1. MECH 3810 Individual Project (Level 3)
Experimental Analysis of the Turbulent
Combustion of Lean Hydrogen-Air
Mixtures in Relation to Nuclear Safety
Stephen Calvert
Dr Malcom Lawes
05/05/2016

2. ii

3. iii
Table of Contents
Acknowledgements ....................................................................................................v
Abstract.....................................................................................................................vi
1. Introduction......................................................................................................... 1
1.1 Introduction ...................................................................................................... 1
1.2 Aims................................................................................................................. 2
1.3 Objectives ........................................................................................................ 2
2. Literature Review................................................................................................... 3
2.2 The Fukushima Daiichi Accident ...................................................................... 3
2.2.1 Overview of the Power Station................................................................... 3
2.2.2 Overview of the Disaster............................................................................ 3
2.2.3 Production of Hydrogen in the Accident..................................................... 3
2.2.4 Hydrogen Explosions in the Accident......................................................... 4
2.3 Flammability Limits of Hydrogen in Air ............................................................. 4
2.4 Fast Deflagration and Detonation..................................................................... 5
2.5 Laminar Burning............................................................................................... 6
2.6 Analysis of Turbulence..................................................................................... 8
2.6.1 RMS Turbulence Velocity and Turbulence Intensity................................... 8
2.6.2 Turbulence Produced From Flow around Obstacles .................................. 8
2.6.3 Turbulence Length and Time scales .......................................................... 9
2.6.4 Effective rms Turbulence Velocity.............................................................. 9
2.7 Regimes of Turbulent Combustion..................................................................10
2.8 Calculation of Turbulent burning velocity of a spherically propagating flame ...11
2.9 Calculation of Turbulent Burning Velocity for a Non-Spherical Centrally Ignited
Flame....................................................................................................................12
2.10 Schlieren Photography Technique ................................................................13
3. Experimental Equipment and Method ...................................................................14
3.1 Equipment.......................................................................................................14
3.1.1 The Combustion Vessel and Fans............................................................14
3.1.2 Intake and Exhaust Flow Systems............................................................15
3.1.3 Ignition System.........................................................................................15
3.1.4 Pressure and Temperature Measurement ................................................15
3.1.5 Schlieren Optics System...........................................................................15
3.2 Method............................................................................................................16
3.2.1 Filling of bomb and creation of combustion mixtures.................................16
3.2.2 Calculating Equivalence Ratio ..................................................................17
3.2.3 Lower Flammability Limit Experiments......................................................17
3.2.3 Turbulent Burning Velocity Experiments ...................................................18
4. Results .................................................................................................................20
4.1 Flammability Limits, Pressure and Temperature .............................................20
4.2 Turbulent Burning Velocity ..............................................................................22
4.2.1 Borghi Diagram.........................................................................................22
4.2.2 Schlieren Radius versus Time ..................................................................22
4.2.3 Turbulent Flame Speed versus Time........................................................23
4.2.4 Turbulent Flame Speed versus Schlieren Radius .....................................23
4.2.5 Turbulent Burning Velocity versus Time....................................................24
4.2.6 Turbulent Burning Velocity versus Schlieren Radius.................................25
4.2.7 Associated Flame Images.........................................................................27
4.2.8 Turbulent Burning Velocity versus Equivalence Ratio and Effective rms
Turbulence Velocity...........................................................................................30
5. Discussion............................................................................................................31
5.1 Lower Flammability Limit.................................................................................31

4. iv
5.1.1 Effect of Increasing rms Turbulence Velocity............................................31
5.1.2 Comparison to Literature ..........................................................................32
5.1.3 Observations of Near Limit Flames Images ..............................................32
5.2 Discussion of Temperatures and Pressures Produced....................................32
5.3 Turbulent Burning Velocity..............................................................................34
5.3.1 Discussion of Repeats..............................................................................34
5.3.2 Turbulent Burning Velocity versus Time ...................................................34
5.3.3 Turbulent Burning Velocity versus Schlieren Radius.................................35
5.3.4 Ratio of Turbulent to Unstretched Laminar Burning Velocities versus
Equivalence ratio...............................................................................................36
5.3.5 Dimensionless Correlation of Turbulent Burning Velocity versus Effective
Turbulence Velocity...........................................................................................37
6. Conclusion ...........................................................................................................38
References...............................................................................................................39
Appendix I: Meeting log............................................................................................41
Appendix II: Fukushima Daiichi Unit 4 Leak Path .....................................................43
Appendix III: Initial Conditions for Flammability Limit and Turbulent Burning Velocity
Experiments .............................................................................................................44
Appendix IV: Schlieren Radius versus Time Data.....................................................45

5. v
Acknowledgements
I would firstly like to thank Dr Malcom Lawes for all of his support and guidance
throughout the course of this project, and for enthusiastically sharing his knowledge
and expertise of combustion science which has helped me develop a new interest and
understanding of it. I am indebted to Ben Thorne also, a PhD student who has taken
the time to help me with the setup of equipment despite having a large workload
himself, also the technicians for providing me and setting up equipment in the lab and
to Georgios Kylafis for introducing me to the lab equipment. Last but not least thank
you to Michael Denton for his support, assistance and company throughout the whole
experimental process.

6. vi
Abstract
Hydrogen explosions in the Fukushima Daiichi disaster, lower flammability limit (LFL),
detonation, turbulence, laminar and turbulent burning were reviewed. LFL and
turbulent burning velocity experiments for hydrogen-air mixtures below 14.0 vol.% were
performed in a 23.2L cylindrical fan stirred combustion vessel at atmospheric pressure
and room temperature, and flames were imaged using high speed schlieren
photography.
The LFL for hydrogen in air was found to be between 6.93 vol.% and 6.97 vol.% for
an rms turbulence velocity (u’) of 0.8 m.s-1
, 6.97 vol.% and 7.01 vol.% for 1.6 m.s-1
and
between 7.11 vol.% and 7.16 vol.% for 2.4 m.s-1
. The effect of buoyancy on flames at
the LFL which prevents downwards propagation was negated by turbulence. Maximum
measured temperatures were much lower than adiabatic combustion product
temperatures. Ratios of maximum pressure produced from combustion to initial
pressure increased with decreasing u’ at the LFL and linearly increased with hydrogen
concentration above 8.5 vol.% at less than adiabatic values. Measurement of turbulent
burning velocity was inaccurate below 0.3 equivalence ratio, fluctuated with increasing
radius at weak turbulence and increased with increasing u’. Ratios of turbulent to
unstretched laminar burning velocity increased exponentially with decreasing
equivalence ratio below 0.37, and a correlation of turbulent burning velocity versus
effective rms turbulence velocity was generated.

7. 1
1. Introduction
In this chapter the report is introduced, followed by a summary of the project aims and
objectives.
1.1 Introduction
The harmful effects of climate change to society calls for the reduction in greenhouse
gasses which society produces; one way in which these emissions can be reduced is
by meeting a greater proportion of our increasing energy demand with nuclear power
which does not directly produce greenhouse gasses. A nuclear reactor can produce
large amounts of energy and also radioactive materials which are hazardous to
humans, meaning nuclear safety is extremely important, and is becoming more so as
the demand for nuclear power rises.
Hydrogen gas is very flammable, and in certain conditions hydrogen mixtures can
produce devastating explosions upon ignition; hydrogen therefore poses a serious
threat to the safety of the nuclear industry and it is important that every effort to prevent
explosions is made. The main instances where hydrogen accumulated in the nuclear
industry and ignited are the Three Mile Island (Henrie and Postma, 1983), Chernobyl
(Denton, 1987) and the Fukushima Daiichi (TEPCO, 2012) disasters; the most damage
was caused in the latter and this was reviewed to discover how the hydrogen was
produced in this disaster, and to examine the scale and properties of properties of the
explosion.
Hydrogen explosions can be prevented by keeping mixtures of hydrogen under the
flammability limits. Many experiments on the flammability limits of hydrogen have been
produced, however few experiments have been performed in a turbulent flow field. In
an environment such as a nuclear reactor building turbulence can exist which may
change the lower flammability limit, therefore this must be accounted for in minimum
allowable concentrations of hydrogen to prevent explosions. The pressures and
temperatures produced by hydrogen combustion should also be analysed to predict
the damage it might cause.
If hydrogen is ignited the burning velocity of the resulting flame is significant as a higher
burning velocity will produce greater damage to the surroundings. As mentioned
previously turbulent flow often exists in nuclear environments; the turbulent burning
velocity of different hydrogen concentration mixtures and different turbulence
intensities was therefore measured so that this data may be used to predict how much
damage an explosion of hydrogen may cause.

8. 2
1.2 Aims
To review the hydrogen explosions in the Fukushima Daiichi disaster and produce
lower flammability limit and turbulent burning velocity data of the combustion hydrogen
in air which can then be used to prevent and predict the damage of hydrogen
explosions in the nuclear industry.
1.3 Objectives
 Highlight how hydrogen explosions have caused damage the Fukushima
Daiichi disaster, how these explosions have occurred and in what form;
 Review the lower flammability limit and detonability limit of hydrogen;
 Review how turbulence can be analysed, and how turbulent burning velocity
can be measured;
 Create experimental procedure;
 Prepare the experimental equipment;
 Carry out the experiments in a safe manner;
 Collect and analyse the results of the experiments;
 Present results, discuss how these results can be used to prevent hydrogen
explosions in the nuclear industry, and how the results compare to current
literature.

