detonation ...

107

Figure 265 - 24 S3D12+2 BR45_80percL=1.8

Figure 266 - 24 S3D12+2 BR45_100percL=1.2

Figure 267 - 24 S3D12+2 BR45_100percL=1.4

Figure 268 - 24 S3D12+2 BR45_100percL=1.6

Figure 269 - 24 S3D12+2 BR45_100percL=1.8

Figure 270 - 24 S3D12+2 BR45_120percL=1.2

31.6 31.8 32 32.2 32.4 32.6 32.80

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 638.63-4: 654.2Avg: 629.6T

R 1(us): 215.9

TR 2(us): 17.0

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 33.5Max P2: 35.3Max P3: 38.2Max P4: 38.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

44.4 44.6 44.8 45 45.2 45.4 45.6 45.80

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 766.42-3: 766.43-4: 812.8Avg: 781.8T

R 1(us): 133.5

TR 2(us): 90.9

TR 3(us): 116.5

TR 4(us): 11.4

Max P1: 66.8Max P2: 67.7Max P3: 81.5Max P4: 72.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.4 39.6 39.8 40 40.2 40.4 40.6 40.8-20

0

20

40

60

80

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 894.12-3: 838.23-4: 894.1Avg: 875.5T

R 1(us): 5.7

TR 2(us): 25.6

TR 3(us): 5.7

TR 4(us): 8.5

Max P1: 93.0Max P2: 92.1Max P3: 82.5Max P4: 76.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.2 31.4 31.6 31.8 32 32.2 32.4-10

0

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 812.82-3: 812.83-4: 838.2Avg: 821.3T

R 1(us): 17.0

TR 2(us): 11.4

TR 3(us): 11.4

TR 4(us): 8.5

Max P1: 81.1Max P2: 70.5Max P3: 87.8Max P4: 72.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.2 31.4 31.6 31.8 32 32.2 32.40

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 766.43-4: 766.4Avg: 746.2T

R 1(us): 156.3

TR 2(us): 11.4

TR 3(us): 28.4

TR 4(us): 8.5

Max P1: 59.0Max P2: 67.8Max P3: 60.3Max P4: 64.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.6 39.8 40 40.2 40.4 40.6 40.8 41-10

0

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 766.43-4: 812.8Avg: 768.0T

R 1(us): 96.6

TR 2(us): 196.0

TR 3(us): 116.5

TR 4(us): 11.4

Max P1: 65.6Max P2: 72.8Max P3: 68.3Max P4: 79.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 118: Design and Optimization of a Deflagration to Detonation ...

108

Figure 271 - 24 S3D12+2 BR45_120percL=1.3

Figure 272 - 24 S3D12+2 BR45_120percL=1.4

Figure 273 - 24 S3D12+2 BR45_120percL=1.4v2

Figure 274 - 24 S3D12+2 BR45_120percL=1.6

Figure 275 - 24 S3D12+2 BR45_120percL=1.8

Figure 276 - 25 S3D12+1 BR30_80percL=1.2

42.4 42.6 42.8 43 43.2 43.4 43.6-20

0

20

40

60

80

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 838.22-3: 812.83-4: 924.9Avg: 858.6T

R 1(us): 142.0

TR 2(us): 28.4

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 93.8Max P2: 93.5Max P3: 87.0Max P4: 89.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.4 32.6 32.8 33 33.2 33.4 33.6 33.8-20

0

20

40

60

80

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 894.12-3: 894.13-4: 924.9Avg: 904.4T

R 1(us): 5.7

TR 2(us): 22.7

TR 3(us): 8.5

TR 4(us): 11.4

Max P1: 94.0Max P2: 93.7Max P3: 93.5Max P4: 95.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.4 33.6 33.8 34 34.2 34.4 34.60

10

20

30

40

50

60

70

80

90

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 865.22-3: 865.23-4: 924.9Avg: 885.1T

R 1(us): 8.5

TR 2(us): 22.7

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 93.6Max P2: 93.1Max P3: 91.2Max P4: 95.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.2 30.4 30.6 30.8 31 31.2 31.4 31.6-20

0

20

40

60

80

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 838.22-3: 812.83-4: 894.1Avg: 848.4T

R 1(us): 11.4

TR 2(us): 28.4

TR 3(us): 8.5

TR 4(us): 11.4

Max P1: 94.0Max P2: 82.7Max P3: 86.8Max P4: 91.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.4 30.6 30.8 31 31.2 31.4 31.60

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 788.93-4: 745.1Avg: 734.8T

R 1(us): 190.3

TR 2(us): 93.8

TR 3(us): 19.9

TR 4(us): 8.5

Max P1: 66.5Max P2: 74.8Max P3: 60.2Max P4: 62.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

42.6 42.8 43 43.2 43.4 43.6 43.80

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 638.63-4: 654.2Avg: 629.6T

R 1(us): 184.7

TR 2(us): 272.7

TR 3(us): 39.8

TR 4(us): 14.2

Max P1: 42.8Max P2: 46.7Max P3: 47.0Max P4: 47.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 119: Design and Optimization of a Deflagration to Detonation ...

109

Figure 277 - 25 S3D12+1 BR30_80percL=1.4

Figure 278 - 25 S3D12+1 BR30_80percL=1.6

Figure 279 - 25 S3D12+1 BR30_80percL=1.8

Figure 280 - 25 S3D12+1 BR30_100percL=1.2

Figure 281- 25 S3D12+1 BR30_100percL=1.4

Figure 282 - 25 S3D12+1 BR30_100percL=1.6

34.8 35 35.2 35.4 35.6 35.8 36 36.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 583.13-4: 654.2Avg: 606.8T

R 1(us): 227.3

TR 2(us): 108.0

TR 3(us): 79.5

TR 4(us): 17.0

Max P1: 33.1Max P2: 35.5Max P3: 38.5Max P4: 36.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36 36.2 36.4 36.6 36.8 37 37.20

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 558.82-3: 596.13-4: 596.1Avg: 583.6T

R 1(us): 215.9

TR 2(us): 176.1

TR 3(us): 130.7

TR 4(us): 34.1

Max P1: 29.6Max P2: 31.2Max P3: 28.2Max P4: 23.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.6 35.8 36 36.2 36.4 36.6 36.80

2

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 506.13-4: 525.9Avg: 542.7T

R 1(us): 372.2

TR 2(us): 355.1

TR 3(us): 355.1

TR 4(us): 292.6

Max P1: 17.2Max P2: 16.6Max P3: 17.0Max P4: 16.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

49.8 50 50.2 50.4 50.6 50.8 51 51.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 638.63-4: 596.1Avg: 635.1T

R 1(us): 420.5

TR 2(us): 338.1

TR 3(us): 193.2

TR 4(us): 241.5

Max P1: 38.8Max P2: 38.9Max P3: 39.4Max P4: 37.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.6 36.8 37 37.2 37.4 37.6 37.8 380

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 654.23-4: 654.2Avg: 649.0T

R 1(us): 179.0

TR 2(us): 110.8

TR 3(us): 150.6

TR 4(us): 22.7

Max P1: 49.8Max P2: 52.0Max P3: 50.1Max P4: 51.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36 36.2 36.4 36.6 36.8 37 37.20

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 623.83-4: 670.6Avg: 644.3T

R 1(us): 184.7

TR 2(us): 119.3

TR 3(us): 184.7

TR 4(us): 14.2

Max P1: 46.8Max P2: 41.2Max P3: 41.0Max P4: 41.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 120: Design and Optimization of a Deflagration to Detonation ...

110

Figure 283 - 25 S3D12+1 BR30_100percL=1.8

Figure 284 - 25 S3D12+1 BR30_120percL=1.2

Figure 285 - 25 S3D12+1 BR30_120percL=1.4

Figure 286 - 25 S3D12+1 BR30_120percL=1.6

Figure 287 - 25 S3D12+1 BR30_120percL=1.8

Figure 288 - 26 S45D8+2 BR45_80percL=1.2

35.8 36 36.2 36.4 36.6 36.8 37 37.20

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 570.73-4: 596.1Avg: 596.8T

R 1(us): 201.7

TR 2(us): 170.5

TR 3(us): 292.6

TR 4(us): 230.1

Max P1: 31.8Max P2: 31.2Max P3: 32.3Max P4: 29.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

55.4 55.6 55.8 56 56.2 56.4 56.60

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 570.73-4: 583.1Avg: 574.8T

R 1(us): 480.1

TR 2(us): 406.3

TR 3(us): 406.3

TR 4(us): 304.0

Max P1: 32.9Max P2: 35.8Max P3: 37.6Max P4: 37.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.2 37.4 37.6 37.8 38 38.2 38.40

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 670.63-4: 724.9Avg: 694.4T

R 1(us): 198.9

TR 2(us): 136.4

TR 3(us): 90.9

TR 4(us): 11.4

Max P1: 69.1Max P2: 69.2Max P3: 65.7Max P4: 62.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.4 34.6 34.8 35 35.2 35.4 35.6 35.80

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 654.23-4: 724.9Avg: 683.2T

R 1(us): 275.6

TR 2(us): 201.7

TR 3(us): 167.6

TR 4(us): 11.4

Max P1: 59.8Max P2: 56.6Max P3: 54.8Max P4: 55.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.8 36 36.2 36.4 36.6 36.8 370

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 547.42-3: 623.83-4: 638.6Avg: 603.3T

R 1(us): 451.7

TR 2(us): 284.1

TR 3(us): 233.0

TR 4(us): 267.0

Max P1: 37.9Max P2: 43.8Max P3: 44.7Max P4: 40.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.6 35.8 36 36.2 36.4 36.6 36.80

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 788.93-4: 788.9Avg: 761.2T

R 1(us): 59.7

TR 2(us): 17.0

TR 3(us): 11.4

TR 4(us): 8.5

Max P1: 79.7Max P2: 76.9Max P3: 65.9Max P4: 61.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 121: Design and Optimization of a Deflagration to Detonation ...

111

Figure 289 - 26 S45D8+2 BR45_80percL=1.4

Figure 290 - 26 S45D8+2 BR45_80percL=1.6

Figure 291 - 26 S45D8+2 BR45_80percL=1.8

Figure 292 - 26 S45D8+2 BR45_100percL=1.2

Figure 293 - 26 S45D8+2 BR45_100percL=1.4

Figure 294 - 26 S45D8+2 BR45_100percL=1.6

31 31.2 31.4 31.6 31.8 32 32.2 32.40

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 705.93-4: 745.1Avg: 712.9T

R 1(us): 179.0

TR 2(us): 144.9

TR 3(us): 17.0

TR 4(us): 11.4

Max P1: 65.6Max P2: 61.5Max P3: 55.1Max P4: 55.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.6 30.8 31 31.2 31.4 31.6 31.80

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 638.63-4: 654.2Avg: 638.9T

R 1(us): 96.6

TR 2(us): 255.7

TR 3(us): 19.9

TR 4(us): 14.2

Max P1: 45.9Max P2: 35.8Max P3: 39.4Max P4: 42.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.4 30.6 30.8 31 31.2 31.4 31.60

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 525.92-3: 525.93-4: 547.4Avg: 533.1T

R 1(us): 446.0

TR 2(us): 733.0

TR 3(us): 667.6

TR 4(us): 613.6

Max P1: 20.3Max P2: 20.1Max P3: 19.3Max P4: 17.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.6 38.8 39 39.2 39.4 39.6 39.8 400

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 766.43-4: 812.8Avg: 755.6T

R 1(us): 65.3

TR 2(us): 164.8

TR 3(us): 193.2

TR 4(us): 8.5

Max P1: 68.4Max P2: 82.0Max P3: 68.3Max P4: 63.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.2 33.4 33.6 33.8 34 34.2 34.4 34.6-10

0

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 812.83-4: 788.9Avg: 769.2T

R 1(us): 136.4

TR 2(us): 11.4

TR 3(us): 125.0

TR 4(us): 11.4

Max P1: 83.4Max P2: 81.9Max P3: 74.2Max P4: 71.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.4 31.6 31.8 32 32.2 32.4 32.6 32.80

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 687.83-4: 766.4Avg: 714.0T

R 1(us): 82.4

TR 2(us): 122.2

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 67.6Max P2: 60.3Max P3: 59.4Max P4: 61.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 122: Design and Optimization of a Deflagration to Detonation ...

