chapter 5 tnt equivalence of...
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109
CHAPTER 5
TNT EQUIVALENCE OF FIREWORKS
5.1 INTRODUCTION
5.1.1 Explosives and Fireworks
Explosives are reactive substances that can release high amount of
energy when initiated (Meyer 1987). Explosive materials may be categorized
by the speed at which they expand (Bahl et al 1981, Chou et al 1991, Khan
and Abbasi 1999). Materials that detonate are said to be "high explosives"
and materials that deflagrate are said to be "low explosives". Explosives may
also be categorized by their sensitivity. Sensitive materials that can be
initiated by a relatively small amount of heat or pressure are primary
explosives and materials that are relatively insensitive are secondary or
tertiary explosives.
Detonation is an explosive phenomenon whereby a shock wave
coupled to a flame front propagates through the reaction mixture at supersonic
speeds relative to ambient gases. Blast waves resulting from the detonation of
strong explosives like TNT exhibit close to ideal wave behaviour (Cook et al
(1989 and 2001) Lees 1996, Balzer et al 2002). The pressure profile over time
of an ideal blast wave can be characterized by its rise time, the peak
overpressure, duration of positive phase and total duration (Sochet 2010).
In deflagrations the decomposition of the explosive material is
propagated by a flame front which moves slowly through the explosive
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material. The volume of a gas-air mixture is generally high and the energy
release rate is relatively slow. The blasts are characterized by more regular
blast waves that propagate at a subsonic speed. Explosives depend on
properties such as sensitivity, velocity and stability. Chemical explosives may
consist of either a chemically pure compound or a mixture of an oxidizer and
fuel.
Due to the effects of the shock wave during detonation, the oxidizer
and fuel interact to trigger chemical reactions. Some of the well-known
explosives are TNT, nitro-glycerine, RDX, PETN, HMX and nitrocellulose.
Fireworks are used for mainly fireworks display purposes and consist of
various chemical compounds. The heat released by explosion is often used to
calculate the TNT equivalency according to principle of energy similarity
(Rui et al 2002)
Figure 5.1 Distribution of energy in an explosion (Rui et al 2002)
The total energy generated by an explosive reaction can be
electromagnetic energy or mechanical energy. These energies in turn can be
Total energy
generated by
explosive reaction
Electromagnetic energy
High frequency electromagnetic energy
Visible light electromagnetic energy
Infrared energy
Low frequency electromagnetic energy
Mechanical energy
Overpressure of shock wave
Earthquake wave and crater formation
Shattering of cartridge and fling of its fragments
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subdivided as shown in Figure 5.1. The compositions of firework mixtures
consist of a fuel, an oxidizer that oxidizes the fuel necessary for combustion,
colour producing chemicals and a binder which holds the compounds
together. In all explosive accidents involving fireworks mixture, the damage
or consequences appear similar to that of a high energetic compound such as
TNT. Since fireworks share similar characteristics of class A explosives like
TNT, and may reach the explosive potential of an explosive chemical, It is a
cause for concern due to associated hazards. An attempt has been made to
employ the ARC thermal characterisation of fireworks mixtures to calculate
its TNT equivalence of explosion. These chemicals often need to be handled
in a very safe manner.
In case of fireworks mixtures the oxidizer and fuel under right
conditions may explode if ignited. Further, all the fireworks compositions are
finely divided powder mixtures. Finely divided metals present a hazard to
violent explosion when ignited, and are susceptible to ignition by static
electricity more easily due to their conductive character. Hence firework
mixtures need to be handled very carefully. A slight deviation from the
strictly followed procedures for safe handling can turn the mixture into an
explosive chemical.
The expected form of an ideal shock wave from an unconfined high
explosive is shown in Figure 5.2.(Held 1983, Formby and Wharton 1996,
Sochet 2010) It is characterised by an abrupt pressure increase at the shock
front, followed by a quasi-exponential decay back to ambient pressure. A
negative phase follows, in which the pressure is less than ambient, and
oscillations between positive and negative overpressure continue as the
disturbance quickly dies away. Correspondingly, a typical design blast load is
represented by a triangular loading with side on pressure, Pso, and duration,
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characterized by the Figure 5.3 (Ngo et al 2007). The area under the pressure-
time curve is the impulse of the blast wave.