9. 3
2. Literature Review
This chapter reviews literature regarding the Fukushima Daiichi accident, the
flammability limits of hydrogen in air, fast deflagration and detonation, analysis of
turbulence and turbulent combustion, turbulent burning velocity and finally the
schlieren photography technique.
2.2 The Fukushima Daiichi Accident
A review of hydrogen production and explosions in this accident with a brief overview
of the power station and the disaster events are presented here.
2.2.1 Overview of the Power Station
Fukushima Daiichi contained six boiling water reactors (BWRs), in which light water is
used as a reactor core coolant and moderator (required to slow neutrons produced by
fission) and boils to produce steam, which is then used for power generation. Preceding
the disaster units 1-3 were all in operation and producing their rated power outputs,
units 4-6 were shut down for inspection (TEPCO, 2012).
2.2.2 Overview of the Disaster
On March 11, 2011 an earthquake struck off-shore of the site which produced
Tsunamis and flooded Fukushima Daiichi causing serious flooding and a major loss of
power. A lack of cooling caused by the loss of power resulted in the boiling of cooling
water, and the core eventually became uncovered. The build-up of steam produced
large pressures which may have caused containment damage and leakage (INPO,
2011).
Venting and leakage released hydrogen and radioactive gasses into the reactor
buildings. Some of the hydrogen also migrated to unit 4, the most widely accepted
theory of where this hydrogen came from is through the back flow of gasses during the
venting of unit 3 (INPO, 2011), which is sensible as the venting systems of units 3 and
4 are linked. The leak path of the hydrogen into Unit 4 is displayed in appendix II. The
escaped hydrogen in units 1, 3 and 4 later ignited, producing explosions in these units
which destroyed the upper structures of their reactor buildings (TEPCO, 2012). The
unit 1 explosion opened a blowout panel in the roof of the unit 2 reactor building,
releasing hydrogen and radioactive material into the atmosphere and preventing an
explosion (TEPCO, 2012).
2.2.3 Production of Hydrogen in the Accident
The TEPCO report (2012) describes that the most likely source of hydrogen was from
the reaction of zirconium in the fuel cladding with steam, as temperatures reached over

10. 4
1000 ⁰C; the source of hydrogen was the same as in the Chernobyl accident (Denton,
1987) , displaying the danger of using zirconium alloy fuel cladding in nuclear reactors.
Kuznetzov et al. (2015) and Yanez et al. (2015) identify that stratified layers of
hydrogen were produced, where buoyancy forces separate hydrogen into layers with
different thicknesses and concentration gradients. These layers were semi-confined as
they were confined by the reactor building roof and open to the building volume below
the layers. Yanez et al. (2015) estimates the layers had a concentration gradient
ranging from 0-15 vol.%, giving an average concentration of 7.5 vol.%; experiments in
this report did not include stratified layers, however turbulence may mix these layers
producing a uniform concentration in other disaster scenarios.
2.2.4 Hydrogen Explosions in the Accident
It was identified by Yanez et.al (2015) that the hydrogen in unit 1 most likely combusted
in a fast (sonic) deflagration regime, and detonation was unlikely as the run up distance
required for deflagration to detonation transition (DDT) was large relative to the
geometry of the roof of the reactor building. Fast deflagration and DDT is reviewed in
section 2.4.
Structural elements and equipment such as cranes which were situated in the roof of
the reactor building acted as turbulisers (Yanez et.al, 2015); this also has occurred in
other disasters such as the Buncefield disaster in which DDT occurred and caused
major damage (Bradley et al., 2011a), highlighting the importance of using turbulence
to recreate accident conditions in experiments. The combustion regime of the
explosions in units 3 and 4 were most likely similar to that of unit 1 as the layout of the
other units were similar meaning turbulisers also existed in those units.
Turbulence can increase turbulent burning velocity, as shown by correlations produced
by Gillespie et.al (2000). Turbulent burning velocity is a measure of how fast a flame
burns, and is discussed further in section 2.8. Turbulence therefore also increases the
likelihood of DDT occurring as a faster turbulent burning velocity increases the strength
of the shockwave which is required for auto ignition and DDT (Bradley et.al, 2008);
because of this turbulence is a major factor in the damage which can be caused by
explosions.
2.3 Flammability Limits of Hydrogen in Air
The lower flammability limit (LFL) is defined as the limiting fuel concentration that can
support significant flame propagation and lead to an explosion (Zlochower and Green,

11. 5
2009). Below this limit a small amount of the flammable mixture can be burnt, however
the flame would be very small and would cause no damage in a disaster scenario.
The limiting fuel concentration has been found to decrease in the presence of
turbulence; the cause of this was explained by Cashdollar et al. (2000), who state that
turbulence generates eddies of burned gas which are shed ahead of the flame front,
serving as multiple sources of ignition and therefore lowering the flammability limit .This
is significant as the flow field in accident conditions is often turbulent as discussed in
section 2.2.3, and therefore the LFL should be found for turbulent conditions.
Turbulence can negate the effects of buoyancy for low concentrations in which flames
rise upwards and quench before the flame can propagate downwards, and also
produce lower pressures (AL-Khishali et al., 1983).
Experiments performed by Cashdollar et al. (2000) in spherical combustion vessels
with volumes of 20 L and 120 L and spark energies of around 20 J and 58 J respectively
have shown that the LFL of hydrogen ≈ 5 +/-0.5 vol.% in the presence of turbulence.
The turbulence was not analysed in these experiments; this can be improved upon by
examining the LFL at specific turbulence parameters, which are discussed in section
2.6. Pressure increases of near limit hydrogen-air mixture turbulent combustion in a
spherical vessel have been found by Cashdollar et al. (2000) for a 120 L vessel and
Thompson et al. (1984) for a large scale 2000 m3
vessel; these are compared to
present experimental results to display how vessel geometry can affect pressure
measurements.
2.4 Fast Deflagration and Detonation
In the fast deflagration combustion regime flames can propagate at speeds
approaching the speed of sound, and these flames propagate at the maximum velocity
achievable for non-detonative regimes (Teodorczyk, 2009). The fast deflagration
regime is induced by turbulence as was the case in the hydrogen explosions in the
Fukushima Daiichi accident, and in this regime shockwaves can be produced which
are decoupled from the flame front (Teodorczyk, 2009. see fig. 2.1). Flames require a
run-up distance to transition to the fast deflagration regime, and the flames analysed
in this report may be similar to the initial stages of the fast deflagration regime.

12. 6
Figure 2.1: Image showing the structure of a turbulent high-speed deflagration for a
stoichiometric hydrogen-oxygen mixture.
Oran and Gamezo (2007) and Teodorczyk (2009) explain that detonation waves are
produced from reactivity gradients (differences in the induction rate of reactants into a
flame over time); a source of a reactivity gradient can be the mixing of hot combustion
products and fuel. Certain regimes of turbulent combustion (see section 2.7) can cause
the unburned gasses to enter the burned gas zone and therefore induce DDT
(Teodorczyk, 2009) as a sharp temperature and therefore reactivity gradient exists; as
these regimes were used in the turbulent burning velocity experiments of this report
(see section 4.2.1) the occurrence of DDT was a real risk.
To ensure detonation did not occur in turbulent burning velocity experiments the
concentration of hydrogen (vol.%) was kept below the lower detonation limit (LDL).
Breitung et al. (2000) describe the detonability limits as the critical conditions which
allow for the propagation of self-sustained detonation. Belles (1962) developed a
theory for predicting the LDL, which states that for detonation to occur the heat of
combustion must exceed the enthalpy increase of the combustion reactants from a
shock wave which could auto-ignite the mixture, otherwise the heat released from
combustion is not sufficient to drive the shock and detonation cannot propagate. Belles
(1962) predicted the lower detonation limit of hydrogen in air to be 15.8 vol.% whereas
Cohen (1992) used Belles theory and found the LDL to be 14.0 vol.% for an initial
pressure and temperature of 1atm and 300 K respectively; Cohen (1992) does not
explain the discrepancy, however for safety reasons mixture concentrations used were
below 14.0 vol.%.
2.5 Laminar Burning
A laminar flame is a flame which propagates through a quiescent environment; this is
reviewed here as properties of laminar burning can be used to quantify the effect of
turbulence on a flame. A common parameter used to characterise the rate of
propagation of an unstretched, one dimensional flowing laminar flame is the
Shockwave
Turbulent reaction
zone

13. 7
unstretched laminar burning velocity, ul ; this is a physio-chemical that is dependant
only on mixture composition, pressure and temperature and is mainly defined as the
velocity of the cold reactants entering the flame (Lawes, 2011). Bradley et al. (2007)
determined the unstretched laminar burning velocity for a hydrogen-air mixtures at
atmospheric conditions and plotted the results with those from literature, this is
displayed in figure 2.2. The experimental points and work from other experimentalists
plotted as shapes were useful for determining ul for very lean mixtures, however below
an equivalence ratio of 0.2 data could only be obtained by extrapolation meaning the
values can only be used as estimates.
Figure 2.2: plot of ul versus equivalence ratio of hydrogen-air mixtures at 300 K
temperature, 0.1 MPa initial pressure. Reproduced from Bradley et al. (2007).[1], [7]
and [8] represent work from other experimentalists, as do the lines.
Another important property of flames is the laminar flame thickness. This parameter
was useful to this report as it can be used to describe the effect of turbulence on a
flame front (see section 2.7). Different definitions of laminar flame thickness have been
used in literature (Gillespie et al., 2000); the definition used in this report was based on
a hydrodynamic length (δl) as this definition is the most commonly used in literature
(e.g. Gillespie et al., 2000 and Kitagawa et al., 2008) and can be calculated by:
δl=
v
ul
(2.01)
Where 𝑣 is the kinematic viscosity (m2
.s-1
) and ul is the laminar burning velocity (m.s-
1
).