112

Figure 295 - 26 S45D8+2 BR45_100percL=1.8

Figure 296 - 26 S45D8+2 BR45_120percL=1.2

Figure 297 - 26 S45D8+2 BR45_120percL=1.4

Figure 298 - 26 S45D8+2 BR45_120percL=1.6

Figure 299 - 26 S45D8+2 BR45_120percL=1.8

Figure 300 - 27 S3D6+1 BR30_80percL=1.2

32.4 32.6 32.8 33 33.2 33.4 33.60

5

10

15

20

25

30

35

40

45

50

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 623.83-4: 638.6Avg: 611.0T

R 1(us): 210.2

TR 2(us): 153.4

TR 3(us): 113.6

TR 4(us): 14.2

Max P1: 44.0Max P2: 47.2Max P3: 41.5Max P4: 36.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

51.8 52 52.2 52.4 52.6 52.8 530

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 638.63-4: 687.8Avg: 655.0T

R 1(us): 261.4

TR 2(us): 352.3

TR 3(us): 227.3

TR 4(us): 252.8

Max P1: 48.6Max P2: 57.3Max P3: 60.4Max P4: 53.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.2 38.4 38.6 38.8 39 39.2 39.4-20

0

20

40

60

80

100

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 766.43-4: 812.8Avg: 749.9T

R 1(us): 136.4

TR 2(us): 90.9

TR 3(us): 127.8

TR 4(us): 11.4

Max P1: 92.3Max P2: 92.8Max P3: 86.7Max P4: 71.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.4 34.6 34.8 35 35.2 35.4 35.60

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 788.93-4: 766.4Avg: 753.7T

R 1(us): 139.2

TR 2(us): 11.4

TR 3(us): 125.0

TR 4(us): 8.5

Max P1: 79.7Max P2: 82.1Max P3: 71.3Max P4: 75.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.6 30.8 31 31.2 31.4 31.6 31.80

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 687.83-4: 766.4Avg: 702.8T

R 1(us): 79.5

TR 2(us): 340.9

TR 3(us): 147.7

TR 4(us): 11.4

Max P1: 64.6Max P2: 59.2Max P3: 65.1Max P4: 58.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.2 37.4 37.6 37.8 38 38.2 38.40

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 558.83-4: 623.8Avg: 623.4T

R 1(us): 497.2

TR 2(us): 414.8

TR 3(us): 465.9

TR 4(us): 468.8

Max P1: 23.6Max P2: 23.9Max P3: 27.5Max P4: 26.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 123: Design and Optimization of a Deflagration to Detonation ...

113

Figure 301 - 27 S3D6+1 BR30_80percL=1.4

Figure 302 - 27 S3D6+1 BR30_80percL=1.6

Figure 303 - 27 S3D6+1 BR30_80percL=1.8

Figure 304 - 27 S3D6+1 BR30_100percL=1.2

Figure 305 - 27 S3D6+1 BR30_100percL=1.4

Figure 306 - 27 S3D6+1 BR30_100percL=1.6

38.6 38.8 39 39.2 39.4 39.6 39.82

4

6

8

10

12

14

16

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 579.5

TR 2(us): 647.7

TR 3(us): 497.2

TR 4(us): 681.8

Max P1: 12.8Max P2: 13.2Max P3: 14.2Max P4: 14.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

40.2 40.4 40.6 40.8 41 41.2 41.4 41.60

1

2

3

4

5

6

7

8

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 769.9

TR 2(us): 599.4

TR 3(us): 622.2

TR 4(us): 497.2

Max P1: 7.5Max P2: 7.5Max P3: 7.4Max P4: 7.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

47 47.2 47.4 47.6 47.8 48 48.2 48.41

1.5

2

2.5

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 747.2

TR 2(us): 605.1

TR 3(us): 497.2

TR 4(us): 1000.0

Max P1: 2.3Max P2: 2.3Max P3: 2.2Max P4: 1.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37 37.2 37.4 37.6 37.8 38 38.20

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1072.93-4: 394.4Avg: InfT

R 1(us): 497.2

TR 2(us): 517.0

TR 3(us): 494.3

TR 4(us): 423.3

Max P1: 22.5Max P2: 24.3Max P3: 28.5Max P4: 31.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.6 37.8 38 38.2 38.4 38.6 38.8 390

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1166.23-4: 583.1Avg: InfT

R 1(us): 497.2

TR 2(us): 656.3

TR 3(us): 661.9

TR 4(us): 568.2

Max P1: 20.1Max P2: 20.5Max P3: 23.2Max P4: 22.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.2 38.4 38.6 38.8 39 39.2 39.42

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 505.7

TR 2(us): 497.2

TR 3(us): 517.0

TR 4(us): 701.7

Max P1: 11.0Max P2: 11.9Max P3: 12.1Max P4: 12.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 124: Design and Optimization of a Deflagration to Detonation ...

114

Figure 307 - 27 S3D6+1 BR30_100percL=1.8

Figure 308 - 27 S3D6+1 BR30_120percL=1.2

Figure 309 - 27 S3D6+1 BR30_120percL=1.4

Figure 310 - 27 S3D6+1 BR30_120percL=1.6

Figure 311 - 27 S3D6+1 BR30_120percL=1.8

Figure 312 - 28 S3D6+1 BR30 INV_80percL=1.2

45.4 45.6 45.8 46 46.2 46.4 46.60

1

2

3

4

5

6

7

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 582.4

TR 2(us): 568.2

TR 3(us): 497.2

TR 4(us): 579.5

Max P1: 6.4Max P2: 6.4Max P3: 6.5Max P4: 5.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.2 36.4 36.6 36.8 37 37.2 37.4 37.60

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 609.6Avg: InfT

R 1(us): 508.5

TR 2(us): 497.2

TR 3(us): 565.3

TR 4(us): 608.0

Max P1: 22.6Max P2: 24.1Max P3: 25.5Max P4: 28.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.6 37.8 38 38.2 38.4 38.6 38.80

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 2682.23-4: 609.6Avg: InfT

R 1(us): 497.2

TR 2(us): 508.5

TR 3(us): 494.3

TR 4(us): 519.9

Max P1: 21.1Max P2: 23.2Max P3: 24.9Max P4: 26.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.4 38.6 38.8 39 39.2 39.4 39.62

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 766.4Avg: InfT

R 1(us): 497.2

TR 2(us): 690.3

TR 3(us): 747.2

TR 4(us): 809.7

Max P1: 15.2Max P2: 16.1Max P3: 17.5Max P4: 17.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

43.6 43.8 44 44.2 44.4 44.6 44.81

2

3

4

5

6

7

8

9

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 539.8

TR 2(us): 497.2

TR 3(us): 664.8

TR 4(us): 590.9

Max P1: 7.6Max P2: 7.9Max P3: 8.1Max P4: 7.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.8 40 40.2 40.4 40.6 40.8 410

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 724.93-4: 596.1Avg: InfT

R 1(us): 644.9

TR 2(us): 497.2

TR 3(us): 622.2

TR 4(us): 443.2

Max P1: 23.7Max P2: 22.1Max P3: 21.5Max P4: 18.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 125: Design and Optimization of a Deflagration to Detonation ...

115

Figure 313 - 28 S3D6+1 BR30 INV_80percL=1.4

Figure 314 - 28 S3D6+1 BR30 INV_80percL=1.6

Figure 315 - 28 S3D6+1 BR30 INV_80percL=1.8

Figure 316 - 28 S3D6+1 BR30 INV_100percL=1.2

Figure 317 - 28 S3D6+1 BR30 INV_100percL=1.4

Figure 318 - 28 S3D6+1 BR30 INV_100percL=1.6

36 36.2 36.4 36.6 36.8 37 37.20

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 496.73-4: 525.9Avg: 582.5T

R 1(us): 497.2

TR 2(us): 545.5

TR 3(us): 480.1

TR 4(us): 108.0

Max P1: 20.6Max P2: 19.2Max P3: 19.6Max P4: 17.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.6 32.8 33 33.2 33.4 33.6 33.80

2

4

6

8

10

12

14

16

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 687.83-4: 515.8Avg: InfT

R 1(us): 497.2

TR 2(us): 590.9

TR 3(us): 818.2

TR 4(us): 599.4

Max P1: 15.5Max P2: 15.0Max P3: 14.5Max P4: 12.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32 32.2 32.4 32.6 32.8 33 33.22

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 639.2

TR 3(us): 733.0

TR 4(us): 804.0

Max P1: 12.4Max P2: 12.3Max P3: 11.9Max P4: 10.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

47.8 48 48.2 48.4 48.6 48.8 492

4

6

8

10

12

14

16

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 2235.2Avg: InfT

R 1(us): 497.2

TR 2(us): 576.7

TR 3(us): 642.0

TR 4(us): 698.9

Max P1: 15.9Max P2: 14.6Max P3: 14.4Max P4: 12.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.8 37 37.2 37.4 37.6 37.8 380

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 924.92-3: 525.93-4: 558.8Avg: 669.9T

R 1(us): 718.8

TR 2(us): 414.8

TR 3(us): 571.0

TR 4(us): 485.8

Max P1: 24.7Max P2: 22.5Max P3: 23.2Max P4: 19.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.8 36 36.2 36.4 36.6 36.8 37 37.20

2

4

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1219.22-3: 515.83-4: 536.4Avg: 757.2T

R 1(us): 497.2

TR 2(us): 536.9

TR 3(us): 539.8

TR 4(us): 661.9

Max P1: 18.9Max P2: 18.4Max P3: 17.4Max P4: 15.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 126: Design and Optimization of a Deflagration to Detonation ...

