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
110 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) High frequency electromagnetic energy Total energy generated by explosive reaction Electromagnet ic energy Mechanical energy Visible light electromagnetic energy Infrared energy Low frequency electromagnetic energy Overpressure of shock wave Earthquake wave and crater formation Shattering of cartridge and fling of its fragments 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
111 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, P so, and duration,
112 characterized by the Figure 5.3 (Ngo et al 2007). The area under the pressuretime curve is the impulse of the blast wave. Pso Ambient P - Pso Positive Negative Phase Phase Duration Duration Time, (min) Figure 5.2 Pressure distributions in a medium during passage of a blast wave P so Impulse Duration t 0 Time, (min) Figure 5.3 Typical design of blast load plot
113 Explosion s origin Highest isobars P P P P Distance I I I I Z Z Z Z Characteristic curve Z 1 Z 2 Distance Over pressure 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 overpressure impulse distance relationship, called here the characteristic curve.
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 (Z 1, Z 2..., Z n ) 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.
115 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; Mass of TNT, (g) TNT Equivalence = 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), E C is the heat of combustion of explosion material (J g -1 ), E TNT 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)
117 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 ( P E ) (5.5) where, r is the distance from the charge (m), P a 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), P s is the positive scaled overpressure (bar), P a is the atmospheric pressure (bar). 5.2.8 Positive Duration Time The scaled duration time is given by, T = T E P / 1 a (5.7) where, T is the positive duration time (sec), T s is the scaled positive duration time, a 0 is the sound velocity (343.2 m s -1 ).
119 5.2.9 Impulse The impulse is given by, I = 1 2 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 P P = 2.4 M 1 + M (5.9) where, P max is the maximum overpressure (bar), P 0 is the ambient overpressure (bar), M f is the Mach number. Flame velocity Mach number = Sound 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), P a 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), P s overpressure (bar), P a is the atmospheric pressure (bar). is the positive scaled 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 (m 3 ). 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 Atom bomb cracker Chinese cracker Palm leaf cracker Flower pot tip Ground spinner tip Heat of reaction, E c, ( J g -1 ) 504.2 443.67 294.99 972.23 961.46 Sample weight, (g) TNT Equivalence, W (g) Scaled range,z, (m) Overpressure, P (bar) 5 0.06 7.99 0.54 10 0.11 6.34 0.90 15 0.16 5.52 1.24 20 0.21 5.03 1.56 25 0.26 4.67 1.87 5 0.04 8.34 0.49 10 0.09 6.62 0.82 15 0.14 5.80 1.12 20 0.18 5.25 1.40 25 0.23 4.88 1.69 5 0.03 9.55 0.37 10 0.06 7.58 0.60 15 0.09 6.62 0.82 20 0.12 6.01 1.02 25 0.15 5.58 1.21 5 0.10 6.42 0.88 10 0.20 5.10 1.52 15 0.30 4.45 2.12 20 0.40 4.04 2.70 25 0.50 3.75 3.26 5 0.10 6.44 0.87 10 0.20 5.11 1.50 15 0.30 4.47 2.09 20 0.40 4.06 2.68 25 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. 12 10 8 6 4 2 0 0 0.05 0.1 0.15 0.2 0.25 0.3 TNT Equivalence, (g) Figure 5.5 Scaled range vs. TNT equivalence for crackers (Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( )) 7 6.5 6 5.5 5 4.5 4 3.5 0 0.1 0.2 0.3 0.4 0.5 TNT Equivalence, (g) Figure 5.6 Scaled range vs. TNT equivalence for tip mixtures (Flowerpot tip ( ), Ground spinner tip ( ))
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. 2.1 1.8 1.5 1.2 0.9 0.6 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 TNT Equivalence, (g) Figure 5.7 Overpressure vs. TNT equivalence for crackers (Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))
125 3.5 3 2.5 2 1.5 1 0.5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 TNT Equivalent, (g) 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.