14. 8
2.6 Analysis of Turbulence
2.6.1 RMS Turbulence Velocity and Turbulence Intensity
A main parameter used for analysing turbulence is the root mean square velocity (u’);
this can be calculated in the x direction by (Lawes. 2010a):
u'
=√u2̅̅̅ (2.02)
Where u is the deviation from the average x component of velocity (m/s). The velocities
in the y (v’) and z (w’) directions can be calculated in the same way and if they are
equal turbulence is isoptropic (Lawes, 2010a). The relationship between u’ and fan
speed (f) for air has been found for the cylindrical bomb used in this report (see section
3.1.1) ; this is applicable to hydrogen-air mixtures as it has been found that turbulence
velocities for hydrogen-air mixtures were the same as those for air (Koroll et al., 1993).
2.6.2 Turbulence Produced From Flow around Obstacles
It is important to analyse the turbulence generated when flames propagate around
obstacles so that the turbulence levels in accidents can be predicted. A study by Gubba
et al. (2011) measured u’ at the surface of an obstacle as a flame propagates over it.
This study found rms turbulence velocities of ~4 m/s were produced when a flame
propagated around a small obstacle (see figure 2.3). These velocities were measured
at the surface of an obstacle and turbulence velocities would most likely be less at
different points away from the surface.
Figure 2.3: Reproduction of the diagram
of the obstacles used for turbulence
intensity measurements by Gubba et al.
(2011).
Figure 2.4: Sketch of the turbulent
eddies produced upon filling a vessel
with water, with labelled length scales.
Reproduced from Lawes (2010b).
L
λ
η

15. 9
2.6.3 Turbulence Length and Time scales
In literature, turbulence is assumed to comprise of many ‘eddies’ of different sizes,
velocities and lifetimes (Lawes 2010a). Eddies originate from shear forces acting on a
flow for example from the contact of a fan stirred hydrogen-air mixture with the walls of
a combustion vessel, and large scale eddies with size L are produced which contain
the largest kinetic energy (Lawes 2010a). Shear forces continuously breaks down
eddies until medium sized Taylor scale eddies (λ) result, and these are broken down
again until smallest Kolmgorov scale η of turbulence is reached, where the turbulent
kinetic energy is dissipated by viscous action (Lawes, 2010a). A sketch of this process
for the filling of a vessel with water is displayed in figure 2.4.
Lawes (1987) performed correlations of u’ for the MKI Combustion Bomb used in this
report, and found that L was approximately 30 mm and was independent of fan speed.
The correlation of Length scale was weak and therefore was taken as an estimate.
Time scales of turbulence represent the time taken for an eddy to move past a point
(Lawes, 2010a). The time scale for each length scale can be calculated in the same
way, e.g. for the integral (Lawes, 2010a):
τl=
L
u'
(2.03)
2.6.4 Effective rms Turbulence Velocity
At the initial stages of flame propagation flame diameter is smaller than the size of the
largest eddies, hence the flame may only be convected bodily by these eddies (Lawes,
2011b). As a flame propagates the effectiveness of turbulence increases until the flame
diameter is much larger than L and the flame burns at a fully developed velocity, as
shown by Abdel-Gayed et al. (1987). Abdel-Gayed et al. (1987) correlated power
spectral density (PSD), made dimensionless by PSD obtained from u’, of turbulence
velocity signals (u(t)) for different measurement frequencies (see fig. 2.5), where an
infinite frequency would give a PSD of zero and a large frequency would give a
maximum PSD as u(t) measurements would be taken over a time period much larger
than the lifetime of the largest eddies, meaning the complete turbulent spectrum can
be measured. The equation of the PSD correlation found is:
S̅(F̅)=
3.3
1+(2πF̅)
5
3+(0.25F̅)
4
+(0.08F̅)
7
(2.04)

16. 10
Figure 2.5: Plot of PSD versus
dimensionless frequency, reproduced from
Abdel-Gayed et al. (1987).
Figure 2.6: Plot showing how u’k can be
obtained by integration of PSD,
reproduced from Lawes (2010b)
Where S̅(F̅) is the dimensionless PSD at a certain frequency 𝐹̅. Integrating (2.04) from
a dimensionless frequency 𝐹̅𝑘 to infinity yields the turbulent energy contained in that
range (see fig. 2.6), and square rooting the energy yields the effective rms turbulence
velocity, u’k at any frequency 𝐹̅𝑘 :
u'k=√u'2 ∫ S̅(F̅)
∞
F̅k
dF̅
(2.05)
𝐹̅𝑘 is equal to 𝜏𝑙 divided by time after ignition, and using (2.03) and the relationship
between speed, distance and time 𝐹̅𝑘 is also equal to (2*R)/L, allowing u’k to be
calculated for any flame radius (R).
2.7 Regimes of Turbulent Combustion
Borghi (1988) identified four regimes of turbulent combustion, which separates the
regimes based on the ratio of turbulence intensity (u’) to laminar burning velocity (ul),
integral length scale of turbulence L to the laminar flame thickness (δL) and the ratio of
chemical (τc) to eddy life times (Lawes 2010b). A Borghi diagram, with work from others
added to it by Lawes (2010b), and with points added from the hydrogen-air mixtures
used in this report are displayed in figure 4.4. The chemical life time (τc) can be
approximated by (Lawes, 2010b):
τc=
δL
ul
(2.06)

17. 11
Figure 2.7: Diagram displaying flame front
of wrinkled and corrugated flame fronts,
where grey areas are pockets of unburned
gas. Reproduced from Lawes (2010b)
Figure 2.8: Diagram showing flame
contour obtained from laser sheet
imaging (solid) and schlieren imaging
(dashed), and different definitions of
flame radius. Reproduced from Lawes
(2010b)
In the wrinkled flamelet regime turbulence wrinkles the flame front (see fig. 2.7),
increasing surface area and therefore the burning rate also (Lawes 2010b). Detonation
is promoted in the corrugated and distributed reaction regimes (Teodorczyk, 2009). In
the Corrugated regime, u’ is greater than ul and causes the flame to fold back on itself,
creating pockets of unburned gas within the products of combustion and/or pockets of
reacted gas in the regions of the combustion reactants (Lawes 2010b, see fig. 2.7). In
the distributed reaction zone τc is greater than τL, and therefore the smallest eddies will
shed before reactants in the eddy have burned which breaks up the flame (Lawes
2010b). In the well-stirred reactor zone short lived eddies constantly break up the
reacting mixture, producing quenching unless fresh reactants can be recirculated
(Lawes 2010b).
2.8 Calculation of Turbulent burning velocity of a spherically propagating
flame
Turbulent burning velocity can be defined in different ways, most commonly by the
entrainment velocity of the unburnt gasses into the cold flame front (ute). The
measurement of mass flow rate presents a challenge as it is difficult to measure
(Bradley et al. 2011b). The measurement of mass flow rate can be avoided if flame
radius is selected in a way such that between a sphere of radius Rj and the sphere of
radius Rb (see fig. 2.8) within which only burned gas exists, there is a volume of
unburned gas equal to the volume of burned gas between Ri and the sphere of radius
Ru (see fig. 2.8) outside of which only unburned gas exists; this radius is termed R 𝜐
(Bradley et al. 2011b). It was shown by Bradley et al. (2003) that when the radius R 𝜐 is
used, ute and utr are equal.
RSch
RA
Ru
Rb

18. 12
The radius Rν can be measured using the Mie scattering technique (Gillespie, 2000;
Bradley et al. 2003), however this method is expensive and Rν cannot be measured
from more readily available techniques such as schlieren. Bradley et al. (2003)
correlated Rν with the radius obtained from schlieren imaging (Rsch), giving equation
2.07 which relates turbulent burning velocity to Rsch:
ute= (
1
1.11
ρb
ρu
)
dRsch
dt
(2.07)
The change in schlieren radius (Rsch) over change in time (dt) is termed the turbulent
flame speed, St in this report. The measured turbulent burning velocity is given the
symbol utk as this is the undeveloped value (see section 2.6.4).
2.9 Calculation of Turbulent Burning Velocity for a Non-Spherical
Centrally Ignited Flame
For non-spherical turbulent flames propagating in multiple directions Checkel and Ting
(1992) and Kitagawa et al. (2008) used image processing software to determine the
cross-sectional area of flames in schlieren images, and assumed the flames were
spherical in shape with a cross-sectional area equal to that of the schlieren image.
Using the radius of the spherical flame at different times after ignition, the change in
the schlieren radius over time can be used to estimate the turbulent burning velocity
by using Bradley et al.’s (2003) method (eq. 2.07). This method is questionable for
flames which have a completely non-spherical shape, however it does provide an
approximation of flame speed and burning velocity, which is useful for quantitatively
comparing the flame burning velocities of hydrogen at different equivalence ratios and
turbulence intensities.
Kitagawa et al. (2008) and Koroll et al. (1993) measured turbulent burning velocities
for hydrogen concentrations of above 12.0 vol.%, as below this repeatability was poor;
despite this lower concentrations were analysed in this report as they may arise in
nuclear environments, and an indication of this will be produced using the method
outlined previously. AL-Khishali et al. (1983) investigated turbulent flame speeds of
near limit mixtures at an initial temperature of 55⁰C and rms turbulence velocities of
over 4 m.s-1
using the same apparatus as used in this report, and this can be built upon
by combusting hydrogen at atmospheric temperature and different rms turbulence
velocities.

19. 13
2.10 Schlieren Photography Technique
‘Schlieren’ describes the gradients of refractive index in an inhomogeneous medium,
which are proportional to density gradients (Settles, c2001). Light is refracted either
towards or away from the cut-off and produces dark and bright spots respectively on a
schlieren image (Lekholm et al., 2011, see fig. 2.9).
Figure 2.10: Schlieren image of
a hydrogen-air flame.
Figure 2.9: Diagram of a simple schlieren
setup, reproduced from Lekholm et al. (2011).
In combustion experiments the sample in figure 2.9 is the flame, and light in most
combustion experiments is captured by high speed cameras once focused (Kitagawa
et al., 2008; Bradley et al 2003; Koroll et al., 1993) producing many flame images per
second. See fig. 3.2 for the schlieren set up used in present experiments. A high
capture rate enables the sequential analysis of flame images with small changes in
Rsch for even very rapidly propagating flames, which is why this method was chosen
for this report. In a spherical combustion bomb spherically propagating flames are
produced, images of the propagation of these flames are captured and the radius Rsch
in equation (2.07) is measured from these images.
Schlieren imaging is a relatively cheap imaging technique compared to for example
Mie scattering (Bradley, 2011b) and therefore was used for the experiments of this
report. Shadowgraphy is an additional relatively cheap imaging technique which may
be used for the imaging of flames and other schlieren objects, however the images
produced can be distorted by turbulence (settles, c2001). Furthermore, schlieren
photography has a higher sensitivity to density gradients therefore emphasizing detail
(Settles, c2001) and giving a more accurate measurement of the schlieren radius than
Shadowgraphy.