116

Figure 319 - 28 S3D6+1 BR30 INV_100percL=1.8

Figure 320 - 28 S3D6+1 BR30 INV_120percL=1.2

Figure 321 - 28 S3D6+1 BR30 INV_120percL=1.4

Figure 322 - 28 S3D6+1 BR30 INV_120percL=1.6

Figure 323 - 28 S3D6+1 BR30 INV_120percL=1.8

Figure 324 - 29 S6D6+2 BR45_80percL=1.2

34 34.2 34.4 34.6 34.8 35 35.2 35.40

2

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1341.13-4: 515.8Avg: InfT

R 1(us): 497.2

TR 2(us): 602.3

TR 3(us): 866.5

TR 4(us): 795.5

Max P1: 14.0Max P2: 13.6Max P3: 13.6Max P4: 12.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.4 39.6 39.8 40 40.2 40.4 40.6 40.82

4

6

8

10

12

14

16

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 647.7

TR 3(us): 644.9

TR 4(us): 920.5

Max P1: 14.7Max P2: 13.7Max P3: 14.2Max P4: 12.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.2 39.4 39.6 39.8 40 40.2 40.4 40.60

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 8940.83-4: 570.7Avg: InfT

R 1(us): 497.2

TR 2(us): 568.2

TR 3(us): 573.9

TR 4(us): 508.5

Max P1: 24.1Max P2: 22.4Max P3: 22.6Max P4: 20.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.8 34 34.2 34.4 34.6 34.8 350

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 515.83-4: 547.4Avg: 583.7T

R 1(us): 497.2

TR 2(us): 480.1

TR 3(us): 605.1

TR 4(us): 409.1

Max P1: 21.5Max P2: 20.5Max P3: 22.2Max P4: 19.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33 33.2 33.4 33.6 33.8 34 34.2 34.42

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 957.9Avg: InfT

R 1(us): 497.2

TR 2(us): 755.7

TR 3(us): 838.1

TR 4(us): 724.4

Max P1: 16.5Max P2: 16.0Max P3: 15.3Max P4: 14.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.8 35 35.2 35.4 35.6 35.8 36 36.20

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 788.93-4: 838.2Avg: 771.6T

R 1(us): 360.8

TR 2(us): 14.2

TR 3(us): 8.5

TR 4(us): 11.4

Max P1: 77.1Max P2: 83.6Max P3: 66.1Max P4: 69.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 127: Design and Optimization of a Deflagration to Detonation ...

117

Figure 325 - 29 S6D6+2 BR45_80percL=1.4

Figure 326 - 29 S6D6+2 BR45_80percL=1.6

Figure 327 - 29 S6D6+2 BR45_80percL=1.8

Figure 328 - 29 S6D6+2 BR45_100percL=1.2

Figure 329 - 29 S6D6+2 BR45_100percL=1.4

Figure 330 - 29 S6D6+2 BR45_100percL=1.6

35.4 35.6 35.8 36 36.2 36.4 36.60

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 687.83-4: 724.9Avg: 694.4T

R 1(us): 88.1

TR 2(us): 136.4

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 59.0Max P2: 53.0Max P3: 56.5Max P4: 55.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.8 30 30.2 30.4 30.6 30.8 31 31.20

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 609.63-4: 638.6Avg: 610.4T

R 1(us): 244.3

TR 2(us): 105.1

TR 3(us): 68.2

TR 4(us): 31.3

Max P1: 41.0Max P2: 40.6Max P3: 34.3Max P4: 39.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.4 35.6 35.8 36 36.2 36.4 36.6 36.82

4

6

8

10

12

14

16

18

20

22

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 766.43-4: 547.4Avg: InfT

R 1(us): 497.2

TR 2(us): 579.5

TR 3(us): 673.3

TR 4(us): 599.4

Max P1: 20.0Max P2: 17.5Max P3: 19.2Max P4: 18.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.4 34.6 34.8 35 35.2 35.4 35.60

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 766.43-4: 788.9Avg: 747.7T

R 1(us): 329.5

TR 2(us): 14.2

TR 3(us): 79.5

TR 4(us): 8.5

Max P1: 75.5Max P2: 74.4Max P3: 76.7Max P4: 68.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.4 29.6 29.8 30 30.2 30.4 30.6 30.8-10

0

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 788.93-4: 812.8Avg: 763.1T

R 1(us): 210.2

TR 2(us): 14.2

TR 3(us): 11.4

TR 4(us): 11.4

Max P1: 88.5Max P2: 87.5Max P3: 68.0Max P4: 69.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31 31.2 31.4 31.6 31.8 32 32.20

10

20

30

40

50

60

70

80

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 638.63-4: 687.8Avg: 655.0T

R 1(us): 335.2

TR 2(us): 278.4

TR 3(us): 156.3

TR 4(us): 14.2

Max P1: 71.0Max P2: 50.2Max P3: 54.3Max P4: 46.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 128: Design and Optimization of a Deflagration to Detonation ...

118

Figure 331 - 29 S6D6+2 BR45_100percL=1.8

Figure 332 - 29 S6D6+2 BR45_120percL=1.2

Figure 333 - 29 S6D6+2 BR45_120percL=1.4

Figure 334 - 29 S6D6+2 BR45_120percL=1.6

Figure 335 - 29 S6D6+2 BR45_120percL=1.8

Figure 336 - 30 S6D6+2 BR30_80percL=1.2

31 31.2 31.4 31.6 31.8 32 32.2 32.40

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 570.73-4: 583.1Avg: 579.0T

R 1(us): 142.0

TR 2(us): 105.1

TR 3(us): 196.0

TR 4(us): 36.9

Max P1: 32.8Max P2: 30.2Max P3: 33.0Max P4: 29.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.8 36 36.2 36.4 36.6 36.8 370

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 687.83-4: 788.9Avg: 710.3T

R 1(us): 284.1

TR 2(us): 204.5

TR 3(us): 144.9

TR 4(us): 8.5

Max P1: 86.4Max P2: 79.6Max P3: 85.3Max P4: 68.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.2 30.4 30.6 30.8 31 31.2 31.40

10

20

30

40

50

60

70

80

90

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 687.82-3: 745.13-4: 838.2Avg: 757.0T

R 1(us): 213.1

TR 2(us): 190.3

TR 3(us): 88.1

TR 4(us): 11.4

Max P1: 88.4Max P2: 78.8Max P3: 83.4Max P4: 71.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.8 31 31.2 31.4 31.6 31.8 320

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 638.63-4: 745.1Avg: 669.2T

R 1(us): 403.4

TR 2(us): 227.3

TR 3(us): 14.2

TR 4(us): 14.2

Max P1: 59.3Max P2: 53.6Max P3: 56.1Max P4: 53.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30 30.2 30.4 30.6 30.8 31 31.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 2980.32-3: 638.63-4: 558.8Avg: 1392.6T

R 1(us): 585.2

TR 2(us): 471.6

TR 3(us): 426.1

TR 4(us): 468.8

Max P1: 32.4Max P2: 35.0Max P3: 34.8Max P4: 35.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.4 39.6 39.8 40 40.2 40.4 40.60

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 570.73-4: 638.6Avg: 601.8T

R 1(us): 488.6

TR 2(us): 417.6

TR 3(us): 448.9

TR 4(us): 386.4

Max P1: 35.8Max P2: 36.5Max P3: 39.9Max P4: 34.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 129: Design and Optimization of a Deflagration to Detonation ...

119

Figure 337 - 30 S6D6+2 BR30_80percL=1.4

Figure 338 - 30 S6D6+2 BR30_80percL=1.6

Figure 339 - 30 S6D6+2 BR30_80percL=1.8

Figure 340 - 30 S6D6+2 BR30_100percL=1.2

Figure 341 - 30 S6D6+2 BR30_100percL=1.4

Figure 342 - 30 S6D6+2 BR30_100percL=1.6

34.8 35 35.2 35.4 35.6 35.8 360

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 570.73-4: 596.1Avg: 592.1T

R 1(us): 156.3

TR 2(us): 130.7

TR 3(us): 176.1

TR 4(us): 122.2

Max P1: 39.0Max P2: 36.0Max P3: 38.2Max P4: 33.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.8 34 34.2 34.4 34.6 34.8 350

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 583.13-4: 596.1Avg: 587.4T

R 1(us): 190.3

TR 2(us): 164.8

TR 3(us): 247.2

TR 4(us): 261.4

Max P1: 31.9Max P2: 28.6Max P3: 31.3Max P4: 30.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.4 35.6 35.8 36 36.2 36.4 36.6 36.80

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 536.43-4: 547.4Avg: 564.5T

R 1(us): 292.6

TR 2(us): 278.4

TR 3(us): 272.7

TR 4(us): 213.1

Max P1: 24.0Max P2: 19.1Max P3: 19.0Max P4: 18.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

43.8 44 44.2 44.4 44.6 44.8 45 45.20

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 2682.22-3: 609.63-4: 609.6Avg: 1300.5T

R 1(us): 497.2

TR 2(us): 522.7

TR 3(us): 451.7

TR 4(us): 366.5

Max P1: 35.6Max P2: 39.9Max P3: 41.8Max P4: 38.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.4 36.6 36.8 37 37.2 37.4 37.60

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 558.82-3: 583.13-4: 479.0Avg: 540.3T

R 1(us): 431.8

TR 2(us): 429.0

TR 3(us): 323.9

TR 4(us): 190.3

Max P1: 38.5Max P2: 41.6Max P3: 43.2Max P4: 41.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.8 33 33.2 33.4 33.6 33.8 340

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 745.12-3: 609.63-4: 670.6Avg: 675.1T

R 1(us): 130.7

TR 2(us): 215.9

TR 3(us): 207.4

TR 4(us): 173.3

Max P1: 52.7Max P2: 45.2Max P3: 46.3Max P4: 38.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 130: Design and Optimization of a Deflagration to Detonation ...

120

Figure 343 - 30 S6D6+2 BR30_100percL=1.8

Figure 344 - 30 S6D6+2 BR30_120percL=1.2

Figure 345 - 30 S6D6+2 BR30_120percL=1.4

Figure 346 - 30 S6D6+2 BR30_120percL=1.6

Figure 347 - 30 S6D6+2 BR30_120percL=1.8

Figure 348 - 31 S6D3+1 BR45_80percL=1.2

33.4 33.6 33.8 34 34.2 34.4 34.6 34.80

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 596.13-4: 596.1Avg: 587.6T

R 1(us): 153.4

TR 2(us): 440.3

TR 3(us): 377.8

TR 4(us): 426.1

Max P1: 28.4Max P2: 29.7Max P3: 30.0Max P4: 27.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

43.8 44 44.2 44.4 44.6 44.8 450

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 687.83-4: 362.5Avg: InfT

R 1(us): 497.2

TR 2(us): 536.9

TR 3(us): 565.3

TR 4(us): 400.6

Max P1: 31.8Max P2: 34.8Max P3: 36.9Max P4: 35.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.4 37.6 37.8 38 38.2 38.4 38.6-10

0

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 670.63-4: 687.8Avg: 670.8T

R 1(us): 352.3

TR 2(us): 261.4

TR 3(us): 338.1

TR 4(us): 210.2

Max P1: 55.5Max P2: 51.8Max P3: 55.9Max P4: 52.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33 33.2 33.4 33.6 33.8 34 34.20

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 609.63-4: 583.1Avg: 596.2T

R 1(us): 196.0

TR 2(us): 358.0

TR 3(us): 451.7

TR 4(us): 235.8

Max P1: 41.8Max P2: 41.6Max P3: 44.2Max P4: 41.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.6 33.8 34 34.2 34.4 34.6 34.8 350

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 2235.22-3: 2063.33-4: 357.6Avg: 1552.0T

R 1(us): 497.2

TR 2(us): 579.5

TR 3(us): 519.9

TR 4(us): 301.1

Max P1: 31.7Max P2: 31.0Max P3: 31.4Max P4: 30.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

51.6 51.8 52 52.2 52.4 52.6 52.8 530

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 687.83-4: 388.7Avg: InfT

R 1(us): 497.2

TR 2(us): 531.3

TR 3(us): 457.4

TR 4(us): 380.7

Max P1: 26.5Max P2: 28.5Max P3: 29.2Max P4: 32.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 131: Design and Optimization of a Deflagration to Detonation ...

