PREMIXED FLAME ACCELERATION IN STRAIGHT AND BEND CLOSED PIPE

MISS HASIMAWATY BINTI MAT KIAH

A thesis submitted in fulfilment of the

requirements for the award of the degree of

Master of Engineering (Gas)

Faculty of Petroleum and Renewable Energy Engineering

Universiti Teknologi Malaysia

SEPTEMBER 2013

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ABSTRACT

There were many studies on premixed flame propagation in tubes, including open tubes and enclosures. Yet, no sufficient data obtained for explosion properties in medium scale piping system to assist engineers or practitioners in determining the potential hazard posed due to explosion. In this work, an experimental study had been carried out to investigate the explosion properties in a pipeline using two pipe configurations, i.e. straight and 90 degree bend. A horizontal steel pipe, with 2 m long(L) and 0.1 m diameter (D), giving L/D ratio of 20 was used in the range of equivalence ratios (Ф) from 0.5 to 1.8. The 90 degree bend pipe had a bend radius of 0.1 m withadded a further 1 m to the length of the pipe (based on the centerline length of the segment). Natural gas/pure oxygen mixture was prepared using partial pressure method and a homogeneous composition was achieved by circulating the mixture using a solid ball which was placed in the mixing cell. It was shown that stoichiometric mixtures gave the highest flame speed measurement, both on straight and bend pipes. Stoichiometric concentration (Ф = 1.0) gave significant maximum overpressure of 5.5 bars for bend pipe, compared to 2.0 bars on straight pipe explosion test; approximately 3 times higher. This was due to bending part that acted like obstacles. This mechanism could induce and created more turbulence, initiated the combustion of unburned pocket at the corner region, causing high mass burning rate and hence, increased the flame speed. It was also shown that the flame speed was enhanced by factor of 3 for explosion in bend pipe compared to straight pipe. It can be concluded that the bend can create greater turbulence effect compared to straight pipe configuration and applying appropriate safety devices before the area of the bends is recommended as one of the effective methods to prevent the explosion from happen.

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TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENTS iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xi

LIST OF EQUATIONS xiii

LIST OF SYMBOLS xiv

LIST OF APPENDICES xvii

1 INTRODUCTION

1.1 Motivation/Introduction 1

1.2 Problem Statement 3

1.3 Objective of Research 5

1.4 Scope of Research 5

2 LITERATURE REVIEW

2.1 Research Background 6

2.2 Gas Explosion 7

2.3 Explosion Properties 10

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2.3.1 Flame Speed, Burning Velocity and Unburned

Gas Velocity10

2.3.1.1 Calculation of the Unburned Gas

Velocity, Sg12

2.3.1.2 Laminar or Turbulent Flame Speed

and Burning Velocity13

2.3.2 Overpressure and Rate of Pressure Rise 19

2.4 Factors Influence the Explosion Properties 25

2.4.1 Mixture Ratios and Stoichiometric

Concentration25

2.4.2 Ignition Position 28

2.4.3 Flammability Limit and Fuel Type 29

2.4.4 Pipe Configuration, Size and Shape 34

3 METHODOLOGY

3.1 Initial Preparation of Equipment and Fuel/Air

Mixture38

3.2 Method of Calculations for the Pressure of Fuel/Air

Mixture45

3.3 Detail of Research Methodology 50

3.4 Calculations of Flame Speed 54

3.5 Data Collection and Analysis 55

4 RESULTS AND DISCUSSION

4.1 Explosion in Straight Pipe 57

4.1.1 Pressure Time/Histories on Straight Pipe 57

4.1.2 Effect of Equivalent Ratio on Explosion

Pressure in Straight Pipe59

4.1.3 Rate of Pressure Rise (dP/dt) on Straight Pipe 61

4.1.4 Flame Speeds on Straight Pipe 62

4.2 Explosion in 90 Degree Bend Pipe 65

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4.2.1 Pressure Development/Profile on 90 Degree