20. 14
3. Experimental Equipment and Method
This section firstly describes the equipment used experiments performed, followed by
an outline of how the flammability limit and turbulent burning velocity experiments were
carried out.
3.1 Equipment
3.1.1 The Combustion Vessel and Fans
Combustion experiments were performed in the Mk I Fan Stirred Bomb, hereafter
referred to as the ‘bomb’ for convenience. The bomb is included in figure 3.1 which
shows the electrical systems and fluid flow paths which were connected to the bomb.
The bomb has a volume of 23.2 L. Fitted at the centre of each of the circular faces are
150 mm diameter viewing windows.
Figure 3.1: schematic diagram of the experimental apparatus setup; solid lines
indicate fluid piping and dashed represent electrical connections.
Four equally spaced fans are fitted which are capable of producing isotropic turbulence
at the 150 mm diameter central spherical region of the combustion vessel. The fans
are controlled by a Mitsubishi Freqrol Z024-S1.5K electronic controller. Lawes (1987)
characterised properties of the turbulence produced over the range of fan speeds and
Non-return
valve

21. 15
found that the integral length scale was approximately 30 mm over the full range, and
the rms turbulence velocity was related to the fan speed, f (rpm) by equation 3.01:
u'
=
16
10000
*f
(3.01)
3.1.2 Intake and Exhaust Flow Systems
Compressed air and hydrogen gas supplies were connected to the intake flow line of
the combustion vessel; non-return valves were connected to both of these supplies,
and the flow was controlled by either a fully open/closed valve or a fine control valve,
and in addition a GCE Multi-stage controller was used to control the flow of the
hydrogen gas (see fig. 3.1). Isolation valves were fitted to the combustion vessel which
were closed whilst mixtures were ignited. An exhaust line was fitted to the combustion
vessel to remove fluid mixtures. An isolation valve was also used in the exhaust line.
An Edwards Speedivac ED100 was used to create a vacuum in the combustion vessel;
this discharged through the exhaust line.
3.1.3 Ignition System
The combustion vessel was centrally ignited by a spark. To provide the spark a Temic
311740 TFK spark unit was used, which was supplied with a voltage of 12 V from a
Farnell L30BT stabilised power supply and created a 50 mJ spark. The voltage was
supplied to the spark unit as a pulse, and a TTI TGP110 pulse generator was used to
supply a pulse signal with period 10 ms, pulse width 5 ms, pulse delay 50 ns and an
amplitude of 10 V. The pulse signal was generated upon the pressing of a trigger
button.
3.1.4 Pressure and Temperature Measurement
During the filling of the combustion vessel a Comark c9555 pressure transducer was
used, which was connected externally to the combustion vessel by a flow line. A
DRUCK Ltd. pressure transducer was used to measure maximum pressures following
combustion, voltage signals from which were amplified by a KIAG Swiss type 5001
amplifier and relayed via a NI USB-6218 BNC DAQ to PC 1 (see fig. 3.1) where
pressure measurements were recorded using Labview. A K-type thermocouple was
used temperature measurement. Initial and maximum following combustion
temperatures were displayed by a CAL 3200 reader.
3.1.5 Schlieren Optics System
The setup of the optics system is displayed in figure 3.2.

22. 16
Figure 3.2: Diagram of the schlieren optics system. Reproduced from Atzler, 1999.
Flames were photographed using a Vision Research Phantom v9.0 URI V4537V90M
1.5G NJ high speed camera. The camera captured images upon the pressing of the
trigger button at 1800 pictures per second (giving an interval of 0.56 ms between
pictures), which was found to allow sufficient visualisation of the flame propagation
whilst not over using computer storage space. Images were saved onto PC 2 (see fig.
3.1).
An Acculase LED laser and mount was used to illuminate the flames, with a laser
wavelength of 650 nm and 20 mW power. The power of the laser was controlled by a
Time Electronics LTD Model 404N potentiometer. The laser beam was expanded by a
beam expander and collimated using a 150 mm diameter lens with a 1000 mm focal
length. The light then passed through the viewing windows, was focused by a 150 mm
diameter lens (also 1000 mm focal length) onto a 2 mm diameter pinhole, and finally
was captured by the high speed camera.
3.2 Method
3.2.1 Filling of bomb and creation of combustion mixtures
Before igniting mixtures the combustion vessel was first flushed through with
compressed air and vacuumed to an absolute pressure of around 100 mbar to remove
contamination. Once decontaminated the combustion vessel was partially filled with
hydrogen gas, and then filled with air to an absolute pressure approximately equal to
atmospheric (1.01325 bar). Mixtures were premixed using the fans. The leakage at
near vacuum was found to be 0.465 mbar/s.
Using Dalton’s Law, equation 3.02 relating the concentration of hydrogen gas in a
mixture to the proportion of the total mixture pressure which the hydrogen gas
contributes to can be deduced:
Vhydrogen
Vtotal
=[H2]vol=
Phydrogen
Ptotal
(3.02)
Plano-Convex Lens
f=1000mm
Bomb
Window Window
He-Ne-Laser
Beam Expander
Pin-Hole
High Speed Camera
max. observable flame diameter 150 mm
Plano-Convex Lens
f=1000mm
LED Laser

23. 17
Where 𝑉ℎ𝑦𝑑𝑟𝑜𝑔𝑒𝑛 and 𝑉𝑡𝑜𝑡𝑎𝑙 are the volume of the hydrogen and total mixture volume
respectively (m3
); [𝐻2] 𝑣𝑜𝑙%
is the percentage concentration of hydrogen by volume,
Phydrogen is the partial pressure of hydrogen in the mixture and Ptotal is the absolute
pressure of the mixture. The partial pressure of hydrogen was the amount which added
hydrogen increased the pressure in the combustion vessel. The pressure of the final
mixture Ptotal was measured and the concentration of hydrogen measured by equation
3.02. The filling the bomb with hydrogen was performed over a maximum time period
of 15 s, meaning the concentration of mixtures may have been 0.7 vol.% lower than
measured.
3.2.2 Calculating Equivalence Ratio
The chemical equation for the stoichiometric (where all oxygen and hydrogen is
reacted) combustion of hydrogen in air is:
H2+0.5O2+1.881N2→H2O+1.881N2 (3.03)
Using equation 3.03 it can be seen that the hydrogen to air molar and therefore volume
ratio of the stoichiometric combustion of hydrogen in air is 0.42 (1/(0.5+1.881) = 0.42).
Knowing the fuel to air ratio of the stoichiometric combustion of hydrogen in air, the
equivalence ratio (φ) of hydrogen in hydrogen-air mixtures was determined using
equation 3.04:
φ= (
VH2
Vair
) / (
VH2
Vair
)
St
= (
[H2]*Vtotal
(1-[H2])*Vtotal
) /0.42=
1
0.42
*
[H2]
1-[H2]
(3.04)
Where (
VH2
Vair
) is the hydrogen to air volume ratio in a mixture and (
VH2
Vair
)
St
is the
stoichiometric hydrogen to air volume ratio, equal to 0.42.
3.2.3 Lower Flammability Limit Experiments
These experiments aimed to determine the lower flammability limit (discussed in
section 2.3) of hydrogen in air at +/- 20 mbar gauge initial pressure and 293+/-3K
temperature (see Appendix III for initial conditions) in the combustion vessel described
in section 3.1.1 at different rms turbulence velocities.
In section 2.3.2 it was found that the lower flammability limit of hydrogen in air in the
presence of turbulence has been found to be around 5% by volume; for all fan speeds
a 4.5% hydrogen concentration (vol.%) was used initially as it was assumed that these
mixtures would not ignite. If the mixture did not produce a flame, the concentration of
hydrogen was increased by approximately 0.1 vol.% until a flame was produced.
Corrected LFLs were estimated by subtracting 0.7 vol.% to account for bomb leakage.

24. 18
Rms turbulence velocities of 0.8 m.s-1
, 1.6 m.s-1
and 2.4 m.s-1
were selected for
flammability limit experiments, as they produced a flow field similar to that which might
be found downstream of obstacles (see section 2.6.2).
3.2.3 Turbulent Burning Velocity Experiments
Rms turbulence velocities of 1.6 m.s-1
and 2.4 m.s-1
were used as they are similar to
what might be found downstream of obstacles, as discussed in section 2.6.2. An rms
turbulence velocity of 0.4 m.s-1
was used instead of 0.8 m.s-1
as this gave very weak
turbulence, and upon comparison with the higher turbulence velocities highlighted the
effect of increasing turbulence.
Hydrogen-air mixtures of 13.82 vol.% and below were used as this concentration is
sufficiently under the lower detonation limit discussed in section 2.4. For a u’ of 1.6 m.s-
1
and 2.4 m.s-1
flames were analysed down to concentrations of 8.54 vol.% and 7.12
vol.% respectively. Lower concentration mixtures could not be analysed due to their
flames producing a weak flame edge on the schlieren images and being torn apart by
turbulence. A lower range of concentrations was used for a u’ of 0.4 m.s-1
as this was
sufficient for comparison to the higher turbulence velocities. Three measurements were
taken at a fan speed of 1000 rpm and similar hydrogen concentrations of 12.93 vol.%,
12.94 vol.% and 12.95 vol.% to determine the experimental scatter; the concentrations
could not be made equal as bomb leakage made the formation of precise mixtures
difficult. The mixtures which were used for each fan speed are summarised in table
3.1.
Table 3.1: Summary of the hydrogen concentrations and equivalence ratios used in
the turbulent burning velocity experiments for each rms turbulence velocity.
Fan Speed (rpm)
250 1000 1500
u’
(m.s-1
):
0.4 1.6 2.4
[𝑯 𝟐] 𝒗𝒐𝒍%
:
12.80,13.33,
13.82
8.54, 9.10, 10.71,
11.70,12.94, 12.95 12.96,
13.33
7.16, 8.86, 9.97, 11.32,
12.34, 13.35
∅:
0.349,0.366,
0.382
0.222, 0.238, 0.281,
0.315,0,354,0.354, 0.355,
0.366
0.182, 0.231, 0.264,
0.304, 0.335, 0.367
Mixtures were ignited at +/- 20 mBar gauge pressure and 293.15 +/- 3 K (see Appendix
III for initial conditions) using the ignition system and the flame propagation was
photographed by the high speed camera. The first image in which a flame appeared
was taken as time zero. Flame images were analysed until any point of the flame front
reached the viewing window. The image frame increment between measurements was
chosen to sufficiently capture the trend in change in flame radius from ignition to when