Figure 5.2 Pressure distributions in a medium during passage of a blast wave
Figure 5.3 Typical design of blast load plot
Ambient P
Time, (min)
Pso
- PsoPositive Phase
Duration
Negative Phase
Duration
Duration
Time, (min)
Impulse
t0
Pso
113
Figure 5.4 Characteristic curve of an explosion: obtained from
overpressure and impulse profile (Alanso et al 2006).
In the case of an explosion it is possible to obtain the over-
pressure–impulse–distance relationship, called here the ‘characteristic curve’.
Highest isobars
Explosion’s origin
Over pressure
Characteristic curve
Distance
Distance Z1 Z2
ZZ
Z
Z
I
II
I
P
P
PP
114
Figure 5.4 (Alanso et al 2006) shows graphically the meaning of the so-called
characteristic curve, traced from the shock wave’s over-pressure–distance and
impulse–distance pro les. Distance to explosion’s centre (Z1, Z2....., Zn) can
also be included, to display all the information in the same diagram (Alanso
et al 2006).
5.1.2 An Overview of Explosion Models and its Applicability to
Fireworks Mixtures
An explosion is a rapid increase in volume and release of energy in
an extreme manner, usually with the generation of high temperatures and the
release of gases. Also, an explosion (meaning a “sudden outburst”) is an
exothermal process (i.e., liberation of energy) that gives rise to a sudden
increase of pressure when occurring at constant volume. It is accompanied
by noise and a sudden release of a blast wave. Thermal explosion theory is
based on the fact that progressive heating raises the heat release of the
reaction until it exceeds the rate of heat loss from the area. At a given
composition of the mixture and pressure, explosion will occur at a specific
ignition temperature that can be determined from the calculations of heat loss
and heat gain. Depending on the shock wave produced, explosions can occur
as detonation or deflagration, with or without a confinement in the
surroundings (Sochet 2010). Corresponding to the magnitude of an explosion,
the two most important and dangerous factors are over pressure, and scaled
distance of damage.
The above discussed parameters are necessary to predict the effects
of thermal explosion and estimate the extent of these hazards. To assess the
significance of damage, models are necessary to calculate dangerous
magnitude as a function of distance from the explosion centre. Most data on
explosion and their effects, and many of the methods of estimating these
effects, relate to explosives.
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Although there are many explosion models available, TNT
equivalence model is widely accepted and in use. In recent years Multi
Energy Model, TNO and Baker -Strehlow-Tang (BS/BST) model also being
in use by many researchers (Beccantini et al 2007, Melani et al., 2009, Sochet
2010).
5.1.3 TNT Equivalence
The blast wave effects of explosions are estimated using TNT
equivalence techniques (Formby and Wharton 1996, Lees 1996). It is cited as
a standard equivalence model for calculating the effects of various explosives
and compares the effects to that of TNT. Parameters such as peak
overpressure, impulse, scaled distance and equivalent weight factor. (Held
1983, Frenando et al 2006, Lees 1996, Cooper 1994, Simoens and Michel
2011) are employed to calculate the TNT equivalence.