Bend Pipe65

4.2.2 Effect of Equivalent Ratio on Explosion

Pressure in 90 Degree Bend Pipe66

4.2.3 Rate of Pressure Rise (dP/dt) on 90 Degree

Bend Pipe69

4.2.4 Flame Speeds on 90 Degree Bend Pipe 71

4.3 Unburnt Gas Velocity, Sg 73

4.3.1 Unburnt Gas Velocity, Sg for Straight and 90

Degree Bend Pipe73

4.4 Comparison with the Previous Published Data 75

4.4.1 Explosion Pressure on Straight Pipe 75

4.4.2 Flame Speed Comparison on Straight Pipe 77

5 CONCLUSION

5.1 Conclusion 79

5.2 Recommendation and Future Research 81

LIST OF PUBLICATIONS AND CONFERENCES 82

REFERENCES 83

Appendices A - D 89 - 101

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LIST OF TABLES

TABLE NO. TITLE PAGE

2.1 Laminar flame speed for stoichiometric composition 15

2.2Fuel-air mixtures concentration at stoichiometric

composition27

2.3Collected pressure and volume ratio for stoichiometric

mixtures at standard test conditions32

2.4Data summary of flame speed and overpressure for methane

explosions36

3.1Calculated gauge pressures (Pa and Pb) at different

concentration of fuel/air mixture for straight pipe48

3.2Calculated gauge pressures (Pa and Pb) at different

concentration of fuel/air mixture for 90 degree bends pipe49

3.3 Special procedure during the test 53

4.1Turbulent enhancement factor for various mixture

concentrations68

4.2Severity factor or deflagration index, KG at lean,

stoichiometric and rich mixture concentrations71

4.3Pressure and flame speed of methane explosion at

stoichiometric75

xi

LIST OF FIGURES

FIGURE NO. TITLE PAGE

2.1 Steps for explosion mechanism 9

2.2 Transmission of flame in cylindrical vessel 11

2.3 Flow path diagram for element in laminar and turbulent form 14

2.4 Growth of turbulent boundary layer in tube 18

2.5 Pressure versus time for various mixture concentrations 20

2.6Pressure versus time at different methane-air mixture

concentrations21

2.7Maximum rate of pressure rise against methane-air

concentrations for various ignition positions22

2.8 Lower flammability and upper flammability limit 30

2.9Flammability limits of fuel-air mixtures at standard

atmospheric condition32

2.10Maximum pressure collected for various fuel-air mixtures at

stoichiometric concentration of the gases mixture33

2.11Flame speed profile and development for methane-air

explosions in various pipe configurations35

3.1 Mixer and straight pipe configuration 39

3.2 Mixer and 90 degree bend pipe configuration 40

3.3 Mixing cell configuration 41

3.4 Data logger configuration 42

3.5 Configuration of explosion piping system (main testing pipe) 43

3.6 Tanks (natural gas, oxygen and nitrogen) 44

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3.7 Vacuum pump configuration 45