25. 19
the window is reached whilst not being overly time consuming, e.g. for a u’ of 2.4 m.s-
1
and a concentration of 13.35 vol.% every frame was analysed, and for a u’ of 0.4 m.s-
1
and 13.82 vol.% every third flame was analysed as it propagated much slower.
To determine the cross-sectional area of flames GIMP was used to make the flame
image completely white (see figures 3.3 and 3.4); at the spark plug region the flame
could not be visualised (see A on fig. 3.3). To overcome this the flame was joined using
an arc which followed the shape of the flame at each side of the spark plug. A Matlab
code was used to count the number of image pixels in the white flame image (see fig.
3.4). The diameter of the viewing window circle (150 mm) was divided by the number
of pixels along the diameter, found using GIMP to be 625 (see fig. 3.3), to give a length
per pixel of 0.24 mm. As the pixels are square the area per pixel is therefore 0.0576
mm2
. The number of pixels in the flame image was multiplied by the area per pixel to
give the flame cross sectional area.
The radius of a circle with a cross sectional area equal to that found for a flame was
used as Rsch (see section 2.9). The burned and unburned hydrogen-air mixture
densities and kinematic viscosities were determined using ‘GASEQ’, a computer
programme which calculates thermochemical properties of gas mixtures.
The experimental scatter of the repeats was determined by finding the average radius
at each time after ignition, calculating the standard deviation from the average values.
Although scatter would increase with decreasing equivalence ratio and increasing fan
speed, this scatter was used for all conditions to provide an indication. A two point
moving average of Rsch and time was taken for all conditions, allowing results to be
presented with reduced random fluctuations produced from experimental inaccuracies;
scatter bars using the standard deviation from the mean of the repeats were included
to display the degree that difference in results may be attributed to scatter.
Figure 3.3: Image of a flame to be
analysed. A labels the spark plug region.
Figure 3.4: Image of the flame in fig.
3.3 following image processing.
150mm, 625 p
A

26. 20
4. Results
This chapter presents the results from flammability limit experiments in section 4.1 and
turbulent burning velocity experiments in section 4.2.
4.1 Flammability Limits, Pressure and Temperature
The flammability limits found for the different fan speeds are presented in table 4.1.
Images of the flame propagation of hydrogen-air mixtures at the flammability limit are
displayed in figure 4.1. Ratios of maximum pressure produced from combustion to
initial pressure versus concentration are plotted in figure 4.2 for concentrations
between the LFL and LDL. Maximum temperatures produced from combustion are
displayed in figure 4.3.
u’(m.s-1
),
φ
Images of Flames at the Lower Flammability Limit
0.8,
0.178
t (ms) 8.33 26.1 53.3 98.9
1.6,
0.179
t (ms) 8.33 26.1 46.7 70.6
2.4,
0.182
t (ms) 33.3 53.3 91.1 252.2
Figure 4.1: Images of flames at the LFL. Each row includes images of the same
flame; this will be the case for subsequent image plots. B and C point to the
denser and less dense flames respectively.
Table 1 – LFL results with corrected values:
u’
(m.s-1
)
LFL
(vol. %)
φ Corrected LFL
(vol.%)
0 6.96-6.97 0.178 6.26-6.27
0.8 6.93-6.97 0.177-0.178 6.23-6.27
1.6 6.97-7.01 0.178-0.179 6.27-6.31
2.4 7.07-7.12 0.181-0.182 6.37-6.42
B
C

27. 21
Pressure measurements showed good repeatability as for concentrations (vol.%) of
12.94, 12.95 and 12.96 the range of pressure ratios was 4.13-4.16.
Figure 4.3: Plot of maximum flame temperature versus hydrogen concentration for
different rms turbulence velocities.
295
300
305
310
315
320
325
330
6 8 10 12 14
Max.Temperature(K)
Concentration (vol.%)
Maximum Flame Temperature versus Hydrogen concentration
2.4 m/s
1.6 m/s
0.8 m/s
Figure 4.2: Plot of the ratio of maximum pressure ratios, including data from present
experiments, literature and a curve of adiabatic values obtained from Gaseq.
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
0 2 4 6 8 10 12 14
Pmax/Po
[H2] (vol.%)
Maximum Pressure Ratio versus Concentration
u' = 2.4 m/s
u' = 1.6 m/s
u' = 0.8 m/s
Cashdollar et al. 120L
Nevada Test Site 2000m3
adiabatic
u’

28. 22
4.2 Turbulent Burning Velocity
This section provides results of turbulent burning velocity experiments. Sub sections
4.2.1, 4.2.2, and 4.2.3 provide plots of Rsch versus time, change in Rsch versus time and
Rsch for the repeat experiments to show the progression leading up to turbulent burning
velocity plots and also experimental scatter; plots of Rsch versus time for the other
mixtures and fan speeds are provided in Appendix IV. Sub sections 4.2.4 and 4.2.5
include plots of utk versus time and Rsch for all mixtures and fan speeds. Flame images
associated with the plots are displayed in 4.2.6. Sub section 4.2.7 presents a plot of
turbulent burning velocity versus equivalence ratio with results from Kitagawa et al.
(2011) added, and also a plot of turbulent burning velocity versus effective turbulence
velocity for a range of concentrations and fan speeds.
4.2.1 Borghi Diagram
Figure 4.4 displays a Borghi diagram with the mixtures from the turbulent burning
velocity experiments and LFL mixtures plotted.
u’
(m.s-1
):
0.4 0.8 1.6 2.4
φ
- 0.349
- 0.366
- 0.178 - 0.178/0.212/
0.222/0.238
x-
0.182/0.231
- 0.382 - 0.281 - 0.264
- 0.315 - 0.304
- 0.354 - 0.335
- 0.366 - 0.367
Figure 4.4: Borghi diagram with flames relating to turbulent burning velocity
experiments plotted. Some points existed on top of each other and are shown as
the same point with multiple numbers for the legend entry.
4.2.2 Schlieren Radius versus Time
A plot of Rsch versus time for the three repeats with a curve of the mean Rsch at each
time is displayed in figure 4.5. The average standard deviation from the mean was
found to be 3.17 mm.
0
1
10
100
0.1 1 10 100 1000
𝑢′/𝑢l
𝐿/𝛿l
Borghi Diagram with Plotted Results
Distributed
Reaction Zone
Corrugated Flamelets
Wrinkled Flamelets
Laminar
Flames
Well -
Stirred
Reactor

29. 23
Figure 4.5: plot of Rsch versus time for the repeat experiments with the mean radius
for each time plotted as a dashed line with +/-3.17 mm scatter bars.
4.2.3 Turbulent Flame Speed versus Time
A graph of turbulent flame speed, St versus time is displayed in figure 4.6. The standard
deviation in Rsch was divided by the time increment (0.56 ms) to give a scatter in
turbulent flame speed of +/- 1.07 m.s-1
.
Figure 4.6: plot of turbulent flame speed (St) versus time for the repeat
experiments. Scatter bars are included on 12.96 vol.%; the other series have
similar scatter and scatter bars were not included on them for clarity; this will also
be the case for following plots.
4.2.4 Turbulent Flame Speed versus Schlieren Radius
Turbulent flame speed versus the schlieren radius for the repeat experiments are
plotted in figure 4.7.
0
10
20
30
40
50
60
0 2 4 6 8 10 12 14
Rsch(mm)
Time (ms)
Schlieren Radius versus Time for a u' of 1.6 m.s-1 and Similar
Concentrations
12.96, 0.355
12.95, 0.354
12.94, 0.354
mean
0
2
4
6
8
0 2 4 6 8 10 12 14
St(m.s-1)
Time (ms)
Turbulent Flame Speed versus Time for a u' of 1.6 m.s-1 and
Similar Concentrations
12.96, 0.355
12.95, 0.354
12.94, 0.354
mean
Conc. (%), φ:
Conc. (%), φ:
Greater scatter at
t>10

30. 24
Figure 4.7: plot of turbulent flame speed (Sn) versus schlieren radius (Rsch) for the
repeat experiments.
4.2.5 Turbulent Burning Velocity versus Time
Displayed in this section are plots of utk versus the time after ignition.
Figure 4.8: plot of turbulent burning velocity versus time for the repeat experiments.
Figure 4.9: plot of turbulent burning velocity versus time for a u’ of 0.4 m.s-1
and a
small range of concentrations.
0
2
4
6
8
0 10 20 30 40 50 60
St(m.s-1)
Rsch (mm)
Turbulent Flame Speed versus Schlieren Radius for a u' of
1.6 m.s-1 and Similar Concentrations
12.96, 0.355
12.95, 0.354
12.94, 0.354
0
2
4
6
8
0 2 4 6 8 10 12 14
utk(m.s-1)
Time (ms)
Turbulent Burning Velocity versus Time for
a u' of 1.6 m.s-1 and Similar Concentrations
12.96, 0.355
12.95, 0.354
12.94, 0.354
0
0.5
1
1.5
2
2.5
3
3.5
0 10 20 30 40 50 60 70
utk(m.s-1)
Time (ms)
Turbulent Burning Velocity versus Time for a
u' of 0.4 m.s-1 and a Range of Concentrations
13.82, 0.382
13.33, 0.366
12.80, 0.349
Conc. (%), φ:
Conc.(%), φ:
Conc. (%), φ:
Convergence at R=50 mm

