A History of Research and a Review of Recent Developments

116
Structural loading from local explosions
shock tube experiments at the US Army Ballistics Research Laboratory were
carried out by Coulter [5.26] in which chamber volumes, entrance areas,
pressures and geometries were varied. It was shown that the pressure wave
expanding into the chamber decays in amplitude and reflects from internal
surfaces. The attenuation of the instantaneous peak pressure was inversely
proportioned to the opening diameter, and its positive duration was directly
proportional to the diameter. For non-circular openings the diameter was
replaced by a ‘mean opening dimension’. Tests at the US Army Waterways
Experiment Station in the early 1980s, using C-4 and TNT charges, showed
that side-on peak pressures in the test chambers (p max) were related to the
peak pressure in the opening (entrance tunnel) (p 0) by the equation
p max /p 0 =0.65(1–0.25α)(R/D) –1.35 ,
(5.32)
where R is the distance of the centre of the opening to the pressure gauge in
the chamber and D is entrance tunnel diameter. a is the angle in radians between
the normal to the centre of the opening and the gauge location. For small
angles it was sufficient to ignore a and within the units of experimental scatter
to simplify the above equation to p max/p 0=0.65(R/D) –1.35 . The values of p max
are due to the first side-on peak at the gauge as the result of incident pressure
and do not take account of internally reflected waves. If information about
reflected waves is required, then a more complex analysis involving a shock
diffraction model is needed. Path lengths of ‘rays’ of successively higher order
reflections are generated, and arrival times calculated; then shock wave
attenuation with distance is found. The procedure is fully described in ref.
[5.24]. The combined pressure pulse in a chamber, found in this way, can be
calculated using the code CHAMBER, originally for a mainframe computer
but converted to run on a desktop computer. Predictions for the initial peak
reflected shock were shown to agree well with test results.
It is clear that the levels of pressure from an internal explosion, whether due to
a high-explosive detonation or a vapour or dust cloud deflagration, can be reduced
by the judicious use of vents. The design of venting systems is governed by the
pressure reductions that are required, so there has been a considerable research
effort in this area. Going back to the work of Christopherson [4.6], which we
mentioned earlier, we noted that he analysed the effect on the pressure in a rigid
rectangular chamber if one end were vented. The ‘partial enclosure’ was the subject
of an empirical relationship in which the results of a small number of observations
were recorded in terms of the charge weight of TNT, the volume (V) in cubic feet,
and the face-on blast impulse on the venting side wall of a cubical enclosure (A T),
in lb m sec/in 2 . His results are plotted in Figure 5.19 on the axes A T/W 1/3 and V/
W(the volume of the chamber per lb of charge). For initial design purposes, the
relationship took the approximate form (Imperial units):
(A T /W 1/3 )(V/W)=15, (V in ft 3 ).
(5.33)