3.8 Flow Chart of the research study 54

3.9 Recorded image by LabView Signal Express 56

4.1Pressure against time at lean, stoichiometric and rich

concentration58

4.2Pressure profile along the pipe for different mixture

concentrations60

4.3 Rate of pressure rise against distance from ignition, x 62

4.4Flame speed profile against L/D at various mixture

concentrations64

4.5 Pressure developments against time 66

4.6 Pressure rise versus L/D at different mixture concentrations 67

4.7Turbulent enhancement factors at various mixture

concentrations69

4.8Rate of pressure rise at lean, stoichiometric and rich

concentration70

4.9 Flame speed on 90 degree bend pipe 72

4.10Unburnt gas velocity, Sg for straight and bending at various

Ф74

4.11Explosion pressure for present and previous studies at

stoichiometric condition for different L/Ds76

4.12 Flame speed comparison at stoichiometric condition 78

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LIST OF EQUATIONS

EQUATION TITLE PAGE

2.1 Flame speed, S or Sf (relation with U or Su and u or Sg) 10

2.2 Expansion ratio, E 12

2.3 Unburnt gas velocity, Sg 12

2.4 Unburnt gas velocity, Sg at bend 13

2.5 Reynold number, Re 13

2.6 Laminar burning velocity, SL 15

2.7 Turbulent flame speed, St 17

2.8 Turbulent factor, β 19

2.9 Severity factor/deflagration index, KG 23

2.10 Ideal gas law relationship 24

2.11 Equivalent ratio/concentration of mixture 26

2.12 Flammability limits, LFLMix (Le Chatelier’s Law) 30

3.1 Mixture pressure 45

3.2 Vessel volume, V 45

3.3 Total pressure for fuel/air mixture, P1 46

3.4 Gas law 46

3.5 Equivalent ratio, Ф 47

3.6Flame speed, S or Sf (relation with distance from ignition, x

or X and time, t)55

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LIST OF SYMBOLS

AFR - Air fuel ratio

ATEX - Atmospheres Explosives

C - Speed of sound, m s-1

CJ - Chapman Jouguet

CP - Hose

Ci - Gas proportion in fuel mixture without air

CH4 - Methane

CTA - Constant Temperature Anemometry

DDT - Deflagration to detonation

D - Diameter, m; Detonation velocity, m s-1

dP/dt - Rate of pressure rise, bar s-1

(dP/dt)max - Maximum rate of pressure rise, bar s-1

E - Expansion ratio

FLACS - Flame Acceleration Simulator

K - Pressure loss coefficient = 1 (for 90 degree bend)

KG - Severity factor or deflagration index

L - Length, m; Volume, L

LEL, LFL - Lower explosive or flammability limit

LFLMix - Flammability limit (Le Chatelier’s law)

mfuel - Mass of fuel, kg

mox - Mass of oxygen, kg

NG - Natural gas

Nb - Number of mole for product

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Nu - Number of mole for reactant

N2 - Nitrogen

nfuel - Mole of fuel

nox - Mole of oxygen

O2 - Oxygen

P - Pressure, bar

PPE - Personal protective equipments

Pexp - Explosion pressure, bar

Pmax - Maximum explosion pressure, bar

Ploss - Head of pressure loss

R - Gas constant

Re - Reynold number

r - Radius, m

S, Sf - Flame speed, m s-1

S/P - Special procedure

SL - Laminar flame or burning velocity, m s-1

So - Mixing parameter

St - Turbulent flame speed or burning velocity, m s-1

sin α - Angle of slope

Tf, Ti - Temperature, oC

t, tf, ti - Time, s

U, Su, Vu - Burning velocity, m s-1

UEL, UFL - Upper explosive or flammability limit

u, Sg - Unburnt gas velocity, m s-1

V, Vo - Volume, m3; Valve number

VOCs - Volatile organic solvents

v - Kinematic viscosity

Xf, Xi, x - Distance of sensors (thermocouple or pressure transducer), m

Z - Compressibility factor

ρ - Density

Ф - Equivalent Ratio

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ΔP - Overpressure, bar

θexp -Time interval between ignition and the moment when explosion

pressure is attained, s

β - Turbulent factor

π - Pi = 3.142

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LIST OF APPENDICES

APPENDIX TITLE PAGE

A1 Schematic configuration of main testing pipe 89

A2 Overall of experimental rig 90

B1 GC analysis for Ф = 0.6 (lean mixture) 91

B2 GC analysis for Ф = 1.0 (stoichiometric mixture) 92

B3 GC analysis for Ф = 1.6 (rich mixture) 93

B4 Summary of GC analysis 94

C1, C2 List of pressure data and calculated percentage (%) accuracy 95

D1 Diagram of test pipe and mixer 98

D2 Tick Sheet in conducting the test 99

CHAPTER 1

INTRODUCTION

1.1 Motivation / Introduction

In process industries, explosion is still a major problem that causes accidents,

losses and properties damages. To prevent this explosion in many process and operation

system like chemical processes plant, process equipment, piping and vent manifold

system, protection against undesired phenomena such as deflagration to detonation

transition (DDT) is highly required and this mechanism need to be controlled properly

[1]. There is sharply increase in the number of piping system, explosive mixtures

handling and collective system, closures and transport due to the strict rules raised by the

environmental and safety personnel in handling the volatile organic solvents (VOCs). It

is compulsory for operators to control over these mixtures to make sure the flammable

gases can be discharged safely [2]. Due to the risk and consequence from the above

situation, protection systems such as venting and correct placement of flame arresters are

considered necessary to reduce the overpressure generated during the unexpected

explosion cases. To apply this safety devices effectively require lots of knowledge and

2

fully understanding regarding the explosion behavior and parameters and well

researched in this area is required.