31. 25
Figure 4.10: plot of turbulent burning velocity versus time for a u’ of 1.6 m.s-1
and a
range of concentrations
4.2.6 Turbulent Burning Velocity versus Schlieren Radius
Displayed in this section are plots of utk versus Rsch.
Figure 4.12: plot of turbulent burning velocity versus schlieren radius for a u’ of 1.6
m.s-1
and similar concentrations.
-2
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30 35 40
utk(m.s-1)
Time (s)
Turbulent Burning Velocity versus Time for a
u' of 1.6 m.s-1 and a Range of Concentrations
13.33, 0.366 12.95, 0.354
11.70, 0.315 10.57, 0.281
9.10, 0.238 8.54, 0.222
0
1
2
3
4
5
6
7
0 10 20 30 40 50 60
utk(m.s-1)
Rsch (mm)
Turbulent Burning Velocity versus Schlieren Radius for
a u' of 1.6 m.s-1 and Similar Concentrations
12.96, 0.355
12.95, 0.354
12.94, 0.354
Figure 4.11: plot of turbulent burning velocity versus time for a u’ of 2.4 m.s-1
and a
range of concentrations
0
2
4
6
8
10
12
14
16
18
20
0 5 10 15 20 25
utk(m.s-1)
Time (ms)
Turbulent Burning Velocity versus Time for a
u' of 2.4 m.s-1 and a Range of Concentrations
13.35, 0.367
12.34, 0.335
11.32, 0.304
9.97, 0.264
8.86, 0.231
7.12, 0.182
Conc.(%), φ:
Conc. (%), φ:
Conc. (%), φ:

32. 26
Figure 4.13: plot of turbulent burning velocity versus schlieren radius for a u’ of 0.4
m.s-1
and a range of concentrations.
Figure 4.14: plot of turbulent burning velocity versus schlieren radius for a u’ of 1.6
m.s-1
and a range of concentrations
Figure 4.15: plot of turbulent burning velocity versus schlieren radius for a u’ of 2.4
m.s-1
and a range of concentrations.
0
1
2
3
0 20 40 60 80
utk(m.s-1)
Rsch (mm)
Turbulent Burning Velocity versus Schlieren Radius for
a u' of 0.4 m.s-1 and a Range of Concentrations
13.82,
0.382
13.33,
0.366
12.80,
0.349
0
2
4
6
8
10
12
14
0 10 20 30 40 50 60
utk(m.s-1)
Rsch (mm)
Turbulent Burning Velocity versus Schlieren Radius for a u' of
1.6 m.s-1 and a Range of Concentrations
13.33, 0.366
12.95, 0.354
11.70, 0.315
10.57, 0.281
9.10, 0.238
0
2
4
6
8
10
12
14
16
18
20
0 10 20 30 40 50 60
utkm/s)
Rsch (mm)
Turbulent Burning Velocity versus Schlieren Radius for a u' of
2.4 m.s-1 and a Range of Concentrations
13.35, 0.367
12.34, 0.335
11.32, 0.304
9.97, 0.264
8.86, 0.231
7.12, 0.182
Conc. (%), φ:
Conc.(%), φ:
Conc. (%), φ:
Fluctuations for low turbulence

33. 27
4.2.7 Associated Flame Images
Schlieren images of the flame propagations relating to turbulent burning velocity
experiments are displayed in figures 4.16-4.18.
φ Flame images for the Repeat Experiments
0.354
t (ms) time zero 3.89 8.89 10.56
0.354
t (ms) time zero 3.89 8.89 10.56
0.355
t (ms) time zero 3.89 8.89 10.56
Figure 4.16: Images of the flame propagations of the repeats.
Figure 4.17: Images of the flame propagations for a u’ of 0.4 m.s-1
.
φ Flame Images for a u’ of 0.4 m.s-1
0.349
t (ms) time zero 26.7 45.6 60.0
0.366
t (ms) time zero 10.0 17.8 28.8
0.382
t (ms) time zero 10.0 17.8 26.1

34. 28
φ Flame Images for a u’ of 1.6 m.s-1
0.212
t (ms) time zero 16.7 26.7 66.7
0.222
t (ms) time zero 14.6 19.6 26.7
0.238
t (ms) 2.78 6.67 12.2 12.8
0.281
t (ms) 3.10 6.21 10.7 14.8
0.315
t (ms) 2.22 5.00 12.2 15.6
0.366
t (ms) 1.11 2.78 7.22 9.44
Figure 4.18: Images of the flame propagations for a u’ 0f 1.6 m.s-1
(see fig.4.14 for
the images of 12.95 vol.%).F labels the barely visible flame front produced for a φ
of 0.222
D

35. 29
φ Flame Images for a u’ of 2.4 m.s-1
0.184
t (ms) t1 = 6.11 ms t2 = 12.8 ms t3 = 17.8 ms t3 = 20.1 ms
0.231
t (ms) t1 = 3.33 ms t2 = 6.11 ms t3 = 9.44 ms t4 = 11.6ms
0.264
t (ms) t1 = 4.44 ms t2 = 7.22 ms t3 = 10.0 ms t4 = 12.8 ms
0.304
t (ms) t1 = 0.56 ms t2 = 2.78 ms t3 = 7.78 ms t4 = 10.6 ms
0.335
t (ms) t1 = 0.56 ms t2 = 2.78 ms t3 = 5.56 ms t4 = 7.78 ms
0.367
t (ms) t1 = 0.56 ms t2 = 2.78 ms t3 = 5.56 ms t4 = 7.78 ms
Figure 4.19: Images for the propagation of flames with a u’ of 2.4 m.s-1
.

36. 30
4.2.8 Turbulent Burning Velocity versus Equivalence Ratio and Effective rms
Turbulence Velocity
Displayed in figure 4.20 is a plot of turbulent burning velocity over ul versus equivalence
ratio for a schlieren radius of 30 mm. Figure 4.21 presents a correlation of turbulent
burning velocity versus effective rms turbulence velocity for results from present
experiments and from Kitagawa et al. (2008).
Figure 4.20: Plot of turbulent burning velocity normalised by ul versus equivalence
ratio for a range of rms turbulence velocities at a Rsch of 30 mm from present
experiments and from Kitagawa et al. (2008).
Figure 4.21: Plot of turbulent burning velocity (utk) versus effective rms turbulence
velocity (u’k) for a range of equivalence ratios and fan speeds. Solid and dashed
trend lines represent decreasing concentration with equal radius and fan speed for
45 and 30 mm respectively, and the logarithmic dashed line is a suggested
correlation curve. Results from Kitagawa et al.(2008) (see fig. 4.19) were included.
0
10
20
30
40
50
60
0.15 0.35 0.55 0.75 0.95 1.15
utk/ul
φ
Turbulent Burning Velocity Normalised by ul versus
Equivalence Ratio at a Schlieren Radius of 30 mm
u' = 2.4 m/s
u' = 1.6 m/s
u' = 0.4 m/s
Kitagawa et al. 0.8 m/s
Kitagawa et al. 1.6 m/s
0
5
10
15
20
25
30
35
40
45
0 2 4 6 8 10 12 14
utk/ul
u'k / ul
Turbulent Burning Velocity versus Effective rms Turbulence
Velocity, Normalised by ul
u’= 2.4 m.s-1
0.367 0.335 0.304
u’= 1.6 m.s-1
0.366 0.354 0.315
u’= 0.4 m.s-1
0.382 0.366 0.349
Rsch=45mm

37. 31
5. Discussion
This chapter presents a discussion of the LFL experiments in 5.1, pressure and
temperature results in 5.2 and finally the results of turbulent burning velocity
experiments in 5.3.
5.1 Lower Flammability Limit
5.1.1 Effect of Increasing rms Turbulence Velocity
The LFL increased slightly upon increasing rms turbulence velocity (u’) from 0.8 m.s-1
to 1.6 m.s-1
(see table 4.1), and increasing more significantly when u’ was 2.4 m.s-1
where the LFL range was 7.07 to 7.12 vol.%, greater the 6.97 to 6.98 vol.% range
found by Denton (2016) for a quiescent flow field in the same combustion vessel; this
increase in LFL contradicts Cashdollar et al.’s (2000) findings of decreasing LFL with
turbulence. Increasing LFL with turbulence was also observed by Al-Khishali et al.
(1983), whom explain that this result may arise when the ratio of chemical to eddy
lifetimes exceeds a critical value. From the Borghi diagram (fig. 4.4) it can be seen that
the LFL for a u’ of 0.8 m.s-1
exists at the border of the distributed and corrugated
regimes, whereas for a u’ of 1.6 m.s-1
and 2.4 m.s-1
the LFL mixtures clearly combust
in the distributed regime; in this regime local quenching can occur (see section 2.7),
which is a likely explanation as to why the LFLs in this regime were higher, and the
LFL for a u’ of 0.8 m.s-1
was similar to that found for laminar as less quenching occured.
LFL may increase with u’ as the ratio of chemical to eddy lifetimes increases and hence
a greater mass of unburned gas is removed from the flame front, meaning the minimum
concentration required to support flame propagation is larger. Experiments performed
by Cashdollar et al. (2000) may have been in the corrugated or wrinkled regimes and
LFL therefore only decreases in these regimes; this requires further investigation.
Turbulence produced in a containment or reactor building of nuclear power stations by
obstacles may decrease the likelihood of hydrogen explosions by increasing LFL,
although only slightly at these rms turbulence velocities. For a u’ of over 16 m.s-1
Al-
Khishali et al. (1983) increased the LFL to over 8 vol.%, and therefore high frequency
fans installed in reactor or containment buildings may prevent hydrogen explosions if
the concentration of the mixtures are near limit. If fans were installed in the reactor
building of Fukushima Daiichi and power was available to operate them, the stratified
layers of hydrogen discussed in section 2.2.3 may have mixed to a concentration below
the LFL at the rms turbulence velocity the fans produce thereby preventing explosion.

