Diffraction, blast waves

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. 

Blast wave (Overpressure and negative phase pressure relative to atmospheric condition) Diffraction loading—forces on a structure resulting from the direct and reflected overpressure... 

The pressures on the sides and roof of the structure build up to the incident overpressure as the blast wave traverses the structure. Traveling behind the blast wave front there is a short period of low pressure caused by a vortex formed at the front edge during the diffraction process (Figures A. 8c and A. 9c). After the vortex has passed, the pressure returns essentially to that in the incident blast wave. The air flow causes some reduction in the loading to the sides and roof, because the drag pressure has a negative value for these surfaces. 

When the blast wave reaches the rear of the structure, it diffracts around the edges and travels across the back surface (Figures A.8d and A.9d). The pressure takes a certain rise time to reach roughly a steady-state value equal to the sum of the overpressure and the drag pressure, the latter again having a negative value for the back surface. 

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. 

The ideal side-on parameters almost never represent the actual pressure loading applied to structures or targets following an explosion. So a number of other properties are defined to either more closely approximate real blast loads or to provide upper limits for such loads. (The processes of reflection and diffraction will be discussed later.) Properties of free-field blast waves other than side-on pressure which can be important in structural loading ares... 

Diffraction. When a blast wave encounters a finite obstacle, it is partially reflected but also diffracts around the obstacle. This process is described here. 

The process of diffraction of a blast wave around a rectangular block object, such as a simple building shape, is well described in Ref. 7, and is paraphrased here. 

The pressure differential between the front and back faces will have its maximum value when the blast wave has not yet completely surrounded the structure, as in Figs. 7c, and d or g and h. Such a pressure differential will produce a lateral (or translational) force tending to cause the structure to deflect and thus move bodily, usually in the same direction as the blast wave. This force is known as the "diffraction loading" because it operates while the blast wave is being diffracted around the structure. 

For blast waves from relatively small explosion sources, the diffraction phase of the loading may dominate, and the drag phase may be relatively or entirely unimportant, because the diffraction times may be as long as or greater than drag pressure durations. 

Figure 7. Stages in the Diffraction of a Blast Wave by a Structure without Openings. (Plan View) (Ref. 7)...

The duration of the reflected pressure depends on the dimensions of the reflecting surface, up to a maximum time approximately equal to the positive phase duration of the incident blast wave. This upper limit corresponds to the total reflection of the entire blast wave without any diffraction around the edges of the reflecting surface. Further details of the duration are provided in Section 3,5.1,... 

The actual pressures on all faces of the structure are in excess of the ambient atmospheric pressure and will remain so, although decreasing steadily, until the positive phase of the blast wave has ended, thus the diffraction loading on a structure without openings is eventually replaced by an inwardly directed pressure. 

As the wave front moves forward, the reflected overpressure on the face of the structure drops rapidly to the side-on overpressure, plus an added drag force due to the wind (dynamic) pressure. At the same time, the air pressure wave bends or "diffracts" around the structure, so that the structure is eventually engulfed by the blast, and approximately the same pressure is exerted on the sides and the roof. The front face, however, is still subjected to wind pressure, although the back face is shielded from it. 

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