Blast wave

Deflagrations and detonations are of importance in any study of the hazards associated with flammable materials as they produce high-temperature gases. These gases and the pressures they produce may be harmful to humans and surrounding structures. Their behavior is considered in this and the following sections. 

As we are primarily interested in blast effects in air, the properties of air that affect the blast wave are also considered in this section. For our purposes, air can be treated as an ideal gas. The speed of sound in an ideal gas is 

The Mach number of a shock wave traveling through air is given by the same expression. The pressure drop (side-on overpressure) across the shock front 

After passage of a shock front, the atmosphere (air) is accelerated to a speed Up in the direction in which the shock moved Up is the particle or wind speed, and may be obtained from either the overpressure or the Mach number. In air. 

When a shock is reflected from an inelastic surface after normal (head-on) incidence, the pressure rise (reflected overpressure) and the 

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The problem of explosion of a vapor cloud is not only that it is potentially very destructive but also that it may occur some distance from the point of vapor release and may thus threaten a considerable area. If the explosion occurs in an unconfined vapor cloud, the energy in the blast wave is generally only a small fraction of the energy theoretically available from the combustion of all the material that constitutes the cloud. The ratio of the actual energy released to that theoretically available from the heat of combustion is referred to as the explosion efficiency. Explosion efficiencies are typically in the range of 1 to 10 percent. A value of 3 percent is often assumed. 

Blast Characteristics Accurate calculation of the magnitude of the blast wave from an exploding pressure vessel is not possible, but it may be estimated from several approximate methods that are available. 

The energy partition between blast wave energy and fragment kinetic energy is as described in paragraph I. 

Response to Blast Waves The effect of blast waves upon eqmp-ment and people is difficult to assess because there is no single blast wave parameter which can fully describe the damage potenti of the... 

The response of a target is a function of the ratio of the blast wave duration and the natural period of vibration of the target (T/T ). Neither of these parameters can be closely defined. 

Deflagration A propagating chemical reaction of a substance in which the reaction front advances into the unreacted substance at less than the sonic velocity in the unreacted material. Where a blast wave is produced that has the potential to cause damage, the term explosive deflagration may be used. 

Explosion A rapid or sudden release of energy that causes a pressure discontinuity or blast wave. 

Most people will tolerate greater risk from activities when the threat to life is offset in time from when the risk (and the benefit) is originally accepted. For example, people may feel worse (and usually accept less risk) about a threat of immediate harm (e.g., the blast wave from an explosion) than a threat of latent harm (e.g., an increase in the chance of getting a fatal disease following a 20-year exposure to a hazardous material, like asbestos), even though the risks may be equivalent. 

P.A. Hookham, D. Hatfield, and M. Rosenblatt, Calculation of the Interaction of Three Spherical Blast Waves Over a Planar Surface with an Adaptive-Grid TVD Code, California Research and Technology Report, Chatsworth, CA, 1991. 

Deflagration The ehemieal reaetion of a substanee in whieh the reaetion front advanees into the unreaeted substanee at less than sonie veloeity. Where a blast wave is produeed that has the potential to eause damage, the term explosive deflagration is used. 

If the explosion occurs in an unconfined vapor cloud, the energy in the blast wave is only a small fraction of the energy calculated as the product of the cloud mass and the heat of combustion of the cloud material. On this basis, explosion efficiencies are typically in the range of 1-10%. 

In the surrounding atmosphere, a blast wave is experienced as a transient change in gas-dynamic-state parameters pressure, density, and particle velocity. Generally, these parameters increase rapidly, then decrease less rapidly to sub-ambient values (i.e., develop a negative phase). Subsequently, parameters slowly return to atmospheric values (Figure 3.7). The shape of a blast wave is highly dependent on the nature of the explosion process. 

If the combustion process within a gas explosion is relatively slow, then expansion is slow, and the blast consists of a low-amplitude pressure wave that is characterized by a gradual increase in gas-dynamic-state variables (Figure 3.7a). If, on the other hand, combustion is rapid, the blast is characterized by a sudden increase in the gas-dynamic-state variables a shock (Figure 3.7b). The shape of a blast wave changes during propagation because the propagation mechanism is nonlinear. Initial pressure waves tend to steepen to shock waves in the far field, and wave durations tend to increase. 

An object struck by a blast wave experiences a loading. This loading has two aspects. First, the incident wave induces a transient pressure distribution over the... 

Figure 3.8. Interaction of a blast wave with a rigid structure (Baker 1973).

In summary, an object s blast loading has two components. The first is a transient pressure distribution induced by the overpressure of the blast wave. This component of blast loading is determined primarily by reflection and lateral rarefaction of the reflected overpressure. The height and duration of reflected overpressure are determined by the peak side-on overpressure of the blast wave and the lateral dimensions of the object, respectively. The Blast loading of objects with substantial... 

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,... 

In the earliest applications of numerical methods for the computation of blast waves, the burst of a pressurized sphere was computed. As the sphere s diameter is reduced and its initial pressure increased, the problem more closely approaches a point-source explosion problem. Brode (1955,1959) used the Lagrangean artificial-viscosity approach, which was the state of the art of that time. He analyzed blasts produced by both aforementioned sources. The decaying blast wave was simulated, and blast wave properties were registered as a function of distance. The code reproduced experimentally observed phenomena, such as overexpansion, subsequent recompression, and the formation of a secondary wave. It was found that the shape of the blast wave at some distance was independent of source properties. 

A similar technique was used by Oppenheim et al. (1977) to analyze the blast waves produced by some gas explosions of a different nature ... 

Flow fields resulting from these combustion modes were computed by means of similarity methods (Section 4.2.1) and used to provide initial conditions for numerical computations. The main conclusion was that blast waves at some distance from the charge were very similar, regardless of whether the combustion mode was detonation or strong deflagration. 

Deflagrative combustion of an extended, flat vapor cloud is very ineffective in producing damaging blast waves because combustion products have a high rate of side relief accompanied by vortex formation. 

For these and other purposes, blast-modeling methods are needed in order to quantify the potential explosive power of the fuel present in a particular setting. The potential explosive power of a vapor cloud can be expressed as an equivalent explosive charge whose blast characteristics, that is, the distribution of the blast-wave properties in the environment of the charge, are known. 

The positive-phase duration of the blast wave from a vapor cloud explosion is in the range of 100 and 300 ms. 

An extensive numerical study was performed by Strehlow et al. (1979) to analyze the structure of blast waves generated by constant velocity and accelerating flames propagating in a spherical geometry. This study resulted in the generation of plots... 

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 ... 

TNT blast is, however, a poor model for a gas explosion blast. In particular, the shape and positive-phase duration of blast waves induced by gas explosions are poorly represented by TNT blast. Nevertheless, TNT-equivalency methods are satisfactory, so long as far-field damage potential is the major concern. 

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