5.2 MATERIALS AND METHODS
5.2.1 TNT Equivalence Model
The term “TNT Equivalence” is used throughout the explosives and
related industries to compare the output of a given explosive to that of TNT
(Frenando et al 2006, Lees 1996; Cooper 1994). This is done for prediction of
blast waves, structural response, and used as a basis for handling and storage
of explosives as well as design of explosive facilities. This method assumes
that the gas mixture is involved in the explosion and that the explosion
propagates in an idealized manner. It is an ideal thermal explosion model
which considers explosion as a single entity; the explosive nature is measured
in terms of TNT equivalence;
TNT Equivalence =Mass of TNT, (g)
Mass of explosive, (g)(5.1)
116
TNT equivalence gives the impact of an explosive material to that of the
effect of TNT. TNT equivalence depends on the nature of the explosive,
distance, heat of detonation and the equivalent weight factor (Held 1983). The
various parameters involved in TNT model are peak overpressure, impulse
and the scaled distance. The equivalent mass of TNT is found by (Sochet
2010), Equation (4.2)
W =ME
E TNT(5.2)
where, W is the TNT Equivalence, is the empirical explosion efficiency, M
is the mass of explosive charge (g), EC is the heat of combustion of explosion
material (J g-1), ETNT is the heat of combustion of TNT (4765 J g-1)
5.2.2 Scaled Range
Scaling of the blast wave properties is a common practice used to
generalize blast data from high explosives. Scaling or model laws are used to
predict the properties of blast waves from large scale explosions based on
tests at a much smaller scale. The scaling law states that self – similar blast
waves are produced at the same scaled distance when two explosives of
similar geometry and of the same explosive material, but of different size, are
detonated in the same atmosphere.
The scaled range is measured as,
Z =R
W / (5.3)
Where, Z is the scaled range (m), R is the distance (m), W is the TNT
Equivalence Weight (g)
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5.2.3 Overpressure
The pressure resulting from the blast wave of an explosion is
known as the overpressure. It is referred to as “positive” overpressure when it
exceeds atmospheric pressure and “negative” during the passage of the wave
when resulting pressure or less than atmospheric pressure. As regards the
magnitude of an explosion, one of the dangerous factor is overpressure, which
is chiefly responsible for damage to humans, structures and environmental
elements.
The overpressure is measured as (Rui et al 2002),
P = 1.02(W) /
R+ 3.99
(W) /
R+ 12.6
(W)R
(5.4)
Where, R is the distance (m), W is the TNT Equivalence Weight (g), the
above equation has been widely used by researchers in the past (Frenando
et al 2006, 2008, Lees 1996, Held 1983, Rui et al 2002)
5.2.4 Multi Energy Model
In this model, combustion develops in a highly turbulent mixture in
obstructed or partially confined areas (Beccantini 2007, Sochet 2010, Melani
et al 2009). Unlike TNT model, it considers explosion not as a single entity
but as a set of sub explosions.
5.2.5 TNO Model
TNO model is based on the degree of confinement and is measured
on a scale of 1 to 10 (Beccantini 2007, Sochet 2010). The number 10
corresponds to index volume of congested areas i.e. strong detonation and 1
corresponds to uncongested areas, i.e. weak deflagration. It is based on the
assumption that blast is generated only when the explosive is partially
118
confined. The parameters that are measured are scaled distance, positive
overpressure, duration time and impulse (Melani et al 2009).
5.2.6 Scaled Distance
Scaled distance is a relationship used to relate similar blast effects
from various explosive weights at various distances. Scaled distance gives a
blaster an idea of expected vibration levels based upon prior blasts detonated.
The scaled distance is measured by,
r = r × (PE
) (5.5)
where, r is the distance from the charge (m), Pa is the ambient pressure (bar),
E is the heat of combustion (J g-1).
5.2.7 Positive Overpressure
The positive overpressure can be found by,
P = (P × P ) (5.6)
where, P is the positive overpressure (bar), Ps is the positive scaled
overpressure (bar), Pa is the atmospheric pressure (bar).
5.2.8 Positive Duration Time
The scaled duration time is given by,
T = T ×EP
/
×1a
(5.7)
where, T is the positive duration time (sec), Ts is the scaled positive duration
time, a0 is the sound velocity (343.2 m s-1).
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5.2.9 Impulse
The impulse is given by,
I =12
× P × T (5.8)
where, T is the positive duration time (s), P is positive overpressure (bar).
5.2.10 BS/ BST Model
Baker-Strehlow-Tang model(Baker et al 1994, 1996, 1998) is based
on the Mach number. It presents a correlation between the reactivity of fuel,
density of obstacles, and confinement. Flame speed is an important parameter
in measuring the blast wave propagation in this model.