Venting in tubes and pipes has been studied intensively [3-4], however there is

uncertainty on the determination of ignition position in advance, leading a major

difficulty of venting an explosion in large L/D configuration. For encountering many

situations and conditions of explosion, specified flame arresters must to be installed at

correct places in order to follow and comply with ATEX (Atmospheres Explosives), a

standard by European Union describing what equipment and work environment is

allowed in an environment with an explosive atmosphere. For the flame arrester,

questions on the best location of these devices and concerns have been raised with safety

standard for flame arresters in regards to the lack of knowledge of where deflagration to

detonation will/can occur in a pipe and the contributing factors on this phenomenon [5].

Understanding the mode of flame acceleration and combustion behavior along the pipe

is essential in order to install/apply appropriate protective systems either passive or

active. Until today, the continuous concerns about to position the flame arrester correctly

as highlighted by the safety concept bring to the main cause for prediction of the burning

mode at various points in a pipe by the researchers.

Furthermore, obstacles such as presence of baffle and bends in pipe are rampant

in many processes and applications. The knowledge of effects on explosion properties

and phenomena including overpressure, burning rate, flame acceleration and

deflagration to detonation transition (DDT) is vital for the proper installation of

explosion safety devices such as venting and flame arrester into the operating system. In

industrial processes, the full-bore obstacles such as tube bends have extensively applied.

Over past years, explosions in pipes and ducts, flame acceleration and DDT were well

researched subject [6], however there were concentrated on the effects of baffle type

obstacles or items in the path of the flow [7-8]. To the author’s knowledge, there is

3

sparse study on the explosions through pipe bends used extensively in industrial

applications, and the effects on flame acceleration, overpressure enhancement and the

contribution on DDT severity.

1.2 Problem Statement

The aim of the research is to provide detailed physical and dynamic flame

propagation mechanism for gas explosion in a medium size (industrial scale) of closed

pipe and determine the effect of pipe configuration on the flame acceleration and

explosion pressure. Data obtained from the experimental work will be compared with

the previous published experimental data and also can be a reference to future researcher

in order to validate the predictive protection system that would be applied to the similar

pipe configuration. Turbulent enhancement factor also can be determined according to

the collected results for both pipe configurations in order to compare the explosion

behaviors and profile or mechanism.

Work by Phylaktou et al [9], using a 3 m long and 162 mm diameter tube (L/D

ratio of 18.5) with closed at both ends, showed that the flame speed and overpressure for

methane-air explosions with 90 degree bend pipe have increased compared to the

explosions conducted in straight pipe. The flame speeds was enhanced in a factor of 5

and this condition is similar to the effect using baffle of 20% blockage ratio at the same

position. Limited studies were done on medium scale. That is why this study was

conducted as to complete the circle of small, medium and large scale in piping system.

In present work, the effect of L/D on explosion properties for L/D ratio of 20 (straight

pipe) and L/D ratio of 38 (90 degree bend pipe) has been investigated.

4

Chatrathi [10] found that for propane-air mixtures in 152.4 mm diameter pipe

with the open end and rear ignition, the development of flame speed increased about

24% after a 90 degree bend placed half-way down a tube. Zhou et al [11], observed that

the flame front experienced a ‘flame shedding’ inside the bend when travelling through a

rectangular 90 degree bend. This observation has a good agreement with 3D particle

modeling of the surge inside of the bend. It is found that large vortexes (turbulent) were

produced just downstream of the inside wall of the bend while flow followed a more

streamlines pattern (laminar) around the outside of the bend.

Other study was done in different methods using constant temperature

anemometry (CTA) to observe the explosion in 90 degree bend [12]. From the work, it

demonstrated that an obstacle such as bend encouraged the enhancement of turbulence

effect over the first 30% of the inner diameter of the pipe rapidly inside the bending part.

Ignition position also affects the explosion properties especially the shape of flame. Sato

et al [13] investigated the effects of ignition position for methane-air explosions using an

open ended small square channel with 90 degree bend and found out that it can influence

the shape of the flame front and its speed. However, with restricted amount of

explosions have been conducted, there is quite sparse comparison with work done in

straight pipe or obstacles.

Present work aims to provide additional information and knowledge related to

the explosion parameters (flame speed, overpressure and rate of pressure rise) for natural

gas-oxygen mixtures and to understand its behavior when involving straight and 90

degree bend pipe. The results collected will be compared with the previous published

experimental results in order to predict the flame pattern and worst explosion pressure

for various pipe configurations. Passive and active safety devices like flame arrester and

venting respectively will be proposed to be installed at certain location along the pipe as

the one of important effective technique to prevent the explosion from happened.