121

Figure 349 - 31 S6D3+1 BR45_80percL=1.4

Figure 350 - 31 S6D3+1 BR45_80percL=1.6

Figure 351 - 31 S6D3+1 BR45_80percL=1.8

Figure 352 - 31 S6D3+1 BR45_100percL=1.2

Figure 353 - 31 S6D3+1 BR45_100percL=1.4

Figure 354 - 31 S6D3+1 BR45_100percL=1.6

40.6 40.8 41 41.2 41.4 41.6 41.80

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 2980.32-3: 558.83-4: 570.7Avg: 1369.9T

R 1(us): 497.2

TR 2(us): 514.2

TR 3(us): 437.5

TR 4(us): 483.0

Max P1: 22.0Max P2: 24.7Max P3: 25.3Max P4: 25.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.6 39.8 40 40.2 40.4 40.6 40.8 410

2

4

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 26822.43-4: 547.4Avg: InfT

R 1(us): 514.2

TR 2(us): 497.2

TR 3(us): 548.3

TR 4(us): 463.1

Max P1: 16.8Max P2: 17.8Max P3: 18.4Max P4: 18.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

42.2 42.4 42.6 42.8 43 43.2 43.40

1

2

3

4

5

6

7

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 747.2

TR 3(us): 804.0

TR 4(us): 585.2

Max P1: 6.1Max P2: 6.0Max P3: 5.8Max P4: 5.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

53.8 54 54.2 54.4 54.6 54.8 550

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 865.23-4: 525.9Avg: InfT

R 1(us): 497.2

TR 2(us): 656.3

TR 3(us): 571.0

TR 4(us): 494.3

Max P1: 21.3Max P2: 23.0Max P3: 25.7Max P4: 27.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.8 40 40.2 40.4 40.6 40.8 410

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 654.23-4: 623.8Avg: 633.9T

R 1(us): 480.1

TR 2(us): 437.5

TR 3(us): 505.7

TR 4(us): 409.1

Max P1: 27.1Max P2: 30.4Max P3: 33.4Max P4: 32.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

40.6 40.8 41 41.2 41.4 41.6 41.80

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1166.23-4: 583.1Avg: InfT

R 1(us): 497.2

TR 2(us): 536.9

TR 3(us): 500.0

TR 4(us): 423.3

Max P1: 21.7Max P2: 24.2Max P3: 26.0Max P4: 26.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 132: Design and Optimization of a Deflagration to Detonation ...

122

Figure 355 - 31 S6D3+1 BR45_100percL=1.8

Figure 356 - 31 S6D3+1 BR45_120percL=1.2

Figure 357 - 31 S6D3+1 BR45_120percL=1.4

Figure 358 - 31 S6D3+1 BR45_120percL=1.6

Figure 359 - 31 S6D3+1 BR45_120percL=1.8

Figure 360 - 32 S6D3+1BR45 INV_80percL=1.2

42.8 43 43.2 43.4 43.6 43.8 44 44.20

2

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 3352.83-4: 570.7Avg: InfT

R 1(us): 497.2

TR 2(us): 661.9

TR 3(us): 698.9

TR 4(us): 602.3

Max P1: 15.9Max P2: 16.4Max P3: 17.8Max P4: 17.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

64.6 64.8 65 65.2 65.4 65.6 65.8-4

-2

0

2

4

6

8

10

12

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 525.6

TR 2(us): 497.2

TR 3(us): 545.5

TR 4(us): 559.7

Max P1: 10.7Max P2: 11.1Max P3: 11.3Max P4: 11.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

44 44.2 44.4 44.6 44.8 45 45.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 924.92-3: 654.23-4: 609.6Avg: 729.6T

R 1(us): 497.2

TR 2(us): 414.8

TR 3(us): 426.1

TR 4(us): 403.4

Max P1: 30.2Max P2: 33.6Max P3: 39.2Max P4: 39.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.8 39 39.2 39.4 39.6 39.8 40 40.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 865.23-4: 383.2Avg: InfT

R 1(us): 497.2

TR 2(us): 508.5

TR 3(us): 409.1

TR 4(us): 358.0

Max P1: 27.3Max P2: 27.9Max P3: 35.9Max P4: 35.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

40 40.2 40.4 40.6 40.8 41 41.20

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 570.7Avg: InfT

R 1(us): 565.3

TR 2(us): 497.2

TR 3(us): 625.0

TR 4(us): 491.5

Max P1: 18.5Max P2: 21.1Max P3: 22.0Max P4: 23.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.2 38.4 38.6 38.8 39 39.2 39.40

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 515.82-3: 536.43-4: 525.9Avg: 526.1T

R 1(us): 258.5

TR 2(us): 335.2

TR 3(us): 193.2

TR 4(us): 31.3

Max P1: 21.7Max P2: 21.2Max P3: 21.8Max P4: 23.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 133: Design and Optimization of a Deflagration to Detonation ...

123

Figure 361 - 32 S6D3+1BR45 INV_80percL=1.4

Figure 362 - 32 S6D3+1BR45 INV_80percL=1.6

Figure 363 - 32 S6D3+1BR45 INV_80percL=1.8

Figure 364 - 32 S6D3+1BR45 INV_100percL=1.2

Figure 365 - 32 S6D3+1BR45 INV_100percL=1.4

Figure 366 - 32 S6D3+1BR45 INV_100percL=1.6

32.4 32.6 32.8 33 33.2 33.4 33.60

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 623.83-4: 654.2Avg: 620.4T

R 1(us): 42.6

TR 2(us): 28.4

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 27.9Max P2: 32.3Max P3: 35.9Max P4: 33.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31 31.2 31.4 31.6 31.8 32 32.20

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 547.42-3: 558.83-4: 583.1Avg: 563.1T

R 1(us): 227.3

TR 2(us): 48.3

TR 3(us): 31.3

TR 4(us): 19.9

Max P1: 20.7Max P2: 21.5Max P3: 24.9Max P4: 23.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.4 31.6 31.8 32 32.2 32.4 32.6 32.80

5

10

15

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 2682.22-3: 506.13-4: 525.9Avg: 1238.1T

R 1(us): 497.2

TR 2(us): 644.9

TR 3(us): 593.8

TR 4(us): 545.5

Max P1: 14.4Max P2: 14.3Max P3: 14.1Max P4: 12.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37 37.2 37.4 37.6 37.8 38 38.2 38.40

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 547.42-3: 547.43-4: 570.7Avg: 555.2T

R 1(us): 136.4

TR 2(us): 718.8

TR 3(us): 164.8

TR 4(us): 34.1

Max P1: 22.6Max P2: 22.8Max P3: 23.2Max P4: 26.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.4 30.6 30.8 31 31.2 31.4 31.6 31.80

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 623.83-4: 654.2Avg: 620.4T

R 1(us): 39.8

TR 2(us): 25.6

TR 3(us): 19.9

TR 4(us): 17.0

Max P1: 28.1Max P2: 30.7Max P3: 33.1Max P4: 32.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.2 31.4 31.6 31.8 32 32.2 32.40

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 547.42-3: 547.43-4: 583.1Avg: 559.3T

R 1(us): 218.8

TR 2(us): 42.6

TR 3(us): 31.3

TR 4(us): 19.9

Max P1: 21.2Max P2: 25.1Max P3: 28.5Max P4: 26.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 134: Design and Optimization of a Deflagration to Detonation ...

124

Figure 367 - 32 S6D3+1BR45 INV_100percL=1.8

Figure 368 - 32 S6D3+1BR45 INV_120percL=1.2

Figure 369 - 32 S6D3+1BR45 INV_120percL=1.4

Figure 370 - 32 S6D3+1BR45 INV_120percL=1.6

Figure 371 - 32 S6D3+1BR45 INV_120percL=1.8

Figure 372 - 33 S45D8+2 BR30_80percL=1.2

31.2 31.4 31.6 31.8 32 32.2 32.40

2

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 515.82-3: 525.93-4: 525.9Avg: 522.6T

R 1(us): 460.2

TR 2(us): 383.5

TR 3(us): 176.1

TR 4(us): 133.5

Max P1: 15.9Max P2: 15.5Max P3: 16.1Max P4: 14.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.2 33.4 33.6 33.8 34 34.2 34.40

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 536.42-3: 536.43-4: 596.1Avg: 556.3T

R 1(us): 108.0

TR 2(us): 56.8

TR 3(us): 31.3

TR 4(us): 17.0

Max P1: 23.1Max P2: 24.9Max P3: 30.0Max P4: 27.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.4 33.6 33.8 34 34.2 34.4 34.6 34.80

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 654.23-4: 654.2Avg: 649.0T

R 1(us): 25.6

TR 2(us): 19.9

TR 3(us): 17.0

TR 4(us): 14.2

Max P1: 35.4Max P2: 38.3Max P3: 38.2Max P4: 35.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30 30.2 30.4 30.6 30.8 31 31.2 31.40

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 536.42-3: 547.43-4: 547.4Avg: 543.7T

R 1(us): 130.7

TR 2(us): 90.9

TR 3(us): 51.1

TR 4(us): 22.7

Max P1: 23.2Max P2: 23.9Max P3: 27.2Max P4: 28.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.2 31.4 31.6 31.8 32 32.2 32.40

2

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 6705.63-4: 515.8Avg: InfT

R 1(us): 497.2

TR 2(us): 559.7

TR 3(us): 673.3

TR 4(us): 639.2

Max P1: 13.7Max P2: 13.5Max P3: 13.0Max P4: 11.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37 37.2 37.4 37.6 37.8 38 38.2 38.40

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 670.63-4: 654.2Avg: 659.7T

R 1(us): 159.1

TR 2(us): 221.6

TR 3(us): 34.1

TR 4(us): 11.4

Max P1: 48.3Max P2: 51.7Max P3: 52.0Max P4: 49.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 135: Design and Optimization of a Deflagration to Detonation ...