The relation is given by,
P PP
= 2.4M
1 + M(5.9)
where, Pmax is the maximum overpressure (bar), P0 is the ambient overpressure
(bar), Mf is the Mach number.
Mach number =Flame velocitySound velocity
(5.10)
The scaled distance is measured by,
r = r ×P
E(5.11)
where, r is the scaled distance from the charge (m), r is the distance from the
charge (m), Pa is the ambient pressure (bar), E is combustion energy (charge),
(J g-1).
120
The positive overpressure can be found by,
P = (P × P ) (5.12)
where, P is the positive overpressure (bar), Ps is the positive scaled
overpressure (bar), Pa is the atmospheric pressure (bar).
The positive scaled impulse is given by,
I =I × a
E × p(5.13)
Where, I is the positive impulse (bar.s), a is the speed of sound, (m s-1), E is
the combustion energy (fuel air mixture), (J g-1), p is the atmospheric
pressure, (bar).
The combustion energy of fuel-air mixture is given by,
(E) = 2 × E × V (5.14)
where, E is the heat of combustion (sample firework mixture), (J g-1), V is
the volume of the vessel (m3).
5.2.11 Micro Calorimetric Test Data for Estimating TNT Equivalence
The experimental methods to assess the thermal instability/runaway
potential are primarily based on micro Calorimetry. It is designed to model
the course of a large-scale reaction on a small scale. Adiabatic Calorimetry is
one of the main experimental tools available to study the self-propagating and
thermally-sensitive reactions. One of the versatile micro calorimeter
techniques known as “Accelerating Rate Calorimetry” has the potential to
provide time-temperature-pressure data during the confined explosion of
121
fireworks mixture. The principle behind Accelerating Rate Calorimeter and its
usefulness in estimating the explosive potential of fireworks mixture have
been dealt with in the previous chapter. The ARC experimentation is designed
to study the explosive characteristics of energetic materials. The sample
quantities in ARC experiments are restricted to a maximum of 1gm to avoid
physical explosion of the sample vessel, unlike the field explosion. When
explosion occurs within confinement, time temperature data can be measured,
which is not viable in actual explosion due to the involvement of large
quantity of samples. The time, temperature, pressure data and the vigour of
explosion can be scaled up to field conditions (Bodman and Chervin 2004,
Badeen et al 2005, Whitmore and Wilberforce 1993).
Esparza 1986, Ohashi et al 2002, Kleine et al 2003 described a
procedure to calculate the TNT equivalent by a pressure based concept. This
approach is based on knowledge of the shock radius- time of arrival diagram
of the shock wave for the explosive under consideration. These data are used
to calculate the Mach number of the shock and the peak overpressure as a
function of distance (Dewey 2005).
ARC characterisation data generated for atom bomb cracker,
Chinese cracker, palm leaf cracker, flowerpot tip and ground spinner tip
mixtures have been dealt. Here an attempt has been made to employ them to
calculate their TNT equivalence of explosion.
5.3 RESULTS AND DISCUSSION
5.3.1 TNT Equivalence Model for Constant Distance
The results have been analyzed using this model for various
firework mixtures. Three cracker samples and two tip samples have been
selected. The distance from the centre of the explosion to the extent at which
the explosion took place has been kept as 3m (for all mixtures). The weight of
122
the samples taken has been varied from 5-25 grams. The results are presented
in Table 5.1 and Figures 5.5-5.8.
