Energy explosions

The heat of explosion is equal to the difference of the internal energies before and after the explosion, AU. The heat of combustion is the difference of the internal energies in case of stoichiometric combustion. The explosion energy equals the work done by the expansion of the gases, i.e. 

41) 1 denotes the state before the explosion and 2 that afterwards. The sign is negative, if work is transferred out of the system boundaries and positive if it is introduced into the system p is the pressure and V the volume. 

The evaluation of the integral requires one to know the changes of pressure and volume during the explosion. Therefore it is difficult to be evaluated. It is easier to relate the thermodynamic states before and after the reaction with each other. This is achieved with the help of Helmholtz s free energy f. We have (cf. [5]) 

In an isothermal process (dT = 0) the entire energy change is transformed into work. This gives 

Helmholtz s energy represents the maximum amount of work which a system can exert on its surroundings. Hence, it constitutes an upper bound for the work done by the explosion. Helmholtz s free energy is not normally found in tables. Therefore calculations based on Eq. (2.46) make use of the internal energy and entropy differences. We then have 

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E Explosion energy available to generate blast and fragment kinetic... 

A common cause of a BLE T] in plants of the hydrocarbon-chemical industry is exposure to fire. With an external fire below the liquid level in a vessel, the heat of vaporization provides a heat sink, as with a teakettle evolved vapors exit tnrough the relief valve. But if the flame impinges on the vessel above the liquid level, the metal will weaken and may cause the vessel to rupture suddenly, even with the relief valve open. The explosive energy for a BLE T] comes from superheat. This energy is at a maximum at the superheat hmit temperature. (SLT is the maximum temperature to which a hquid can be heated before homogeneous nucleation occurs with explosive vaporization of the hquid and accompanying overpressure.) The SLT... 

The shock pressures attainable with direct explosive contact depend on the shock impedance (shock velocity times material density) of the specimen material, and on the explosive energy of the contacting explosive. High-energy explosives placed directly on high-shock impedance materials can produce shock pressures of several tens of GPa. 

The energy term E must be defined to calculate energy-scaled standoff R. The energy term represents the sensible heat that is released by that portion of the cloud contributing to the blast wave. Any of the accepted methods of calculating vapor cloud explosive energy are applicable to the Baker-Strehlow method. These methods include ... 

The thermodynamic method has limitations. Since the method ignores the intermediate stages, it cannot be used to determine shock-wave parameters. Furthermore, a shock wave is an irreversible thermodynamic process this fact complicates matters if these energy losses are to be fully included in the analysis. Nevertheless, the thermodynamic approach is a very attractive way to obtain an estimate of explosion energy because it is very easy and can be applied to a wide range of explosions. Therefore, this method has been applied by practically every worker in the field. 

Unfortunately, there is no consensus on the measure for defining the energy of an explosion of a pressure vessel. Erode (1959) proposed to define the explosion energy simply as the energy, ex,Br> must be employed to pressurize the initial volume from ambient pressure to the initial pressure, that is, the increase in internal energy between the two states. The internal energy 1/ of a system is the sum of the kinetic, potential, and intramolecular energies of all the molecules in the system. For an ideal gas it is... 

Vessel Rupture. The energy needed to rupture a vessel is very low, and can be neglected in calculation of explosion energy. For a typical steel vessel, rupture energy is on the order of 1 to 10 kJ, that is, less than 1% of the energy of a small explosion. 

Fragments. As will be explained in Section 6.4, between 20% and 50% of available explosion energy may be transformed into kinetic energy of fragments and liquid or solid contents. 

This energy measure is equal to Brode s definition of the energy, multiplied by a factor 2. The reason for the multiplication is that the Brode definition applies to free-air burst, while Eq. (6.3.15) is for a surface burst. In a fiee-air burst, explosion energy is spread over twice the volume of air. 

Equation (6.3.15) is not accurate for the calculation of explosion energy of vessels filled with real gases or superheated liquids. A better measure in these cases is the work that can be performed on surrounding air by the expanding fluid, as calculated from thermodynamic data for the fluid. In this section, a method will be described for calculating this energy, which can then be applied to the basic method in order to determine the blast parameters. 

The main sources of deviation lie in estimates of energy and in release-process details. It is unclear whether the energy equations given in preceding sections are good estimates of explosion energy. In addition, energy translated into kinetic... 

It is not clear which measure of explosion energy is most suitable. Note that, in the method presented in Section 6.3, the energy of gas-filled pressure vessel bursts is calculated by use of Brode s formula, and for vessels filled with vapor, by use of the formula for work done in expansion. 

The fraction of explosion energy which contributes to fragment generation is unclear. Its effect on initial fragment velocity deserves more attention in relation... 

This gives, for explosion energy of the saturated liquid,... 

Step 6 Calculate the explosion energy. Explosion energy is calculated with Eq. (6.3.26) ... 

The volume of the vapor is 0.10 x 22.7 = 2.27 m. The explosion energy of the vapor can be calculated by multiplying the expansion work per unit volume by the vapor volume ... 

Explosion energy can be calculated by employing a slight variation on Eq. (6.3.26), by multiplying expansion work per unit volume by fluid volume, instead of multiplying expansion work per unit mass by fluid mass. Both propane and butane must be considered. This gives, for example, for vapor energy for the 50% fill-ratio case ... 

Process plants are categorized into different hazard classifications, according to the potential explosion energy available from vessel rupture, condensed-phase explosion, confined vapor (building) explosion, or VCE. 

Nevertheless, as has been emphasized by Ramaty et al. (2000), the kind of boost to the cosmic-ray flux per supernova implied by Eq. (9.57) is untenable on energetic grounds. From present-day abundances, one can estimate the quantity Q/W, the number of Be atoms per erg of cosmic-ray energy. Given an iron yield of 0.2 M per average supernova (of both types) today, and a Be/Fe ratio of 10-6, one finds a yield of 4 x 1048 Be atoms per supernova. If the typical supernova explosion energy is 1051 erg and the cosmic-ray acceleration efficiency is 10 per cent, this... 

E is the energy of explosion (energy), P] is the ambient pressure (force/area),... 

An analysis by Crowl22 using batch thermodynamic availability resulted in the following expression to predict the maximum explosion energy of a gas contained within a vessel ... 

Table 2-4 converts the probit to percentages. The result shows that there are no deaths and that less than 10% of the exposed people suffer eardrum ruptures. This assumes complete conversion of explosion energy. 

Based on the accident investigation, the explosive energy was equivalent to 0.3 ton TNT. Therefore the fraction of energy manifested in the explosion is 0.3/2.69 = 11.2%. This 11.2% is considerably higher than the 2% normally observed (see section 6-13) for unconfined vapor cloud explosions. The higher energy conversion is a result of the explosion occurring in a partially confined area. 

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