5

1.3 Objectives of Research

This research study embarks on the following objectives:

a) To determine/measure the data of explosion properties in closed pipe

with and without 90 degree bends such as flame speeds, rate of pressure

rise, overpressures and unburnt gas velocity at different concentrations of

natural gas/oxygen mixture.

b) To investigate the effects of pipe configuration (straight and 90 degree

bends) can have on flame acceleration, overpressure enhancement and

compare the data obtained with the previous published experimental data.

1.4 Scope of Research

Study on the effect of pipe configuration, i.e. straight and bend. Only straight and

90 degree were used and investigated. The fuel used is natural gas/oxygen with

equivalent ratio, Ф = 0.5 to 1.8. Parameters to be studied are flame speed, overpressure

and rate of pressure rise. These parameters are very important in basically determining

the explosion severity and hazard posed during explosion. Determination of critical

points and parts for the high pressure was accessed in order to install passive or active

safety device as one of the protection measured technique. This study investigates the

explosion properties in a pipe of L/D equal to 20 which can be simulated as an industrial

scale pipeline.

CHAPTER 2

LITERATURE REVIEW

2.1 Research Background

With increasing number of pipelines explosions every year, research on

improving the safety design of process equipment has become a major concern among

researchers. In the pipeline system, the ignited air-fuel mixtures can lead to the critical

growth of the explosion properties such as uncontrolled and harmful of overpressures.

The fast development of overpressure is influenced by the natural confined behavior of

the pipe and its long length which is jointed and installed separately in many

applications of the process industries. It is well known that turbulence flow in the pipe

will increase the diffusion of heat and mass due to the wrinkling of the flame front and

thereby cause higher burning rate [14]. The ongoing reaction of gas mixtures will induce

the transformation of flame propagation from deflagration to detonation type.

Consequently, increasing burning rate causes the rate of pressure rise in confined space

increases and leads to destructive explosion. As these parameters largely contribute to

the explosion behavior, further studies need to be carried out on these parameters to

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quantify the effect they can have on the explosion severity and to avoid such condition

to occur.

2.2 Gas Explosion

Explosion is a process where combustion of a premixed gas cloud (fuel-air

mixture) that causes rapid increase of pressure, volume and followed by the excessive

release of energy or heat. The critical boost of this pressure and its development can be

influenced and caused by a few factors such as run-away reactions, nuclear reactions,

leaking or storage failure of high pressure vessels, high explosives metal, vapor

explosions and burned of mist or dust in existence of air or other oxidizers. One classic

example of the most serious accidents in the history of chemical industry was happened

on 1 June 1974 at Flixborough (Nypro plant). A report explained that the plant was

entirely busted. The incident killed 28 people and total of 89 people were critically

injured and suffered. Almost two thousands of residences and more than hundred shops

destroyed. The estimated losses were more than 100 million dollars.

In an accidental explosion, the expansion can be mechanical (via the sudden

rupture of a pressure vessel) or it can be the result of a rapid chemical reaction.

Explosion basically can be categorized as confined and unconfined explosion. Confined

explosion are explosion within tanks, process equipment, closed closures/rooms

(confined space) and in underground installations. Meanwhile, unconfined gas

explosions occur in an open area such as process plants. The development of pressure

during the explosion in a confined vessel is not much affected by a high flame velocity

and therefore even a slow combustion process will generate and increase the pressure

8

[15]. Basically, reasons such as fuel and oxidizer type used, location or position of

igniter applied in the test system and etc can manipulate the explosion mechanism in

many ways of reaction. The difference between these two type explosions is that the

value for overpressure for confined explosion is higher than the unconfined ones. In a

confined place, the speed of flame increases and its acceleration may be more than a few

hundred meters per second. When the gas is burning, the temperature increases as well

as burning rate will increase, therefore causing the development of pressure. Without

proper application of safety equipments to relief the explosion pressure, this would lead

to rapid increase in pressure.