Table 5.1 Calculation of scaled range and overpressure for fireworks
Sample name
Heat of reaction , Ec,
( J g-1)
Sample weight,
(g)
TNTEquivalence,
W (g)
Scaledrange ,Z,
(m)
Overpressure,P (bar)
Atom bomb
cracker504.2
5 0.06 7.99 0.5410 0.11 6.34 0.9015 0.16 5.52 1.2420 0.21 5.03 1.5625 0.26 4.67 1.87
Chinesecracker 443.67
5 0.04 8.34 0.4910 0.09 6.62 0.8215 0.14 5.80 1.1220 0.18 5.25 1.4025 0.23 4.88 1.69
Palmleaf
cracker294.99
5 0.03 9.55 0.3710 0.06 7.58 0.6015 0.09 6.62 0.8220 0.12 6.01 1.0225 0.15 5.58 1.21
Flowerpot tip 972.23
5 0.10 6.42 0.8810 0.20 5.10 1.5215 0.30 4.45 2.1220 0.40 4.04 2.7025 0.50 3.75 3.26
Groundspinner
tip961.46
5 0.10 6.44 0.8710 0.20 5.11 1.5015 0.30 4.47 2.0920 0.40 4.06 2.6825 0.50 3.77 3.23
123
5.3.1.1 Scaled range vs. TNT equivalence for crackers
From the Figures 5.5 and 5.6 it is evident that the scaled range
decreases as the TNT equivalence increases for crackers and tip mixtures.
Figure 5.5 Scaled range vs. TNT equivalence for crackers (Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))
Figure 5.6 Scaled range vs. TNT equivalence for tip mixtures (Flowerpot tip ( ), Ground spinner tip ( ))
0
2
4
6
8
10
12
0 0.05 0.1 0.15 0.2 0.25 0.3
TNT Equivalence, (g)
3.5
4
4.5
5
5.5
6
6.5
7
0 0.1 0.2 0.3 0.4 0.5
TNT Equivalence, (g)
124
This is because TNT equivalence depends on the mass of the
sample taken. As the mass increases, TNT equivalence also increases. Hence
it can be inferred that the mass also has an effect over the scaled range. Thus
for tip samples, it can be observed that the effect of TNT equivalence over
scaled range resembles to the cracker samples due to similar mixture
composition.
5.3.1.2 Overpressure vs. TNT equivalence for firework mixtures
From the Figures 5.7 and 5.8, it can be observed that for the
crackers and tip mixtures the overpressure increases as the TNT equivalence
increases. This is because of the relationship between weight and TNT
equivalence. As the weight increases, TNT equivalence increases and since
overpressure and TNT equivalence have a direct correlation, the overpressure
increases. Thus, the weight is an important factor in determining the increase
or decrease of the overpressure.
Figure 5.7 Overpressure vs. TNT equivalence for crackers
(Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))
0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
0 0.05 0.1 0.15 0.2 0.25 0.3
TNT Equivalence, (g)
125
Figure 5.8 Overpressure vs. TNT equivalence for tip mixtures
(Flowerpot tip ( ), Ground spinner tip ( ))
5.3.2 TNT Equivalence Model for Varied Distance
The results have been analyzed using this model for various
firework mixtures. Three cracker samples and two tip samples have been
taken. The distance from the centre of explosion to the point where the
explosion takes place has been varied as 3, 5, 10, 15, 20 m for each mixture
sample. The weight of the samples taken was 1g (constant for all mixture
samples). The results are presented in Table 5.2 and Figures 5.9-5.12.
0
0.5
1
1.5
2
2.5
3
3.5
0 0.1 0.2 0.3 0.4 0.5 0.6
TNT Equivalent, (g)
126
Table 5.2 Calculation of scaled range and overpressure for fireworks
Sample name
Heat of reaction , Ec, ( J g-1)
TNTEquivalence,
W, (g)
Distance,(m)
Scaledrange, Z,
(m)
Overpressure,P, (bar)
Atom bomb
cracker 504.2 0.01
3 13.67 0.18
5 22.77 0.11
10 45.55 0.05
15 68.32 0.03
20 91.09 0.02
Chinesecracker
443.67 0.009
3 14.26 0.17
5 23.76 0.10
10 47.53 0.05
15 71.30 0.03
20 95.06 0.02
Palm leaf cracker
294.99 0.006
3 16.34 0.13
5 27.23 0.08
10 54.46 0.04
15 81.69 0.02
20 108.92 0.02
Flowerpot tip
972.23 0.02
3 10.98 0.28
5 18.30 0.17
10 36.59 0.08
15 54.89 0.05
20 73.19 0.04
Groundspinner
tip961.46 0.02
3 11.02 0.28
5 18.36 0.16
10 36.73 0.08
15 55.09 0.05
20 73.46 0.04
127
5.3.2.1 Scaled range vs. Distance for firework mixtures
From the Figures 5.9 and 5.10, it can be observed that for crackers
and tip mixture the scaled range increases as the distance increases.