125

Figure 373 - 33 S45D8+2 BR30_80percL=1.4

Figure 374 - 33 S45D8+2 BR30_80percL=1.6

Figure 375 - 33 S45D8+2 BR30_80percL=1.8

Figure 376 - 33 S45D8+2 BR30_100percL=1.2

Figure 377 - 33 S45D8+2 BR30_100percL=1.4

Figure 378 - 33 S45D8+2 BR30_100percL=1.6

31.8 32 32.2 32.4 32.6 32.8 33 33.20

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 583.13-4: 596.1Avg: 591.7T

R 1(us): 414.8

TR 2(us): 392.0

TR 3(us): 278.4

TR 4(us): 122.2

Max P1: 40.2Max P2: 38.3Max P3: 37.4Max P4: 34.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.8 33 33.2 33.4 33.6 33.8 340

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 525.92-3: 536.43-4: 547.4Avg: 536.6T

R 1(us): 403.4

TR 2(us): 653.4

TR 3(us): 568.2

TR 4(us): 429.0

Max P1: 23.3Max P2: 23.8Max P3: 24.4Max P4: 22.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.8 37 37.2 37.4 37.6 37.8 384

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 772.7

TR 2(us): 877.8

TR 3(us): 497.2

TR 4(us): 1002.8

Max P1: 8.5Max P2: 8.6Max P3: 8.7Max P4: 7.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.4 35.6 35.8 36 36.2 36.4 36.6 36.80

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 654.23-4: 670.6Avg: 659.7T

R 1(us): 312.5

TR 2(us): 264.2

TR 3(us): 184.7

TR 4(us): 221.6

Max P1: 51.1Max P2: 51.0Max P3: 57.3Max P4: 49.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.4 33.6 33.8 34 34.2 34.4 34.6 34.80

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 687.83-4: 724.9Avg: 694.4T

R 1(us): 250.0

TR 2(us): 281.3

TR 3(us): 238.6

TR 4(us): 11.4

Max P1: 47.5Max P2: 49.4Max P3: 58.0Max P4: 49.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32 32.2 32.4 32.6 32.8 33 33.2 33.40

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 570.72-3: 623.83-4: 623.8Avg: 606.1T

R 1(us): 267.0

TR 2(us): 355.1

TR 3(us): 295.5

TR 4(us): 329.5

Max P1: 33.1Max P2: 37.5Max P3: 38.0Max P4: 35.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 136: Design and Optimization of a Deflagration to Detonation ...

126

Figure 379 - 33 S45D8+2 BR30_100percL=1.8

Figure 380 - 33 S45D8+2 BR30_120percL=1.2

Figure 381 - 33 S45D8+2 BR30_120percL=1.4

Figure 382 - 33 S45D8+2 BR30_120percL=1.6

Figure 383 - 33 S45D8+2 BR30_120percL=1.8

Figure 384 - 34 S45D4 BR45 @end_80percL=1.2

33.4 33.6 33.8 34 34.2 34.4 34.60

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1166.23-4: 406.4Avg: InfT

R 1(us): 497.2

TR 2(us): 534.1

TR 3(us): 505.7

TR 4(us): 477.3

Max P1: 20.5Max P2: 22.4Max P3: 21.8Max P4: 20.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.4 39.6 39.8 40 40.2 40.4 40.60

10

20

30

40

50

60

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 654.23-4: 654.2Avg: 654.2T

R 1(us): 366.5

TR 2(us): 338.1

TR 3(us): 241.5

TR 4(us): 193.2

Max P1: 49.5Max P2: 51.1Max P3: 55.5Max P4: 48.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.4 32.6 32.8 33 33.2 33.4 33.60

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 670.63-4: 745.1Avg: 684.8T

R 1(us): 332.4

TR 2(us): 247.2

TR 3(us): 19.9

TR 4(us): 11.4

Max P1: 55.5Max P2: 61.6Max P3: 61.8Max P4: 54.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.8 34 34.2 34.4 34.6 34.8 350

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 638.63-4: 638.6Avg: 638.6T

R 1(us): 318.2

TR 2(us): 235.8

TR 3(us): 179.0

TR 4(us): 201.7

Max P1: 44.0Max P2: 43.1Max P3: 44.1Max P4: 41.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.6 32.8 33 33.2 33.4 33.6 33.80

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 558.83-4: 609.6Avg: InfT

R 1(us): 497.2

TR 2(us): 571.0

TR 3(us): 554.0

TR 4(us): 625.0

Max P1: 26.6Max P2: 26.2Max P3: 27.7Max P4: 24.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.6 39.8 40 40.2 40.4 40.6 40.80

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 583.13-4: 609.6Avg: 596.2T

R 1(us): 465.9

TR 2(us): 377.8

TR 3(us): 304.0

TR 4(us): 332.4

Max P1: 30.1Max P2: 32.9Max P3: 34.9Max P4: 35.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 137: Design and Optimization of a Deflagration to Detonation ...

127

Figure 385 - 34 S45D4 BR45 @end_80percL=1.4

Figure 386 - 34 S45D4 BR45 @end_80percL=1.6

Figure 387 - 34 S45D4 BR45 @end_80percL=1.8

Figure 388 - 34 S45D4 BR45 @end_100percL=1.2

Figure 389 - 34 S45D4 BR45 @end_100percL=1.4

Figure 390 - 34 S45D4 BR45 @end_100percL=1.6

38.2 38.4 38.6 38.8 39 39.2 39.40

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 609.63-4: 558.8Avg: InfT

R 1(us): 497.2

TR 2(us): 590.9

TR 3(us): 525.6

TR 4(us): 525.6

Max P1: 20.3Max P2: 21.8Max P3: 23.9Max P4: 23.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

43.2 43.4 43.6 43.8 44 44.2 44.40

2

4

6

8

10

12

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 565.3

TR 3(us): 747.2

TR 4(us): 704.5

Max P1: 11.1Max P2: 11.2Max P3: 11.1Max P4: 10.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

47 47.2 47.4 47.6 47.8 48 48.20.5

1

1.5

2

2.5

3

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 599.4

TR 3(us): 573.9

TR 4(us): 727.3

Max P1: 2.9Max P2: 2.8Max P3: 2.6Max P4: 2.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.4 38.6 38.8 39 39.2 39.4 39.6 39.80

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 788.92-3: 583.13-4: 583.1Avg: 651.7T

R 1(us): 497.2

TR 2(us): 494.3

TR 3(us): 403.4

TR 4(us): 375.0

Max P1: 30.0Max P2: 31.9Max P3: 33.4Max P4: 37.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.2 38.4 38.6 38.8 39 39.2 39.40

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 8940.82-3: 609.63-4: 547.4Avg: 3365.9T

R 1(us): 497.2

TR 2(us): 605.1

TR 3(us): 525.6

TR 4(us): 508.5

Max P1: 23.8Max P2: 26.6Max P3: 28.7Max P4: 30.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.4 39.6 39.8 40 40.2 40.4 40.6 40.84

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 539.8

TR 2(us): 497.2

TR 3(us): 519.9

TR 4(us): 605.1

Max P1: 16.1Max P2: 17.4Max P3: 18.1Max P4: 19.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 138: Design and Optimization of a Deflagration to Detonation ...

128

Figure 391 - 34 S45D4 BR45 @end_100percL=1.8

Figure 392 - 34 S45D4 BR45 @end_120percL=1.2

Figure 393 - 34 S45D4 BR45 @end_120percL=1.4

Figure 394 - 34 S45D4 BR45 @end_120percL=1.6

Figure 395 - 34 S45D4 BR45 @end_120percL=1.8

Figure 396 - 35 S45D4 BR45 @ign_80percL=1.2

46.4 46.6 46.8 47 47.2 47.4 47.6-1

0

1

2

3

4

5

6

7

8

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 579.5

TR 3(us): 517.0

TR 4(us): 752.8

Max P1: 7.8Max P2: 7.8Max P3: 7.6Max P4: 7.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37 37.2 37.4 37.6 37.8 38 38.2 38.40

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 596.13-4: 623.8Avg: 609.8T

R 1(us): 380.7

TR 2(us): 411.9

TR 3(us): 329.5

TR 4(us): 377.8

Max P1: 30.4Max P2: 33.5Max P3: 36.8Max P4: 40.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.6 37.8 38 38.2 38.4 38.6 38.8 390

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 536.42-3: 596.13-4: 596.1Avg: 576.2T

R 1(us): 488.6

TR 2(us): 474.4

TR 3(us): 409.1

TR 4(us): 326.7

Max P1: 26.5Max P2: 30.4Max P3: 34.7Max P4: 33.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

40.2 40.4 40.6 40.8 41 41.2 41.42

4

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 8940.8Avg: InfT

R 1(us): 565.3

TR 2(us): 497.2

TR 3(us): 542.6

TR 4(us): 616.5

Max P1: 15.9Max P2: 17.3Max P3: 19.0Max P4: 19.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

46.2 46.4 46.6 46.8 47 47.2 47.4-2

0

2

4

6

8

10

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 548.3

TR 2(us): 497.2

TR 3(us): 536.9

TR 4(us): 696.0

Max P1: 9.2Max P2: 9.2Max P3: 9.0Max P4: 8.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.6 34.8 35 35.2 35.4 35.6 35.80

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 596.12-3: 609.63-4: 654.2Avg: 620.0T

R 1(us): 28.4

TR 2(us): 19.9

TR 3(us): 19.9

TR 4(us): 17.0

Max P1: 28.3Max P2: 30.0Max P3: 33.1Max P4: 32.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 139: Design and Optimization of a Deflagration to Detonation ...

129

Figure 397 - 35 S45D4 BR45 @ign_80percL=1.4

Figure 398 - 35 S45D4 BR45 @ign_80percL=1.6

Figure 399 - 35 S45D4 BR45 @ign_80percL=1.8

Figure 400 - 35 S45D4 BR45 @ign_100percL=1.2

Figure 401 - 35 S45D4 BR45 @ign_100percL=1.4

Figure 402 - 35 S45D4 BR45 @ign_100percL=1.6

29 29.2 29.4 29.6 29.8 30 30.20

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 558.82-3: 570.73-4: 654.2Avg: 594.6T

R 1(us): 76.7

TR 2(us): 36.9

TR 3(us): 19.9

TR 4(us): 14.2

Max P1: 24.6Max P2: 30.6Max P3: 33.3Max P4: 32.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.8 30 30.2 30.4 30.6 30.8 310

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 547.42-3: 547.43-4: 558.8Avg: 551.2T

R 1(us): 241.5

TR 2(us): 190.3

TR 3(us): 159.1

TR 4(us): 176.1

Max P1: 20.5Max P2: 19.7Max P3: 20.2Max P4: 17.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.8 32 32.2 32.4 32.6 32.8 33 33.20

5

10

15

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 4470.42-3: 515.83-4: 525.9Avg: 1837.4T

R 1(us): 497.2

TR 2(us): 619.3

TR 3(us): 559.7

TR 4(us): 505.7

Max P1: 14.9Max P2: 14.7Max P3: 14.7Max P4: 12.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.4 36.6 36.8 37 37.2 37.4 37.60

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 536.42-3: 558.83-4: 609.6Avg: 568.3T

R 1(us): 255.7

TR 2(us): 34.1

TR 3(us): 22.7

TR 4(us): 22.7

Max P1: 23.9Max P2: 25.1Max P3: 28.8Max P4: 28.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30 30.2 30.4 30.6 30.8 31 31.2 31.40

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 670.63-4: 687.8Avg: 656.0T

R 1(us): 31.3

TR 2(us): 17.0

TR 3(us): 14.2

TR 4(us): 14.2

Max P1: 35.3Max P2: 41.8Max P3: 41.3Max P4: 38.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30 30.2 30.4 30.6 30.8 31 31.2 31.40

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 506.12-3: 558.83-4: 596.1Avg: 553.6T

R 1(us): 383.5

TR 2(us): 42.6

TR 3(us): 28.4

TR 4(us): 22.7

Max P1: 21.1Max P2: 22.7Max P3: 25.8Max P4: 26.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 140: Design and Optimization of a Deflagration to Detonation ...