When the fuel-air mixture is ignited, the flame will propagate in two modes;

deflagration and detonation. Figure 2.1 shows mechanism for an explosion to happen

from ignition to detonation. Bjerketvedt et al [15] stated that the ordinary mode of flame

propagation during the gas explosion is deflagration, as expected to be similar to the

present work. Deflagration is defined as a combustion wave propagating at subsonic

velocity where the burning velocity, U is smaller than the speed of sound, C in the

unburned gas ahead of the flame. The typical flame speeds for deflagration are normally

the highest about a thousand meter per second (1 to 1000 m/s) with the maximum

explosion pressures can reach up to a few bars. The main mechanism of propagation of

combustion is a flame front moving through a gas mixture in technical terms the reaction

zone (combustion chemistry) takes place through the medium of heat and mass diffusion

process for laminar flame. It propagates with a velocity 3-4 m/s. In the most benign

form, the deflagration may only flash flame [15].

9

Figure 2.1 Steps for explosion mechanism [15]

The definition of detonation is a combustion wave propagating at supersonic

velocity relative to the unburnt gas immediately ahead of the flame. Deflagration is

different from detonation which is a supersonic exothermic front accelerating through a

medium that finally drives a shock front propagating directly in front of it. The

detonation velocity, D, is larger than the speed of sound, C, in the unburnt gas. At

supersonic velocity, combustion wave propagation occurred relative to the unburnt gas

immediately ahead of the flame [15] which the propagation mechanism can change to

supersonic explosion. This phenomenon of ignitable mixtures of combustible gas and air

(or oxygen) occurs when a sudden transition deflagration to detonation (DDT) of

explosive combustion. Detonation is defined as explosive compound decomposed by

releasing a shockwave rather than the heat generated by deflagration [16]. The

detonation velocity can reach the maximum value up to 2000 m/s and the maximum

pressures generated are close to 20 bars.

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2.3 Explosion Properties

Gas explosion is one of the worst accidents in the world because it can cause

huge damage and fatalities. The present work is conducted to measure and determine the

explosion properties such as flame speed, burning velocity, unburned gas velocity,

explosion pressure, rate of pressure rise, laminar flame speed, turbulent flame speed,

burning velocity, etc. Explosion behavior such as flame propagation, flame acceleration

and transition to detonation was comprehensively reviewed recently by Ciccarelli and

Dorofeev [6].

2.3.1 Flame Speed, Burning Velocity and Unburned Gas Velocity

The measured rate of the growth or expansion of the flame front in a combustion

reaction represents the value of flame speed. Bjerketvedt et al [15] defined the flame

speed, S or Sf as the velocity of the flame relative to the ground or another fixed frame.

Whereas flame speed is generally used for a fuel, a related term is explosive velocity,

which is the same relationship measured for an explosive. The burning velocity, U or Su,

is the velocity of the flame front with respect to the unburnt gas immediately ahead of

the flame. Equation 2.1 shows the relation between flame speed, S, burning velocity, U

and unburned gas velocity ahead of flame, u or Sg.

S = U + u (2.1)

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Figure 2.2 shows the transmission of flame in cylindrical vessel. During the

explosion, flame front will expand due to increase of flame temperature. The flame will

propagate through the length of pipe with the unburned gas mixtures in front of the

flame and the burned gas mixtures behind the flame. The density different of both gases

mixtures affected its transmission process. The density of unburned gas is lower than

burned gas. The burning rate will increase and hence lead to the increase of flame speed,

Sf and pressure development.

Figure 2.2 Transmission of flame in cylindrical vessel [15]

Factors such as expansion of combustion product, unsteadiness and turbulent

deformation of the flame can cause the flame speed to be higher than burning velocity.

Normal flame speeds observed for hydrocarbon-air mixtures in a range of 10-100 m/s

and the speeds can possibly increase up to 1000 m/s under certain conditions. The

unburned gases in front of the flame can induce turbulence effect in that reaction area

which produces small and large eddies as it flows through objects or orifices medium.

The effect of this turbulence can cause a rapid increase in flame speed and develop the

acceleration of the flame. According to Dahoe et al [14], flame acceleration are divided

to three phases which is flame stretching and folding, flame front wrinkling (caused by

turbulent eddies and fluid dynamic instabilities) and flame surface (creation by shock of

flame interactions). The flame will accelerate more rapidly at higher level of flame

surface wrinkling but the final choking velocity is similar for all geometric

configurations and governed only by properties of the gas mixture.