Peak overpressure

Making a detailed estimate of the full loading of an object by a blast wave is only possible by use of multidimensional gas-dynamic codes such as BLAST (Van den Berg 1990). However, if the problem is sufficiently simplified, analytic methods may do as well. For such methods, it is sufficient to describe the blast wave somewhere in the field in terms of the side-on peak overpressure and the positive-phase duration. Blast models used for vapor cloud explosion blast modeling (Section 4.3) give the distribution of these blast parameters in the explosion s vicinity. 

The upper half of Figure 3.9 represents how a spherical explosive charge of diameter d produces a blast wave of side-on peak overpressure P and positive-phase duration r" " at a distance R from the charge center. Experimental observations show that an explosive charge of diameter Kd produces a blast wave of identical side-on peak overpressure p and positive-phase duration Kt at a distance KR from the charge center. (This situation is represented in the lower half of Figure 3.9.) Consequently,... 

Figure 4.5. Flame velocity, peak overpressure, and overpressure duration in gas cloud explosions following vessels bursts (Giesbrecht et al. 1981).

Figure 4.6. Decay of peak overpressure with distance for ignited subcritical 10-mm diameter hydrogen gas jets at various velocities, Uq. A = mean value.

The very first stage of flame propagation upon ignition, during which the flame has a spherical shape, mainly determines the blast peak overpressure produced by the entire vapor cloud explosion. 

With respect to blast effects, Rosenblatt and Hassig s (1986) conclusions are fully in line with those of Raju and Strehlow (1984). Except in a limited area at the cloud s edge, the blast peak overpressures are produced by the very first stage of flame propagation, during which the flame is spherical. 

Figure 4.17. Side-on blast peak overpressure due to (a) a TNT surface burst. (Kingery and Panill 1964) and (b) a free-air burst of TNT (Glasstone and Dolan 1977).

Once the equivalent charge weight of TNT is estimated, the blast peak overpressures in the field can be found by applying this charge weight to the scaled distance in the blast chart (Figure 4.18). 

The most important blast-wave parameters are peak overpressure and positive impulse i, as shown in Figure 6.11. The deep negative phase and second shock are clearly visible in this figure. 

The peak overpressure developed immediately after a burst is an important parameter for evaluating pressure vessel explosions. At that instant, waves are generated at the edge of the sphere. The wave system consists of a shock, a contact surface, and rarefaction waves. As this wave system is established, pressure at the contact surface drops from the pressure within the sphere to a pressure within the shock wave. 

Scaled peak overpressure and positive impulse as a function of scaled distance are given in Figures 6.17 and 6.18. The scaling method is explained in Section 3.4. Figures 6.17 and 6.18 show that the shock wave along the axis of the vessel is initially approximately 30% weaker than the wave normal to its axis. Since strong shock waves travel faster than weak ones, it is logical that the shape of the shock wave approaches spherical in the far field. Shurshalov (Chushkin and Shurshalov... 

Table 6.10 presents some damage effects. It may give the impression that damage is related only to a blast wave s peak overpressure, but this is not the case. For certain types of structures, impulse and dynamic pressure (wind force), rather than overpressure, determine the extent of damage. Table 6.10 was prepared for blast waves of nuclear explosions, and generally provides conservative predictions for other types of explosions. More information on the damage caused by blast waves can be found in Appendix B. 

Use the following equation to calculate side-on peak overpressure - po and side-on impulse from nondimensional side-on peak overpressure and nondimensional side-on impulse 7 ... 

The method presented above is based on the similarity of the blast waves of pressure vessel bursts and high explosives. This similarity holds only at some distance from the explosion. In the near field, the peak overpressure and impulse from a pressure... 

TNT-equi valency methods express explosive potential of a vapor cloud in terms of a charge of TNT. TNT-blast characteristics are well known fiom empirical data both in the form of blast parameters (side-on peak overpressure and positive-phase duration) and of corresponding damage potential. Because the value of TNT-equiva-lency used for blast modeling is directly related to damage patterns observed in major vapor cloud explosion incidents, the TNT-blast model is attractive if overall damage potential of a vapor cloud is the only concern. 

If the scaled distance R is known, the corresponding side-on blast peak overpressure can be read from the chart in Figure 7.1. 

Figure 7.2a. Sachs-scaled side-on peak overpressure of blast from a hemispherical fuel-air charge.

Blast effects. Once the equivalent charge weight of TNT in kilograms has been determined, the side-on peak overpressure of the blast wave at some distance R from the charge can be found with Eq. (7.3) ... 

TABLE 7.2. Side-On Peak Overpressure for Several Distances from Charge Expressing Explosive Potential of a Vapor Cloud at a Storage Site for Liquefied Hydrocarbons... 

Distance from Charge (m) Scaled Distance from Charge (mfkg ) Side-on Peak Overpressure (bar)... 

The nondimensionalized side-on peak overpressures and their respective positive-phase durations can be transformed into real values for side-on peak overpressures and positive-phase durations by calculating ... 

TABLE 7.5a. Side-On Peak Overpressure and Positive-Phase Duration of Blast Produced by Charge I (E = 6870 MJ, Strength Number 7)... 

TABLE 7.5b. Side-On Peak Overpressure and Positive-Phase Duration ... 

Blast effects. The side-on peak overpressures and positive-phase durations of blast waves produced by the respective charges for any selected distance, R, can be found by calculating separately for each charge... 

In each case, two different methods were used in arriving at estimates the HSE TNT-equivalency method and the multienergy method. The results, in the form of side-on blast peak overpressures for various distances from blast centers, are listed in Table 7.10. In addition, some peak overpressures estimated by Sadee et al. (1976/ 1977) from Flixborough-incident damage patterns are included. The photographs in Figures 7.6a and 7.6b illustrate the practical effects of such overpressures. 

Figure 7.6. (a) Damage to canteen building 130 m from explosion center. Estimated peak overpressure level 0.45-0.55 bar (Sadee et al. 1976/1977). (b) Damage to row of houses 535 m from explosion center. Estimated peak overpressure level 0.10-0.12 bar (Sadee et al. 1976/1977). 

The nondimensional side-on peak overpressure at the control building is read from Figure 6.22. For R = 6.9, = 0.030. 

Thus, the calculated blast parameters at the control budding are a side-on peak overpressure of 4.2 kPa and a side-on impulse of 31 Pa.s. Note that this pressure... 

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