130

Figure 403 - 35 S45D4 BR45 @ign_100percL=1.8

Figure 404 - 35 S45D4 BR45 @ign_120percL=1.2

Figure 405 - 35 S45D4 BR45 @ign_120percL=1.4

Figure 406 - 35 S45D4 BR45 @ign_120percL=1.6

Figure 407 - 35 S45D4 BR45 @ign_120percL=1.8

Figure 408 - 36 S45D4 BR30 @end_80percL=1.2

30.2 30.4 30.6 30.8 31 31.2 31.4 31.60

2

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1341.12-3: 506.13-4: 525.9Avg: 791.0T

R 1(us): 497.2

TR 2(us): 608.0

TR 3(us): 414.8

TR 4(us): 474.4

Max P1: 16.3Max P2: 16.1Max P3: 16.0Max P4: 14.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.4 32.6 32.8 33 33.2 33.4 33.6 33.80

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 536.42-3: 536.43-4: 583.1Avg: 552.0T

R 1(us): 650.6

TR 2(us): 284.1

TR 3(us): 34.1

TR 4(us): 14.2

Max P1: 26.1Max P2: 25.7Max P3: 31.3Max P4: 29.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

28.6 28.8 29 29.2 29.4 29.6 29.8 300

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 609.62-3: 670.63-4: 670.6Avg: 650.2T

R 1(us): 28.4

TR 2(us): 17.0

TR 3(us): 14.2

TR 4(us): 14.2

Max P1: 38.7Max P2: 39.8Max P3: 40.2Max P4: 36.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

29.8 30 30.2 30.4 30.6 30.8 31 31.20

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 536.42-3: 525.93-4: 547.4Avg: 536.6T

R 1(us): 400.6

TR 2(us): 164.8

TR 3(us): 184.7

TR 4(us): 28.4

Max P1: 22.4Max P2: 22.7Max P3: 22.7Max P4: 23.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.6 30.8 31 31.2 31.4 31.6 31.8 320

2

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 506.12-3: 515.83-4: 515.8Avg: 512.6T

R 1(us): 440.3

TR 2(us): 321.0

TR 3(us): 315.3

TR 4(us): 292.6

Max P1: 17.5Max P2: 17.1Max P3: 17.2Max P4: 15.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.8 39 39.2 39.4 39.6 39.8 40 40.20

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 4470.42-3: 583.13-4: 547.4Avg: 1867.0T

R 1(us): 497.2

TR 2(us): 508.5

TR 3(us): 440.3

TR 4(us): 468.8

Max P1: 22.2Max P2: 23.7Max P3: 25.5Max P4: 26.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 141: Design and Optimization of a Deflagration to Detonation ...

131

Figure 409 - 36 S45D4 BR30 @end_80percL=1.4

Figure 410 - 36 S45D4 BR30 @end_80percL=1.6

Figure 411 - 36 S45D4 BR30 @end_80percL=1.8

Figure 412 - 36 S45D4 BR30 @end_100percL=1.2

Figure 413 - 36 S45D4 BR30 @end_100percL=1.4

Figure 414 - 36 S45D4 BR30 @end_100percL=1.6

38.6 38.8 39 39.2 39.4 39.6 39.82

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 1031.6Avg: InfT

R 1(us): 497.2

TR 2(us): 585.2

TR 3(us): 562.5

TR 4(us): 536.9

Max P1: 13.5Max P2: 14.5Max P3: 16.0Max P4: 15.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39 39.2 39.4 39.6 39.8 40 40.22

3

4

5

6

7

8

9

10

11

12

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 616.5

TR 2(us): 622.2

TR 3(us): 497.2

TR 4(us): 656.3

Max P1: 10.9Max P2: 11.6Max P3: 11.5Max P4: 10.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

46 46.2 46.4 46.6 46.8 47 47.2 47.41

1.5

2

2.5

3

3.5

4

4.5

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 525.6

TR 2(us): 610.8

TR 3(us): 679.0

TR 4(us): 497.2

Max P1: 4.3Max P2: 4.2Max P3: 4.1Max P4: 3.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.6 38.8 39 39.2 39.4 39.6 39.8 400

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 724.93-4: 596.1Avg: InfT

R 1(us): 497.2

TR 2(us): 531.3

TR 3(us): 471.6

TR 4(us): 474.4

Max P1: 21.1Max P2: 23.2Max P3: 25.2Max P4: 25.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.6 36.8 37 37.2 37.4 37.6 37.80

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1788.22-3: 583.13-4: 558.8Avg: 976.7T

R 1(us): 497.2

TR 2(us): 664.8

TR 3(us): 559.7

TR 4(us): 454.5

Max P1: 19.5Max P2: 22.2Max P3: 23.4Max P4: 23.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.6 38.8 39 39.2 39.4 39.6 39.80

2

4

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 2438.43-4: 479.0Avg: InfT

R 1(us): 497.2

TR 2(us): 539.8

TR 3(us): 642.0

TR 4(us): 522.7

Max P1: 16.2Max P2: 16.7Max P3: 18.1Max P4: 17.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 142: Design and Optimization of a Deflagration to Detonation ...

132

Figure 415 - 36 S45D4 BR30 @end_100percL=1.8

Figure 416 - 36 S45D4 BR30 @end_120percL=1.2

Figure 417 - 36 S45D4 BR30 @end_120percL=1.4

Figure 418 - 36 S45D4 BR30 @end_120percL=1.6

Figure 419 - 36 S45D4 BR30 @end_120percL=1.8

Figure 420 - 37 S45D4 BR30 @ign_80percL=1.2

42.2 42.4 42.6 42.8 43 43.2 43.4 43.63

4

5

6

7

8

9

10

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 733.0

TR 3(us): 647.7

TR 4(us): 752.8

Max P1: 8.4Max P2: 8.6Max P3: 9.0Max P4: 8.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.8 40 40.2 40.4 40.6 40.8 41 41.20

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 670.6Avg: InfT

R 1(us): 497.2

TR 2(us): 590.9

TR 3(us): 639.2

TR 4(us): 650.6

Max P1: 20.7Max P2: 21.4Max P3: 24.1Max P4: 24.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.2 38.4 38.6 38.8 39 39.2 39.40

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1341.12-3: 623.83-4: 515.8Avg: 826.9T

R 1(us): 497.2

TR 2(us): 571.0

TR 3(us): 397.7

TR 4(us): 392.0

Max P1: 23.9Max P2: 24.3Max P3: 26.9Max P4: 28.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.8 38 38.2 38.4 38.6 38.8 39 39.20

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1277.33-4: 558.8Avg: InfT

R 1(us): 497.2

TR 2(us): 639.2

TR 3(us): 548.3

TR 4(us): 542.6

Max P1: 18.7Max P2: 19.5Max P3: 21.3Max P4: 22.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41.6 41.8 42 42.2 42.4 42.6 42.82

3

4

5

6

7

8

9

10

11

12

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 608.0

TR 2(us): 497.2

TR 3(us): 542.6

TR 4(us): 622.2

Max P1: 10.5Max P2: 10.7Max P3: 11.0Max P4: 11.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.6 36.8 37 37.2 37.4 37.6 37.80

2

4

6

8

10

12

14

16

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 838.23-4: 506.1Avg: InfT

R 1(us): 497.2

TR 2(us): 585.2

TR 3(us): 747.2

TR 4(us): 556.8

Max P1: 15.3Max P2: 15.1Max P3: 14.9Max P4: 13.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 143: Design and Optimization of a Deflagration to Detonation ...

133

Figure 421 - 37 S45D4 BR30 @ign_80percL=1.4

Figure 422 - 37 S45D4 BR30 @ign_80percL=1.6

Figure 423 - 37 S45D4 BR30 @ign_80percL=1.8

Figure 424 - 37 S45D4 BR30 @ign_100percL=1.2

Figure 425 - 37 S45D4 BR30 @ign_100percL=1.4

Figure 426 - 37 S45D4 BR30 @ign_100percL=1.6

32.8 33 33.2 33.4 33.6 33.8 340

2

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1577.82-3: 506.13-4: 536.4Avg: 873.4T

R 1(us): 519.9

TR 2(us): 448.9

TR 3(us): 386.4

TR 4(us): 321.0

Max P1: 16.4Max P2: 15.9Max P3: 15.6Max P4: 14.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33 33.2 33.4 33.6 33.8 34 34.2 34.40

2

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1577.83-4: 515.8Avg: InfT

R 1(us): 497.2

TR 2(us): 616.5

TR 3(us): 661.9

TR 4(us): 610.8

Max P1: 13.3Max P2: 13.0Max P3: 12.9Max P4: 11.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.2 35.4 35.6 35.8 36 36.2 36.4 36.63

4

5

6

7

8

9

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 659.1

TR 3(us): 1116.5

TR 4(us): 1332.4

Max P1: 8.5Max P2: 8.2Max P3: 8.3Max P4: 6.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38 38.2 38.4 38.6 38.8 39 39.2 39.40

2

4

6

8

10

12

14

16

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 812.83-4: 654.2Avg: InfT

R 1(us): 497.2

TR 2(us): 593.8

TR 3(us): 605.1

TR 4(us): 590.9

Max P1: 15.3Max P2: 15.0Max P3: 15.0Max P4: 13.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34 34.2 34.4 34.6 34.8 35 35.20

2

4

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1072.93-4: 525.9Avg: InfT

R 1(us): 548.3

TR 2(us): 497.2

TR 3(us): 511.4

TR 4(us): 451.7

Max P1: 19.0Max P2: 18.0Max P3: 17.9Max P4: 16.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.8 34 34.2 34.4 34.6 34.8 350

2

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 525.93-4: 525.9Avg: InfT

R 1(us): 497.2

TR 2(us): 579.5

TR 3(us): 551.1

TR 4(us): 488.6

Max P1: 16.2Max P2: 16.4Max P3: 16.4Max P4: 14.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 144: Design and Optimization of a Deflagration to Detonation ...

134

Figure 427 - 37 S45D4 BR30 @ign_100percL=1.8

Figure 428 - 37 S45D4 BR30 @ign_120percL=1.2

Figure 429 - 37 S45D4 BR30 @ign_120percL=1.4

Figure 430 - 37 S45D4 BR30 @ign_120percL=1.6

Figure 431 - 37 S45D4 BR30 @ign_120percL=1.8

Figure 432 - 38 S3D6 BR45 @end_80percL=1.2

35.4 35.6 35.8 36 36.2 36.4 36.60

2

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 496.7Avg: InfT

R 1(us): 497.2

TR 2(us): 588.1

TR 3(us): 704.5

TR 4(us): 656.3

Max P1: 12.2Max P2: 11.6Max P3: 11.5Max P4: 10.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

44.8 45 45.2 45.4 45.6 45.8 463

4

5

6

7

8

9

10

11

12

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 713.1

TR 3(us): 963.1

TR 4(us): 1161.9

Max P1: 11.4Max P2: 11.0Max P3: 10.8Max P4: 9.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35 35.2 35.4 35.6 35.8 36 36.2 36.40

2

4

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1577.82-3: 515.83-4: 536.4Avg: 876.7T

R 1(us): 497.2

TR 2(us): 542.6

TR 3(us): 644.9

TR 4(us): 599.4

Max P1: 19.6Max P2: 18.9Max P3: 18.2Max P4: 15.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.6 33.8 34 34.2 34.4 34.6 34.8 350

2

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 547.43-4: 525.9Avg: InfT

R 1(us): 497.2

TR 2(us): 596.6

TR 3(us): 358.0

TR 4(us): 306.8

Max P1: 16.5Max P2: 16.8Max P3: 16.6Max P4: 15.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35 35.2 35.4 35.6 35.8 36 36.2 36.40

5

10

15

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 3831.83-4: 506.1Avg: InfT

R 1(us): 497.2

TR 2(us): 593.8

TR 3(us): 670.5

TR 4(us): 619.3

Max P1: 14.0Max P2: 13.7Max P3: 13.4Max P4: 11.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.2 39.4 39.6 39.8 40 40.2 40.4 40.60

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 654.22-3: 638.63-4: 583.1Avg: 625.3T

R 1(us): 460.2

TR 2(us): 411.9

TR 3(us): 411.9

TR 4(us): 258.5

Max P1: 29.1Max P2: 32.7Max P3: 36.7Max P4: 35.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 145: Design and Optimization of a Deflagration to Detonation ...