38. 32
5.1.2 Comparison to Literature
The LFLs for the different rms turbulence velocities were at least 0.8 vol.% higher than
the turbulent LFL of 5 +/-0.5 vol.% found by Cashdollar et al. (2000) using spherical
vessels even with accounting for bomb leakage. A major source of difference in LFL
was caused by the difference in spark energy used; Cashdollar et al. (2000) used a
much greater energy of 20 to 58 J compared to the 50 mJ used for the LFL experiments
of this report; a greater initial spark energy increases the temperature of hydrogen
around the spark and creates a greater number of free radicals (Gillespie et al., 2000)
which then react with hydrogen and oxygen molecules and each other to complete the
combustion reaction process, and both of these effects of spark enhance flame
propagation explaining why a lower minimum concentration was found to support
significant flame propagation by Cashdollar et al. (2000). This shows the extent to
which spark energy can affect the LFL of hydrogen-air mixtures, and large (and
preferably all) sparks should be avoided where hydrogen and other flammable gases
are present in the nuclear industry.
5.1.3 Observations of Near Limit Flames Images
From figure 4.1 it can be seen that all of the flames at the LFL were clearly significant
as they eventually covered the viewing window. For a u’ of 1.6 m.s-1
the LFL flame
propagated faster than that for 0.8 m.s-1
, and the flame surface area was larger upon
reaching the window edge. For a time of 33.3 ms following the first flame image, the
LFL flame at 2.4 m.s-1
appears to have been split in two, where the flame closest to the
centre is smaller and more dense as the image is darker and the other is less dense,
more spread out and has risen further (see B and C on figure 4.1); it is most likely that
the flames rose due to buoyancy and at different rates because of the density
differences. The flame may have been split by local quenching. At a time of 91.1 ms
the denser flame moved to the top of the bomb and began to propagate downwards;
as shown by Al-Khishali et al. (1983) laminar flames cannot propagate downwards at
near limit concentrations, and this observation provides evidence of turbulence
negating the effect of buoyancy discussed in section 2.3. This flame acted as a semi-
confined flame as it was restricted by the top of the bomb; the combustion of hydrogen
in Fukushima Daiichi may have been similar where the flame was confined by the
reactor roof, and turbulence may have supported downward propagation and hence
produced a more severe flame than what would arise in quiescent conditions.
5.2 Discussion of Temperatures and Pressures Produced
Measured maximum temperatures (see fig. 4.3) were much lower than the adiabatic
(where no heat transfer occurs) temperature of combustion products for all

39. 33
concentrations used, e.g. for a concentration of 12.96 vol.% the adiabatic temperature
of combustion is 1317.4 K, whereas a maximum temperature of 322.15 K was
measured experimentally. This difference was partially caused by heat losses in the
system as heat can transfer to the combustion bomb walls, which the presence of
turbulence in a combustion bomb promotes (Al-Khishali, 1983). Much lower than
adiabatic temperatures may have been measured because of limitations of the thermo
couple and temperature display; a delay of approximately 15 seconds was observed
between ignition and peak temperature, and the flame temperature may have rapidly
decreased from adiabatic before this could be displayed giving a lower measured
temperature. Large scatter in maximum temperature was produced below a
concentration of 11.0 vol.%, possibly because local quenching gave varying volumes
of burned gas and turbulence dissipated heat randomly. Maximum temperatures
produced in the presence of 1.6 m.s-1
and 2.4 m.s-1
u’ were similar and noticeably lower
than for 0.8 m.s-1
, most likely because the latter produced less heat transfer. Measured
temperatures were below 325 K for all concentrations; this shows that although
combustion products may have a very high temperature upon forming, turbulence may
rapidly decrease temperatures and therefore prevent damage such as the melting of
structural elements in a nuclear containment vessel which could cause leakage.
At the LFL maximum pressure ratios increased with decreasing rms turbulence velocity
(see fig. 4.2) as the maximum pressure ratio was 1.03, 1.86 and 3.27 for a u’ of 2.4
m.s-1
, 1.6 m.s-1
and 0.8 m.s-1
respectively. The higher turbulence velocities may have
produced flame quenching outside of the viewing window giving a lower final burned
gas volume and therefore a lower maximum pressure produced from the flame. The
pressure ratio for a u’ of 0.8 m.s-1
was close to adiabatic, which is unexpected as
temperature was not and accounting for leakage this pressure ratio would be greater
than adiabatic, therefore suggesting that the LFL maximum pressure was inaccurately
high. Nevertheless the trend of LFL pressure ratios at different rms turbulence
velocities shows turbulence may decrease the pressures produced for mixtures at the
LFL and therefore reduce the damage caused by near limit deflagrations.
Pressures found by Cashdollar et al. (2000) and at the 2000 m3
Nevada test site
(Thompson et al., 1984) were greater than that found in the present experiments for
the same concentrations, most likely because of the bomb leakage discussed in 3.2.1,
and accounting for the leakage the curve would shift to the left and pressure ratios
would be similar to that found by Cashdollar et al. (2000) and Thompson et al. (1984).
This shows that the pressure ratios found might be similar to those which would arise
for hydrogen-air concentrations below 14 vol.% in a nuclear reactor building or

40. 34
containment which have a much larger volume than the bomb described used in this
report.
5.3 Turbulent Burning Velocity
5.3.1 Discussion of Repeats
From the plots of Rsch versus time for the repeats (fig. 4.5) it can be seen that flames
had varying radii at time zero; this was caused by the experimental technique used
(see section 3.2.3) as the actual point of ignition may take place at any point between
the capture interval of 0.56 ms. The difference in initial radius did not affect flame
speeds or burning velocities following the first image as these are proportional to
changes in radius, however the times which these velocities exist do not represent the
actual time after ignition.
Following a time of around 6 ms the curves for 12.96 vol.% and 12.95 vol.% converge
and reached the window at similar times of around 10 ms and with similar radii of 51
mm and 56 mm respectively, whereas the curve for 12.94 vol.% diverges and reaches
a radius of 51 mm in a time of 12 ms, similar to the other repeats. Difference in flame
speed (see fig. 4.6) and therefore radius for the same time may be attributed to the
randomness of turbulence wrinkling the flames in different ways, as displayed by the
images in figure 4.14, hence giving the flames different surface areas and therefore
different burning rates. Variance in flame speed may also have been caused by the
mixtures having slightly different concentrations.
Curves of turbulent flame speed versus Rsch (see fig. 4.5) showed better agreement
between repeats than versus time. This shows that despite repeat mixtures
propagating at different speeds at different times, once the same radius was reached
the turbulent flame speed was similar. Turbulent flame speeds converged at an Rsch of
around 50 mm; this may be because the flame diameter was 100 mm which is
significantly larger than the size of the largest eddies in the flow field (30 mm), hence
the turbulence is more effective (see 2.6.4) and flames are wrinkled in a less random
manner.
5.3.2 Turbulent Burning Velocity versus Time
The values and trend of utk versus time for the repeats (see fig. 4.8) was the same as
that found for St versus time (see fig. 4.6), which is expected as utk is linearly
proportional to St (see equation 2.07) and the burned to unburned density ratio for
hydrogen is close to one.

41. 35
For a u’ of 1.6 m.s-1
(fig. 4.10) the curves for equivalence ratios 0.366 and 0.354 were
very similar and the φ of 0.315 flame clearly burned slower reaching a maximum utk of
5 m.s-1
compared to 6.5 m.s-1
and 7.5 m.s-1
for 0.354 and 0.366 respectively. When φ
was decreased from 0.315 to 0.281 utk increased to levels similar to that of the 0.366
equivalence ratio flame, and utk increased slightly again for most times after ignition
upon decreasing equivalence ratio to 0.238. Turbulent burning velocity also increased
upon decreasing φ from 0.304 to 0.264 for a u’ of 2.4 m.s-1
. This is unexpected as upon
these decreases in φ the flames enter the distributed reaction (see fig. 4.4) zone where
local quenching occurs, and it would be expected that local quenching would decrease
burning velocity. This may be explained by the flame edge appearing fainter in some
images (see D on fig. 4.18) and clearer in subsequent ones giving sudden increases
in flame surface area and therefore also measured utk for equivalence ratios below
0.315, however for an φ of 0.281 the flame front was clear throughout. If the increase
in utk with decreasing φ was not completely a result of the analysis technique,
hydrogen-air flames below an equivalence ratio of around 0.3 may increase in
propagation speed despite decreasing in equivalence ratio and may therefore also
produce significant damage to surroundings.
As can be seen from figure 4.10, when equivalence ratio was decreased from 0.238 to
0.222 for a u’ of 1.6 m.s-1
utk values showed large fluctuations and even decreased to
below 0 m.s-1
at a time of 7 ms. Upon inspection of the flame images for an equivalence
ratio of 0.222 (figure D on 4.18) it can be seen that the image flame front has become
much more faint than for higher equivalence ratios, which is the source of the large
fluctuations, and also the low turbulent burning velocities as parts of the flame may
have propagated which were not visible on the images, hence giving a lower turbulent
burning velocity than actual. At an equivalence ratio of 0.212 the flame was lifted off of
the centre and was also very faint, preventing the measurement of utk. For a u’ of 2.4
m.s-1
utk decreased upon decreasing equivalence ratio from 0.231 to 0.184, however
the trend showed less fluctuation than for a u’ of 1.6 m.s-1
and φ of 0.222 despite φ
being much lower, and from figure 4.19 it can be seen that the flame front at a φ of
0.184 is relatively clear on the image; this may be because the higher u’ increased
mixing of burned and unburned gasses more and hence increased the density and
therefore clarity on images of the flame front.
5.3.3 Turbulent Burning Velocity versus Schlieren Radius
The trend of utk versus Rsch for the repeats (see fig.4.12) was similar to that of St versus
Rsch.