Figure 5.9 Scaled range vs. Distance for crackers
(Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))
Figure 5.10 Scaled distance vs. Distance for tip mixtures
(Flowerpot tip ( ), Ground spinner tip ( ))
0
20
40
60
80
100
120
0 5 10 15 20 25
Distance, (m)
0
20
40
60
80
0 5 10 15 20 25
Distance, (m)
128
This is because the weight of the sample is kept constant and thus
the TNT equivalence remains the same. Hence, the scaled range increases as
it holds a direct relation with distance.
5.3.2.2 Overpressure vs. Distance for firework mixtures
From the Figures 5.11 and 5.12, it can be observed that the
overpressure decreases as the distance increases for cracker samples and tip
compositions. This is because of the inverse relation between the distance and
the overpressure. Thus the overpressure value decreases for an increase in the
value of distance.
Figure 5.11 Overpressure vs. Distance for crackers
(Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))
0
0.05
0.1
0.15
0.2
0 5 10 15 20 25
Distance, (m)
129
Figure 5.12 Overpressure vs. Distance for tip mixtures
(Flowerpot tip ( ), Ground spinner tip ( ))
5.3.3 TNO Multi Energy Model
The results have been analyzed for this model using various
firework mixtures. The distance from the centre of the explosion to the point
where the explosion takes place is kept as 5-25 m (5, 10, 15, 20, 25 m
respectively). The ambient pressure is 1.0132 bar.
0
0.05
0.1
0.15
0.2
0.25
0.3
0 5 10 15 20 25
Distance, (m)
130
Table 5.3 Calculation of impulse for fireworks
Samplename
Heat of reaction
EC
( J g-1)
Positive scaled over
pressure Ps, (bar)
Scaled positiveduration
time Ts, (s)
Positive Over
pressure P, (bar)
Scaled distance
Positive durationTime, T
(s)
Impulse I,
(bar.s)
Atom bomb
cracker504.2 25.953 306.499 26.30
0.65
424.6 5583.5
1.30
1.95
2.60
3.25
Chinese cracker
443.67 16.732 163.197 16.95
0.68
216.65 1836.11
1.35
2.03
2.71
3.39
Palm leaf
cracker294.99 14.422 412.37 14.61
0.78
477.81 3490.40
1.55
2.33
3.10
3.88
Flower pot tip
972.23 30.156 967.6 30.56
0.52
1668.47 25954.2
1.04
1.57
2.09
2.61
Ground spinner
tip 961.46 2.354 1108.48 2.38
0.53
1904.31 2261.12
1.05
1.58
2.10
2.63
131
5.3.3.1 Scaled distance vs. Distance for fireworks
From the Figures 5.13 and 5.14, it can be observed that the scaled distance increases as the distance increases for cracker samples and tip
compositions.
Figure 5.13 Scaled distance vs. Distance for crackers (Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))
Figure 5.14 Scaled distance vs. Distance for tip mixtures (Flowerpot tip ( ), Ground spinner tip ( ))
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 5 10 15 20 25 30
Distance, (m)
0
0.5
1
1.5
2
2.5
3
0 5 10 15 20 25 30
Distance, (m)
132
This is because of the direct relation between the distance and the
scaled distance. It can also be inferred from this model that the value of
impulse largely depends on the positive overpressure and the positive duration
time. Larger the value of these parameters, higher is the impulse which is
nothing but the maximum peak overpressure. The value of impulse also varies
for different firework mixtures.