135

Figure 433 - 38 S3D6 BR45 @end_80percL=1.4

Figure 434 - 38 S3D6 BR45 @end_80percL=1.6

Figure 435 - 38 S3D6 BR45 @end_80percL=1.8

Figure 436 - 38 S3D6 BR45 @end_100percL=1.2

Figure 437 - 38 S3D6 BR45 @end_100percL=1.4

Figure 438 - 38 S3D6 BR45 @end_100percL=1.6

38.6 38.8 39 39.2 39.4 39.6 39.80

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 670.6Avg: InfT

R 1(us): 497.2

TR 2(us): 522.7

TR 3(us): 542.6

TR 4(us): 596.6

Max P1: 18.1Max P2: 18.4Max P3: 20.1Max P4: 21.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41.2 41.4 41.6 41.8 42 42.2 42.4 42.60

2

4

6

8

10

12

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 522.7

TR 3(us): 571.0

TR 4(us): 539.8

Max P1: 9.9Max P2: 10.0Max P3: 9.9Max P4: 10.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

44.8 45 45.2 45.4 45.6 45.8 46 46.2-0.5

0

0.5

1

1.5

2

2.5

3

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 818.2

TR 2(us): 497.2

TR 3(us): 690.3

TR 4(us): 832.4

Max P1: 2.6Max P2: 2.4Max P3: 2.2Max P4: 2.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41.8 42 42.2 42.4 42.6 42.8 43 43.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 670.63-4: 596.1Avg: 663.8T

R 1(us): 514.2

TR 2(us): 392.0

TR 3(us): 318.2

TR 4(us): 332.4

Max P1: 29.7Max P2: 33.8Max P3: 37.2Max P4: 40.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.8 40 40.2 40.4 40.6 40.8 410

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 3352.83-4: 558.8Avg: InfT

R 1(us): 588.1

TR 2(us): 497.2

TR 3(us): 667.6

TR 4(us): 480.1

Max P1: 23.6Max P2: 26.7Max P3: 27.5Max P4: 28.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.6 38.8 39 39.2 39.4 39.6 39.8 402

4

6

8

10

12

14

16

18

20

22

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 13411.23-4: 2438.4Avg: InfT

R 1(us): 585.2

TR 2(us): 497.2

TR 3(us): 619.3

TR 4(us): 747.2

Max P1: 17.9Max P2: 19.6Max P3: 21.1Max P4: 20.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 146: Design and Optimization of a Deflagration to Detonation ...

136

Figure 439 - 38 S3D6 BR45 @end_100percL=1.8

Figure 440 - 38 S3D6 BR45 @end_120percL=1.2

Figure 441 - 38 S3D6 BR45 @end_120percL=1.4

Figure 442 - 38 S3D6 BR45 @end_120percL=1.6

Figure 443 - 38 S3D6 BR45 @end_120percL=1.8

Figure 444 - 39 S3D6 BR45 @ign_80percL=1.2

41.4 41.6 41.8 42 42.2 42.4 42.61

2

3

4

5

6

7

8

9

10

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 812.5

TR 2(us): 633.5

TR 3(us): 497.2

TR 4(us): 738.6

Max P1: 9.1Max P2: 9.0Max P3: 8.6Max P4: 8.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

65.2 65.4 65.6 65.8 66 66.2 66.40

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 1117.6Avg: InfT

R 1(us): 579.5

TR 2(us): 551.1

TR 3(us): 497.2

TR 4(us): 460.2

Max P1: 23.2Max P2: 24.2Max P3: 25.8Max P4: 27.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41.2 41.4 41.6 41.8 42 42.2 42.4 42.60

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 454.62-3: 1490.13-4: 439.7Avg: 794.8T

R 1(us): 480.1

TR 2(us): 369.3

TR 3(us): 474.4

TR 4(us): 446.0

Max P1: 30.9Max P2: 35.9Max P3: 35.7Max P4: 40.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

37.8 38 38.2 38.4 38.6 38.8 390

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1915.92-3: 487.73-4: 654.2Avg: 1019.3T

R 1(us): 497.2

TR 2(us): 483.0

TR 3(us): 474.4

TR 4(us): 551.1

Max P1: 24.5Max P2: 27.6Max P3: 29.9Max P4: 29.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

40.8 41 41.2 41.4 41.6 41.8 424

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 1915.9Avg: InfT

R 1(us): 497.2

TR 2(us): 582.4

TR 3(us): 551.1

TR 4(us): 664.8

Max P1: 15.7Max P2: 16.4Max P3: 17.9Max P4: 18.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31 31.2 31.4 31.6 31.8 32 32.20

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 654.23-4: 687.8Avg: 641.7T

R 1(us): 36.9

TR 2(us): 14.2

TR 3(us): 14.2

TR 4(us): 14.2

Max P1: 35.6Max P2: 38.0Max P3: 39.6Max P4: 38.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 147: Design and Optimization of a Deflagration to Detonation ...

137

Figure 445 - 39 S3D6 BR45 @ign_80percL=1.4

Figure 446 - 39 S3D6 BR45 @ign_80percL=1.6

Figure 447 - 39 S3D6 BR45 @ign_80percL=1.8

Figure 448 - 39 S3D6 BR45 @ign_100percL=1.2

Figure 449 - 39 S3D6 BR45 @ign_100percL=1.4

Figure 450 - 39 S3D6 BR45 @ign_100percL=1.6

30.4 30.6 30.8 31 31.2 31.4 31.6 31.80

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 623.82-3: 654.23-4: 670.6Avg: 649.5T

R 1(us): 22.7

TR 2(us): 17.0

TR 3(us): 17.0

TR 4(us): 14.2

Max P1: 34.4Max P2: 39.0Max P3: 37.2Max P4: 37.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.4 30.6 30.8 31 31.2 31.4 31.6 31.80

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 515.82-3: 547.43-4: 547.4Avg: 536.9T

R 1(us): 318.2

TR 2(us): 161.9

TR 3(us): 76.7

TR 4(us): 28.4

Max P1: 21.4Max P2: 21.7Max P3: 22.1Max P4: 26.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.8 36 36.2 36.4 36.6 36.8 370

2

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 2438.43-4: 515.8Avg: InfT

R 1(us): 497.2

TR 2(us): 630.7

TR 3(us): 733.0

TR 4(us): 690.3

Max P1: 13.1Max P2: 12.9Max P3: 12.5Max P4: 11.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34 34.2 34.4 34.6 34.8 35 35.20

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 515.82-3: 515.83-4: 570.7Avg: 534.1T

R 1(us): 116.5

TR 2(us): 76.7

TR 3(us): 34.1

TR 4(us): 17.0

Max P1: 25.5Max P2: 25.7Max P3: 31.0Max P4: 30.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.2 31.4 31.6 31.8 32 32.2 32.40

5

10

15

20

25

30

35

40

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 558.82-3: 654.23-4: 670.6Avg: 627.9T

R 1(us): 39.8

TR 2(us): 19.9

TR 3(us): 14.2

TR 4(us): 11.4

Max P1: 33.2Max P2: 38.2Max P3: 38.2Max P4: 38.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30.8 31 31.2 31.4 31.6 31.8 320

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 525.92-3: 536.43-4: 596.1Avg: 552.8T

R 1(us): 306.8

TR 2(us): 59.7

TR 3(us): 31.3

TR 4(us): 19.9

Max P1: 21.4Max P2: 21.8Max P3: 27.9Max P4: 28.0

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 148: Design and Optimization of a Deflagration to Detonation ...

138

Figure 451 - 39 S3D6 BR45 @ign_100percL=1.8

Figure 452 - 39 S3D6 BR45 @ign_120percL=1.2

Figure 453 - 39 S3D6 BR45 @ign_120percL=1.4

Figure 454 - 39 S3D6 BR45 @ign_120percL=1.6

Figure 455 - 39 S3D6 BR45 @ign_120percL=1.8

Figure 456 - 40 S6D3 BR30 @ign_80percL=1.2

34.4 34.6 34.8 35 35.2 35.4 35.60

2

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 583.12-3: 479.03-4: 525.9Avg: 529.3T

R 1(us): 497.2

TR 2(us): 554.0

TR 3(us): 414.8

TR 4(us): 463.1

Max P1: 16.0Max P2: 15.7Max P3: 15.4Max P4: 13.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.2 36.4 36.6 36.8 37 37.2 37.40

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 536.42-3: 525.93-4: 583.1Avg: 548.5T

R 1(us): 110.8

TR 2(us): 73.9

TR 3(us): 34.1

TR 4(us): 17.0

Max P1: 27.4Max P2: 28.5Max P3: 34.7Max P4: 32.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33 33.2 33.4 33.6 33.8 34 34.2 34.40

5

10

15

20

25

30

35

40

45

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 638.62-3: 670.63-4: 670.6Avg: 659.9T

R 1(us): 19.9

TR 2(us): 19.9

TR 3(us): 17.0

TR 4(us): 11.4

Max P1: 36.2Max P2: 39.9Max P3: 40.1Max P4: 38.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

30 30.2 30.4 30.6 30.8 31 31.2 31.40

5

10

15

20

25

30

35

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 536.42-3: 536.43-4: 596.1Avg: 556.3T

R 1(us): 130.7

TR 2(us): 161.9

TR 3(us): 34.1

TR 4(us): 17.0

Max P1: 24.8Max P2: 24.4Max P3: 32.0Max P4: 31.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

31.4 31.6 31.8 32 32.2 32.4 32.60

2

4

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 506.12-3: 487.73-4: 536.4Avg: 510.1T

R 1(us): 525.6

TR 2(us): 511.4

TR 3(us): 156.3

TR 4(us): 119.3

Max P1: 17.9Max P2: 17.3Max P3: 18.0Max P4: 17.4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.6 36.8 37 37.2 37.4 37.6 37.8 382

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 583.1Avg: InfT

R 1(us): 497.2

TR 2(us): 599.4

TR 3(us): 707.4

TR 4(us): 778.4

Max P1: 16.0Max P2: 15.5Max P3: 14.7Max P4: 13.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 149: Design and Optimization of a Deflagration to Detonation ...

