Normal reflection, blast waves

In preparing this figure, the authors of Ref. 28 assumed no wave attenuation through the wall thickness H, so Pr and ir are the normally reflected blast loading parameters on the loaded side of the wall or slab. 

Figure 7-44 shows the sequence of events involved in diffraction of a blast wave about a circular cylinder (Bishop and Rowe 1967). In these figures the shock fronts are shown as thick lines and their direction of movement by arrows normal to the shock front. In Figure 1.13a, the incident shock / and reflected shock Rare joined to the cylinder surface by a Mach stem M. R is now much weaker and is omitted in succeeding figures. 

However, it is normal practice in blast-resistant design to assume conservatively that the VCE blast wave is fully reflected from the front wall as an ideal shock. 

This keynote paper gives a general discussion of blast waves developed by high explosive detonations, their effects on structures and people, and risk assessment methods. The properties of free-field waves and normally and obliquely reflected waves are reviewed. Diffraction around block shapes and slender obstacles is covered next. Blast and gas pressures from explosions within vented structures are sumnarized. 

Normal Reflection. An upper limit to blast loads is obtained if one interposes an infinite, rigid wall in front of the wave, and reflects the wave normally. 

All flow behind the wave is stopped, and pressures are considerably greater than side-on. The pressure in normally reflected waves is usually designated pr(t), and the peak reflected overpressure, Pr. The integral of overpressure over the positive phase, defined in Equation (13), is the reflected specific impulse ir. Durations of the positive phase of normally reflected waves are almost the same as for side-on waves, thigh explosive blast sources than have most blast parameters. 

For a building with a flat roof (pitch less than 10°) it is normally assumed that reflection does not occur when the blast wave travels horizontally. Consequently, the roof will experience the side-on overpressure combined with the dynamic wind pressure, the same as the side walls. The dynamic wind force on the roof acts in the opposite direction to the overpressure (upward). Also, consideration should be given to variation of the blast wave with distance and time as it travels across a roof element. The resulting roof loading, as shown in Figure 3.8, depends on the ratio of blast wave length to the span of the roof element and on its orientation relative to the direction of the blast wave. The effective peak overpressure for the roof elements are calculated using Equation 3.11 similar to the side wall. 

The shape of (he rear wall loading is similar to that for side and roof loads, however the rise time ami duration arc influenced by a not well understood pattern of spillover from the roof and side walls and from ground reflection effects. The rear wall blast load lags that for the front wall by L/U, the lime for the blast wave to travel the length, L, of the building. The effective peak overpressure is similar to that for side walls and is calculated using Equation 3.11 (Ph is normally used to designate the rear wall peak overpressure instead of P,). Available references indicate two distinct values for the rise lime and positive phase duration. 

For peak overpressures up to 20 psi (138 kPa), the expected range for most accidental vapor cloud explosions, Newmark 1956 provides a simple formula for the blast wave reflection coefficient at normal, 0°, incidence as follows ... 

Figure 28.11. Fatality curves predicted for 70-kg man applicable to blast situations where the thorax is near a surface against which a shocked blast wave reflects at normal incidence.

Fig. 38. Peak reflected overpressure (Ap ) following normal reflection of a blast wave from a flat surface dynamic pressure q).

The reflection coefficient R=Piaax/P20 s M, the Mach number of a blast wave, which is just in front of the surface of the PUR foam (P20 denotes here the normal reflection pressure of air shock with Mg=Mi), is presented on Fig. 6 by a solid line. The dotted line represents computed pressure values. One can mention that on this curve there is no amplification effect (R<1) up to Mi l.2. The least effect is caused by two forces first, the reflection of the rarefaction wave from a boundary of the foam and second, inertia losses due to filtration effects. Even in the case of a blast wave the second force seems to be negligible with Mi>1.3. 

Chapter II, Blast Wave Reflections and Interactions, presents a number of articles on the interaction of blast waves with real surfaces. For example, Rayevsky et al. have studied the normal reflection of a blast wave from a rigid wall coated with polyurethane foam. They found that, contrary to intuition, the foam layer significantly increased the peak reflected pressure on the wall. Lyakhov and coworkers report on shock reflections from a body with a hot or cold gas layer. Kuhl et al. present a detailed simulation of a double-Mach reflection from a dusty wall. By using a nondiffusive numerical scheme and adaptive mesh refinement, they were able to directly calculate the mixing in the unstable wall jet and dusty boundary layer flow. Similarity coordinates were used to average the fluctuating flow and thereby determine the dusty boundary layer profiles. Shepherd et al. report on the repeated reflections of detonation-driven blast waves in containers. 

The blast wave produced by a sudden release of a fluid depends on many factors (AIChE, 1994), This includes the type of fluid released, energy it can produce on expansion, rate of energy release, shape of the vessel, type of rupture, and the presence of reflecting surfaces in the surroundings. Materials below their normal boiling point cannot BLEVE. 

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