5.3.4 BS/BST Multi Energy Model
The results of this model have been analysed for various firework
mixtures. Three cracker samples and two tip samples have been used. The
ambient pressure is 1.0132 bar. The velocity of sound is 343.2 m s-1.
Table 5.4 Calculation of flame velocity
Sample name Peak overpressure,
Pmax ,(bar)
Machnumber, Mf
Flame velocity, (m s-1)
Atom bomb cracker 25.95 11.02 3783.57
Chinese cracker 16.74 07.34 2520.42Palm leaf cracker 14.43 6.37 2189.03Flower pot tip 30.15 12.91 4431.43Ground spinner tip 2.35 1.06 366.40
The Mach number ranges within 1.06 – 12.91. If the value falls
within this range, Scaled impulse can be deduced directly from the
characteristic curves depending upon the range of Mach number.
The distance from the centre of the explosion to the point where the
explosion takes place is taken as 5-25 m. The impulse and the positive
pressure values are obtained from Table 4.4. Volume of the obstructed area =
1 X 10-5m3.
133
Table 5.5 Calculation of positive scaled impulse for firework mixtures
Sample name
Heat of reaction
EC,( J g-1)
Volume of the
obstructed area V,
(m3)
Combustion energy E, (J g-1 m3)
Distance, (m)
Scaleddistance
, (m)
Positive scaled
impulse, I , (bar.s)
Atom bomb
cracker 504.2
1 × 10
0.010
5 23.24
8.810 46.4915 69.7320 92.9825 116.22
Chinesecracker
443.67 0.008
5 24.25
3.0210 48.5115 72.7720 97.0225 121.28
Palmleaf
cracker 294.99 0.005
5 27.79
6.5710 55.5815 83.3720 111.1725 138.96
Flowerpot tip
972.23 0.019
5 18.67
31.5710 37.3515 56.0220 74.7025 93.37
Groundspinner
tip961.46 0.019
5 18.74
2.8710 37.4915 56.2320 74.9825 93.72
134
From the Figures 5.15 and 5.16, it can be observed that the scaled
distance increases as the distance increases. This effect of tip mixture samples
is similar to that of the cracker samples. However, the curves of the two tip
samples are quite close. Since scaled impulse depends on the impulse,
indirectly the positive overpressure and the positive duration time has an
effect over the scaled impulse.
Figure 5.15 Scaled distance vs. Distance for cracker samples (Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))
Figure 5.16 Scaled distance vs. Distance for tip samples (Flowerpot tip ( ), Ground spinner tip ( ))
020406080
100120140160
0 5 10 15 20 25 30
Distance, (m)
0
20
40
60
80
100
120
140
160
0 5 10 15 20 25 30Distance, (m)
135
5.4 SUMMARY
The TNT equivalence technique is used as a standard tool to
evaluate thermal explosion parameters. The Multi Energy Models are
alternative methods to TNT equivalence and a study of these models has been
conducted using the Thermal explosion data obtained from the Accelerating
Rate Calorimeter. TNT equivalence model compares the output of a given
explosive to that of TNT explosive. The TNO Multi energy model and
BS/BST model consider the obstacles or obstructions present within the
explosion region and have been applied as dust explosion models with the
available data. However, it is difficult to compare all the three models
directly, as they are based on different assumptions and the parameters vary
respectively. The overpressure and scaled distance are important parameters
in estimating the explosive potential of various firework mixtures. From this
study it has been observed that the firework mixtures, under certain conditions
can be equivalent to an explosive and hence have to be handled carefully. It
has also been observed that TNT equivalence model and TNO Multi energy
model do not consider the sound velocity, whereas the BS/BST model
depends on the sound velocity. All the three models can be applied to
determine the explosion limits. In summary,
Pressure rises due to thermal decomposition of fireworks.
Overpressure decreases with increase in distance.
TNT equivalence of fireworks mixture varies with different
weights.
The damage causing ability of the fireworks depends on the
initial mass and it decreases with distances.
The studies confirm that the damage causing ability of the blast
on structures due to explosive decomposition of fireworks
increases with increase in over pressure.