126 Table 5.2 Calculation of scaled range and overpressure for fireworks Sample name Atom bomb cracker Chinese cracker Palm leaf cracker Flower pot tip Ground spinner tip Heat of reaction, E c, ( J g -1 ) TNT Equivalence, W, (g) 504.2 0.01 443.67 0.009 294.99 0.006 972.23 0.02 961.46 0.02 Distance, (m) Scaled range, Z, (m) Overpressure, P, (bar) 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 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 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 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 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. 120 100 80 60 40 20 0 0 5 10 15 20 25 Distance, (m) Figure 5.9 Scaled range vs. Distance for crackers (Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( )) 80 60 40 20 0 0 5 10 15 20 25 Distance, (m) Figure 5.10 Scaled distance vs. Distance for tip mixtures (Flowerpot tip ( ), Ground spinner tip ( ))
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. 0.2 0.15 0.1 0.05 0 0 5 10 15 20 25 Distance, (m) Figure 5.11 Overpressure vs. Distance for crackers (Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))
129 0.3 0.25 0.2 0.15 0.1 0.05 0 0 5 10 15 20 25 Distance, (m) 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.
130 Table 5.3 Calculation of impulse for fireworks Sample name Atom bomb cracker Chinese cracker Palm leaf cracker Flower pot tip Ground spinner tip Heat of reaction E C ( J g -1 ) Positive scaled over pressure P s, (bar) Scaled positive duration time T s, (s) Positive Over pressure P, (bar) 504.2 25.953 306.499 26.30 443.67 16.732 163.197 16.95 294.99 14.422 412.37 14.61 972.23 30.156 967.6 30.56 961.46 2.354 1108.48 2.38 Scaled distance 0.65 1.30 1.95 2.60 3.25 0.68 1.35 2.03 2.71 3.39 0.78 1.55 2.33 3.10 3.88 0.52 1.04 1.57 2.09 2.61 0.53 1.05 1.58 2.10 2.63 Positive duration Time, T (s) Impulse I, (bar.s) 424.6 5583.5 216.65 1836.11 477.81 3490.40 1668.47 25954.2 1904.31 2261.12
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. 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0 5 10 15 20 25 30 Distance, (m) Figure 5.13 Scaled distance vs. Distance for crackers (Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( )) 3 2.5 2 1.5 1 0.5 0 0 5 10 15 20 25 30 Distance, (m) Figure 5.14 Scaled distance vs. Distance for tip mixtures (Flowerpot tip ( ), Ground spinner tip ( ))
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 Atom bomb cracker Peak overpressure, P max, (bar) Mach number, M f Flame velocity, (m s -1 ) 25.95 11.02 3783.57 Chinese cracker 16.74 07.34 2520.42 Palm leaf cracker 14.43 6.37 2189.03 Flower pot tip 30.15 12.91 4431.43 Ground 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 10-5 m 3.
133 Table 5.5 Calculation of positive scaled impulse for firework mixtures Sample name Atom bomb cracker Chinese cracker Palm leaf cracker Flower pot tip Ground spinner tip Heat of reaction E C, ( J g -1 ) 504.2 Volume of the obstructed area V, (m 3 ) 1 10 Combustion energy E, (J g -1 m 3 ) 0.010 443.67 0.008 294.99 0.005 972.23 0.019 961.46 0.019 Distance, (m) Scaled distance, (m) 5 23.24 10 46.49 15 69.73 20 92.98 25 116.22 5 24.25 10 48.51 15 72.77 20 97.02 25 121.28 5 27.79 10 55.58 15 83.37 20 111.17 25 138.96 5 18.67 10 37.35 15 56.02 20 74.70 25 93.37 5 18.74 10 37.49 15 56.23 20 74.98 25 93.72 Positive scaled impulse, I, (bar.s) 8.8 3.02 6.57 31.57 2.87
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. 160 140 120 100 80 60 40 20 0 0 5 10 15 20 25 30 Distance, (m) Figure 5.15 Scaled distance vs. Distance for cracker samples (Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( )) 160 140 120 100 80 60 40 20 0 0 5 10 15 20 25 30 Distance, (m) Figure 5.16 Scaled distance vs. Distance for tip samples (Flowerpot tip ( ), Ground spinner tip ( ))
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.