139

Figure 457 - 40 S6D3 BR30 @ign_80percL=1.4

Figure 458 - 40 S6D3 BR30 @ign_80percL=1.6

Figure 459 - 40 S6D3 BR30 @ign_80percL=1.8

Figure 460 - 40 S6D3 BR30 @ign_100percL=1.2

Figure 461 - 40 S6D3 BR30 @ign_100percL=1.4

Figure 462 - 40 S6D3 BR30 @ign_100percL=1.6

33.8 34 34.2 34.4 34.6 34.8 350

2

4

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 1676.42-3: 536.43-4: 547.4Avg: 920.1T

R 1(us): 497.2

TR 2(us): 534.1

TR 3(us): 485.8

TR 4(us): 417.6

Max P1: 17.9Max P2: 18.3Max P3: 17.5Max P4: 15.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

32.8 33 33.2 33.4 33.6 33.8 34 34.22

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 26822.4Avg: InfT

R 1(us): 497.2

TR 2(us): 772.7

TR 3(us): 852.3

TR 4(us): 619.3

Max P1: 13.9Max P2: 13.2Max P3: 12.9Max P4: 10.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.4 35.6 35.8 36 36.2 36.4 36.6 36.84.5

5

5.5

6

6.5

7

7.5

8

8.5

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 571.0

TR 3(us): 644.9

TR 4(us): 718.8

Max P1: 8.1Max P2: 8.1Max P3: 8.2Max P4: 6.8

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.8 39 39.2 39.4 39.6 39.8 402

4

6

8

10

12

14

16

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 8940.8Avg: InfT

R 1(us): 497.2

TR 2(us): 542.6

TR 3(us): 625.0

TR 4(us): 704.5

Max P1: 15.5Max P2: 14.4Max P3: 14.5Max P4: 12.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

35.8 36 36.2 36.4 36.6 36.8 37 37.20

2

4

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 724.92-3: 525.93-4: 547.4Avg: 599.4T

R 1(us): 497.2

TR 2(us): 488.6

TR 3(us): 446.0

TR 4(us): 397.7

Max P1: 19.8Max P2: 18.7Max P3: 18.0Max P4: 15.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.2 33.4 33.6 33.8 34 34.2 34.40

2

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 670.63-4: 525.9Avg: InfT

R 1(us): 497.2

TR 2(us): 940.3

TR 3(us): 571.0

TR 4(us): 855.1

Max P1: 16.7Max P2: 15.6Max P3: 15.6Max P4: 13.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 150: Design and Optimization of a Deflagration to Detonation ...

140

Figure 463 - 40 S6D3 BR30 @ign_100percL=1.8

Figure 464 - 40 S6D3 BR30 @ign_120percL=1.2

Figure 465 - 40 S6D3 BR30 @ign_120percL=1.4

Figure 466 - 40 S6D3 BR30 @ign_120percL=1.6

Figure 467 - 40 S6D3 BR30 @ign_120percL=1.8

Figure 468 - 41 S6D3 BR30 @end_80percL=1.2

33.6 33.8 34 34.2 34.4 34.6 34.80

2

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1219.23-4: 525.9Avg: InfT

R 1(us): 497.2

TR 2(us): 605.1

TR 3(us): 642.0

TR 4(us): 596.6

Max P1: 12.9Max P2: 12.4Max P3: 12.1Max P4: 10.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

47.8 48 48.2 48.4 48.6 48.8 493

4

5

6

7

8

9

10

11

12

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 636.4

TR 3(us): 852.3

TR 4(us): 960.2

Max P1: 11.5Max P2: 11.1Max P3: 11.3Max P4: 9.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

36.8 37 37.2 37.4 37.6 37.8 380

2

4

6

8

10

12

14

16

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 1341.13-4: 536.4Avg: InfT

R 1(us): 497.2

TR 2(us): 590.9

TR 3(us): 633.5

TR 4(us): 667.6

Max P1: 15.6Max P2: 15.8Max P3: 15.1Max P4: 13.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

33.8 34 34.2 34.4 34.6 34.8 35 35.20

2

4

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 705.92-3: 547.43-4: 558.8Avg: 604.0T

R 1(us): 497.2

TR 2(us): 667.6

TR 3(us): 440.3

TR 4(us): 389.2

Max P1: 18.1Max P2: 17.8Max P3: 17.4Max P4: 15.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

34.2 34.4 34.6 34.8 35 35.2 35.40

2

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 2063.33-4: 506.1Avg: InfT

R 1(us): 630.7

TR 2(us): 500.0

TR 3(us): 460.2

TR 4(us): 957.4

Max P1: 13.1Max P2: 12.5Max P3: 12.2Max P4: 11.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

46 46.2 46.4 46.6 46.8 47 47.2 47.40

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 638.63-4: 558.8Avg: InfT

R 1(us): 536.9

TR 2(us): 497.2

TR 3(us): 627.8

TR 4(us): 508.5

Max P1: 22.3Max P2: 24.1Max P3: 24.7Max P4: 25.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 151: Design and Optimization of a Deflagration to Detonation ...

141

Figure 469 - 41 S6D3 BR30 @end_80percL=1.4

Figure 470 - 41 S6D3 BR30 @end_80percL=1.6

Figure 471 - 41 S6D3 BR30 @end_80percL=1.8

Figure 472 - 41 S6D3 BR30 @end_100percL=1.2

Figure 473 - 41 S6D3 BR30 @end_100percL=1.4

Figure 474 - 41 S6D3 BR30 @end_100percL=1.6

36.6 36.8 37 37.2 37.4 37.6 37.80

2

4

6

8

10

12

14

16

18

20

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: 596.13-4: 596.1Avg: InfT

R 1(us): 497.2

TR 2(us): 687.5

TR 3(us): 508.5

TR 4(us): 551.1

Max P1: 17.8Max P2: 18.4Max P3: 18.5Max P4: 18.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.8 39 39.2 39.4 39.6 39.8 40 40.22

4

6

8

10

12

14

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 957.9Avg: InfT

R 1(us): 497.2

TR 2(us): 644.9

TR 3(us): 605.1

TR 4(us): 715.9

Max P1: 12.7Max P2: 13.4Max P3: 13.5Max P4: 12.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

43.2 43.4 43.6 43.8 44 44.2 44.4-1

0

1

2

3

4

5

6

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 534.1

TR 2(us): 500.0

TR 3(us): 517.0

TR 4(us): 497.2

Max P1: 5.2Max P2: 5.1Max P3: 4.9Max P4: 4.2

Sensor 1

Sensor 2

Sensor 3

Sensor 4

45.4 45.6 45.8 46 46.2 46.4 46.6-5

0

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 2438.4Avg: InfT

R 1(us): 554.0

TR 2(us): 497.2

TR 3(us): 511.4

TR 4(us): 534.1

Max P1: 16.8Max P2: 18.8Max P3: 21.0Max P4: 20.6

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.8 40 40.2 40.4 40.6 40.8 410

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 4470.42-3: 623.83-4: 596.1Avg: 1896.7T

R 1(us): 497.2

TR 2(us): 500.0

TR 3(us): 414.8

TR 4(us): 414.8

Max P1: 23.6Max P2: 24.9Max P3: 26.3Max P4: 25.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

39.4 39.6 39.8 40 40.2 40.4 40.6 40.80

2

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 508.5

TR 3(us): 630.7

TR 4(us): 562.5

Max P1: 16.0Max P2: 16.9Max P3: 17.7Max P4: 17.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 152: Design and Optimization of a Deflagration to Detonation ...

142

Figure 475 - 41 S6D3 BR30 @end_100percL=1.8

Figure 476 - 41 S6D3 BR30 @end_120percL=1.2

Figure 477 - 41 S6D3 BR30 @end_120percL=1.4

Figure 478 - 41 S6D3 BR30 @end_120percL=1.6

Figure 479 - 41 S6D3 BR30 @end_120percL=1.8

Figure 480 - 42 oxygen_oxygen01

39.6 39.8 40 40.2 40.4 40.6 40.8 412

3

4

5

6

7

8

9

10

11

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 497.2

TR 2(us): 534.1

TR 3(us): 596.6

TR 4(us): 676.1

Max P1: 9.5Max P2: 10.0Max P3: 10.9Max P4: 10.5

Sensor 1

Sensor 2

Sensor 3

Sensor 4

53.4 53.6 53.8 54 54.2 54.4 54.6-2

0

2

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 528.4

TR 2(us): 497.2

TR 3(us): 505.7

TR 4(us): 548.3

Max P1: 14.2Max P2: 14.8Max P3: 15.5Max P4: 16.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38 38.2 38.4 38.6 38.8 39 39.2 39.40

5

10

15

20

25

30

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 3831.82-3: 583.13-4: 609.6Avg: 1674.8T

R 1(us): 497.2

TR 2(us): 656.3

TR 3(us): 565.3

TR 4(us): 488.6

Max P1: 20.7Max P2: 23.2Max P3: 26.2Max P4: 24.7

Sensor 1

Sensor 2

Sensor 3

Sensor 4

38.2 38.4 38.6 38.8 39 39.2 39.4 39.60

5

10

15

20

25

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 670.62-3: 558.83-4: 609.6Avg: 613.0T

R 1(us): 497.2

TR 2(us): 573.9

TR 3(us): 446.0

TR 4(us): 502.8

Max P1: 19.2Max P2: 20.8Max P3: 22.3Max P4: 24.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

40.4 40.6 40.8 41 41.2 41.4 41.62

4

6

8

10

12

14

16

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: 1788.2Avg: InfT

R 1(us): 497.2

TR 2(us): 661.9

TR 3(us): 534.1

TR 4(us): 681.8

Max P1: 13.7Max P2: 13.9Max P3: 15.9Max P4: 15.1

Sensor 1

Sensor 2

Sensor 3

Sensor 4

41 41.2 41.4 41.6 41.8 42 42.2 42.4-100

0

100

200

300

400

500

600

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 2438.42-3: 1915.93-4: 1915.9Avg: 2090.1T

R 1(us): 0.0

TR 2(us): 0.0

TR 3(us): 42.6

TR 4(us): 8.5

Max P1: 552.8Max P2: 574.1Max P3: 312.0Max P4: 252.9

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Page 153: Design and Optimization of a Deflagration to Detonation ...

143

Figure 481 - 42 oxygen_oxygen02

Figure 482 - 42 oxygen_oxygen03

35.6 35.8 36 36.2 36.4 36.6 36.8 37-200

0

200

400

600

800

1000

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: 2980.32-3: 2980.33-4: 2438.4Avg: 2799.6T

R 1(us): 2.8

TR 2(us): 2.8

TR 3(us): 2.8

TR 4(us): 2.8

Max P1: 970.9Max P2: 962.4Max P3: 768.5Max P4: 561.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4

23.2 23.4 23.6 23.8 24 24.2 24.4-2

0

2

4

6

8

10

12

14

16

18

Time (ms)

Pre

ssur

e (

psi

g)

Speed: (m/s)1-2: Inf2-3: Inf3-4: InfAvg: InfT

R 1(us): 656.3

TR 2(us): 497.2

TR 3(us): 517.0

TR 4(us): 525.6

Max P1: 13.3Max P2: 13.8Max P3: 13.9Max P4: 16.3

Sensor 1

Sensor 2

Sensor 3

Sensor 4