42. 36
When a u’ of 0.4 m.s-1
was used utk (see fig. 4.13) fluctuated increasingly with
increasing Rsch for decreasing equivalence ratios prior to an Rsch of approximately 40
mm; equivalence ratios of 0.315 to 0.366 for a u’ of 1.6 m.s-1
(see fig. 4.12) also display
this trend but with less frequent fluctuations which continue until the viewing window
was reached, and the curves for a u’ of 2.4 m.s-1
were smoother (see fig. 4.13).
Fluctuations at the weakest turbulence may have been caused by the influence of
geometric stretch; as the radius of spherical flames increases the stretch rate of flames
increases (Lawes, 2011). Geometric stretch rate can change the burning velocity of
laminar flames and produce fluctuations over increasing radius, as shown by Lawes
(2011). Turbulence stretches flames locally by fluid dynamic strain, which is equal to u’
divided by Taylor microscale of turbulence, and is more dominant than geometric
stretch except at weak turbulences (Lawes, 2010b). For a u’ of 0.4 m.s-1
, where
combustion was at the boundary of the corrugated and wrinkled regimes (see fig. 4.3),
geometric stretch may have influenced burning velocity to a greater extent and
produced fluctuations, whereas for higher rms turbulence velocities aerodynamic strain
dominated and this may have counteracted burning velocity fluctuations.
Increasing u’ increased utk for the same equivalence ratios and flame radius (see
figures 4.11, 4.12 and 4.13). Increasing u’ increases flame wrinkling and therefore
surface area, which gives a greater burning rate (Lawes, 2010b). Schlieren imaging
gives a 2D projection of the flame, hence cannot measure area increases in the third
plane and although Rsch and therefore flame surface areas are equal for these different
turbulence velocities, the actual flame surface area is most likely larger for higher
turbulence velocities. This contributes to existing evidence that turbulence and
obstacles in a nuclear environment may increase the burning velocity of flames.
5.3.4 Ratio of Turbulent to Unstretched Laminar Burning Velocities versus Equivalence
ratio
Burning velocity ratios (utk/ul) for u’ of 1.6 m.s-1
and 2.4 m.s-1
were found to increase
with decreasing equivalence ratio by the curve displayed in fig. 4.20, with the burning
velocity ratios for the higher u’ being large for the same equivalence ratio. Burning
velocity ratio at an equivalence ratio of 0.182 for a u’ of 2.4 m.s-1
was an outlier to this
curve, most likely because measurement of flame surface area was inaccurate (as
discussed in 5.3.2). The large gradient of these curves displays the extent to which
turbulence can increase the burning velocity at very lean mixtures, and therefore
increase the severity of a lean hydrogen-air flame. For a u’ of 0.4 m.s-1
burning velocity
ratios were much lower showing that weak turbulences increase burning velocity to a
lesser extent. The data from Kitagawa et al. (2008) for equivalence ratios between 0.4

43. 37
and 1.0 followed the trend of the u’ of 1.6 m.s-1
curve well. Figure 4.19 may provide a
good estimate of the burning velocity ratios expected from lean to stoichiometric
hydrogen-air flames with similar rms turbulence velocities.
5.3.5 Dimensionless Correlation of Turbulent Burning Velocity versus Effective
Turbulence Velocity
Figure 4.21 displays turbulent burning velocities verses effective rms turbulence
velocity obtained from different fan speeds, Rsch and equivalence ratios, and a
correlation was proposed for this data. The curve contains scatter of around +/- 10;
scatter may have arisen because of the random nature of turbulence at these flame
radii where turbulence is not fully effective, especially for an Rsch of 30 mm where
scatter is greater (see fig. 4.10). Data points from Kitagawa et al. (2008) were around
10 lower than the correlation proposed; this highlights the poor repeatability which very
lean hydrogen-air turbulent combustion can bring. Kitagawa et al. (2008) used an
integral length scale of 10.3 mm meaning turbulence was more effective at an Rsch of
30 mm, however unstretched laminar burning velocities were higher placing the data
below and to the left of the data from the experiments of this report. This correlation
may still be used as a very rough indication of the turbulent burning velocities which
may arise at different turbulence effectiveness’ and equivalence ratios.
Further experiments should be performed to complete the curve. Improving this
correlation would be beneficial as it can be used to predict what the burning velocities
of hydrogen-air combustion in for example a nuclear reactor building roof could be for
the initial stages of combustion. Length scales of turbulence are a function vessel (or
reactor building roof) for example L in the reactor building roof of the Fukushima Daiichi
units might be 3m; flames in this environment with a relatively large radius of 3m would
have a u’k/u’ equal to that of a 30 mm radius flame in a 30 mm length scale flow, and
providing u’ and equivalence ratios are equal these flames be represented by the same
point on the correlation, demonstrating how fig. 4.20 can be used for the scaling of
different flames and how turbulent burning velocities in larger vessels may be
predicted.

44. 38
6. Conclusion
The lower flammability limit of hydrogen-air mixtures in turbulent flow was found to be
6.93 to 6.97 vol.% for a u’ of 0.8 m.s-1
which was almost equal to the laminar LFL found
by Denton (2016), 6.97 to 7.01 vol.% for a u’ of 1.6 m.s-1
, and was 7.07 to 7.12 vol.%
for a u’ of 2.4 m.s-1
. The increase in LFL with increasing u’ was most likely caused by
quenching which can occur in the distributed combustion regime, showing that fans
may be used to reduce the risk of explosion in the nuclear industry. Turbulence was
found to increase the severity of near limit flames by negating the effects of buoyancy.
Measured maximum temperatures were much lower than adiabatic most likely
because of measurement technique limitations and heat dissipation by turbulence.
Maximum pressure rises at the LFL were lower for greater rms turbulence velocities
suggesting turbulence may decrease pressures produced from near limit hydrogen-air
mixtures. Accounting for bomb leakage the maximum pressure ratios were similar to
that found in a 120 L bomb and 2000 m3
large test facility meaning they may be used
to indicate the pressures which can arise from hydrogen-air flames in larger vessels.
Measured turbulent burning velocity increased with decreasing equivalence ratio below
0.3, most likely because of inaccuracy in the measurement technique; different
techniques should be investigated for the measurement of the turbulent burning
velocity of these flames. Combustion in the distributed regime may reduce fluctuations
produced from geometric stretch. Although increasing u’ can increase LFL, it also
increases turbulent burning velocity and thereby may increase the damage caused by
these flames. The ratio of turbulent to unstretched laminar burning velocities increased
exponentially upon decreasing equivalence ratio below 0.37, and this curve may be
used to predict burning velocity ratios at different equivalence ratios for similar rms
turbulence velocities. A correlation of turbulent burning velocity versus effective rms
turbulence velocity was produced which contained large scatter, nevertheless this
correlation could be used as an indication of turbulent burning velocity for different
turbulence effectiveness’ and hydrogen-air mixtures which may arise in the nuclear
industry, and this correlation should be improved in future.

45. 39
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Yanez, J, Kuznetsov, M and Souto-Iglesias, A. 2015. An analysis of the hydrogen
explosion in the Fukushima-Daiichi accident. International Journal of Hydrogen
Energy. 40, pp.826t-828o.
Zlochower, I. and Green, G. 2009. The limiting oxygen concentration and flammability
limits of gases and gas mixtures. Journal of Loss Prevention in the Process
industries. 22(4), pp.499-505.

47. 41
Appendix I: Meeting log

48. 42

49. 43
Appendix II: Fukushima Daiichi Unit 4 Leak Path
Obtained from the TEPCO accident analysis report (TEPCO, 2012).

50. 44
Appendix III: Initial Conditions for Flammability Limit and
Turbulent Burning Velocity Experiments
Table A1 - Initial conditions for LFL mixtures and mixtures with lower conditions to
show concentrations below the LFL did not produce flames:
Table A2 – Initial conditions for hydrogen-air mixtures used in turbulent burning
velocity experiments:
Fan
Speed
(rpm)
Conc
(vol.%)
To (K) Po (mbar,g
)
ν*10-5
m2
/s
ρu
(kg/m3
)
ρb (kg/m3
) ul
(m/s)
0.4
12.8 292.15 3 1.71 1.0604 1.0604 0.27
13.33 293.15 0 1.73 1.0508 1.05076 0.3
13.82 293.15 0 1.74 1.0452 1.04516 0.36
1.6
8.19 293.15 0 1.67 1.1082 1.10819 0.08
8.54 292.15 6 1.64 1.108 1.10803 0.08
9.1 294.15 20 1.67 1.0943 1.09429 0.08
10.57 292.15 9 1.68 1.0853 1.08534 0.12
11.7 293.15 13 1.7 1.0691 1.06905 0.17
12.94 295.15 10 1.76 1.0475 1.0475 0.28
12.95 294.15 13 1.75 1.0511 1.05106 0.28
12.96 295.15 15 1.75 1.0475 1.0475 0.28
13.33 292.15 0 1.72 1.0544 1.05436 0.3
2.4
7.16 296.15 6 1.63 1.1088 1.10883 0.08
8.86 296.15 2 1.68 1.0896 1.08959 0.08
9.97 295.15 0 1.7 1.0807 1.08068 0.1
11.32 295.15 3 1.72 1.0658 1.06582 0.15
12.34 294.15 0 1.73 1.0582 1.05819 0.22
13.35 295.15 2 1.75 1.0433 1.04329 0.3
Fan Speed (rpm) Conc. (vol.%) Po (mbar, gauge) To (K) Propagation?
6.88 5 294.15 N
6.92 -1 294.15 N
6.93 3 292.15 N
6.97 20 296.15 Y
6.91 -15 293.15 N
6.90 -13 293.15 N
6.97 0 294.15 N
7.01 0 293.15 Y
6.98 20 296.15 N
7.07 20 296.15 N
7.12 20 293.15 Y
500
1000
1500

51. 45
Appendix IV: Schlieren Radius versus Time Data
0
10
20
30
40
50
60
70
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00
Rsch(mm)
time (ms)
RSch versus time for u' of 0.4 m.s-1
13.82 vol.%,
eq.ratio=0.382
13.33 vol.%,
eq.ratio=0.366
12.80 vol.%,
eq.ratio=0.349
0
10
20
30
40
50
60
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00
Rsch(mm)
time (ms)
RSch versus time for u' of 1.6 m.s-1
13.33 vol%, eq. ratio=0.315
12.95 vol.%, eq.ratio=0.354
11.70 vol.%, eq.ratio=0.315
10.71 vol.%, eq.ratio=0.281
9.10 vol.%, eq.ratio=0.238
8.54 vol.%, eq.ratio=0.222
0
10
20
30
40
50
60
0.00 5.00 10.00 15.00 20.00 25.00
RSch(mm)
time (ms)
RSch versus time for u' of 2.4 m.s-1
13.35 vol.%, eq.ratio=0.367
12.34 vol.%, eq.ratio=0.335
11.32 vol.%, eq.ratio=0.304
9.97 vol.%, eq.ratio=0.264
8.86 vol.%, eq.ratio=0.231
7.12 vol.%, eq.ratio=0.182