A History of Research and a Review of Recent Developments
A History of Research and a Review of Recent Developments
A History of Research and a Review of Recent Developments
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110<br />
Structural loading from local explosions<br />
enable extremely complex systems with up to 1000 branches to be analysed for<br />
a very wide range <strong>of</strong> inlet geometries <strong>and</strong> bomb orientations. Codes <strong>of</strong> this type<br />
can be used, for example, to model the effect <strong>of</strong> shock waves in the ducting<br />
system <strong>of</strong> aircraft or ship structures, <strong>and</strong> are valuable tools in analysing the<br />
strength <strong>of</strong> such structures under attack by terrorist explosive devices. Most <strong>of</strong><br />
the codes are marketed by the developers, <strong>and</strong> a comparison <strong>of</strong> their capabilities<br />
is beyond the purpose <strong>of</strong> this book. However, one code which was commissioned<br />
by the US Army Corps <strong>of</strong> Engineers, Omaha District, <strong>and</strong> written at the University<br />
<strong>of</strong> Nevada, has been described in some detail by Fashbaugh [5.15]. The code,<br />
which can be used on a PC computer, enables the shock propagation in ducting<br />
systems (SPIDS) to be calculated sequentially. The shock propagation in a main<br />
duct, for example, is calculated <strong>and</strong> the time history <strong>of</strong> pressures <strong>and</strong> temperatures<br />
is stored on a computer file. This file then specifies pressures <strong>and</strong> temperatures<br />
at the inlet <strong>of</strong> a branch duct from which the shock propagation in the duct can<br />
be deduced. This procedure can be repeated for large numbers <strong>of</strong> branches—up<br />
to ten for each specific duct. There are limitations, one <strong>of</strong> which is that reflected<br />
shock waves from branch ducts into main ducts are not accounted for; neither<br />
are shock wave losses as the wave passes the entrance to a branch duct.<br />
Simulation is achieved by evaluating flow losses from a point s just outside<br />
the duct entrance to a point e inside the entrance, using the collected results <strong>of</strong><br />
many experimental programmes. The duct entrance static pressure p e is related<br />
to the pressure outside the duct, p s, by the relationship<br />
where p te/p ts is the stagnation pressure ratio, given by<br />
(5.28)<br />
(5.29)<br />
T e <strong>and</strong> T s are static temperatures at points e <strong>and</strong> s; T te <strong>and</strong> T ts are stagnation<br />
temperatures. A(1) <strong>and</strong> A(2) are empirical coefficients that depend on the<br />
entrance geometry <strong>and</strong> position <strong>of</strong> the explosion, <strong>and</strong> M s is the flow Mach<br />
number outside the duct. The shock wave attenuation due to internal friction<br />
in the ducting is represented by a friction factor, given in terms <strong>of</strong> (h/D) 1/2 , as<br />
discussed earlier, where h is the average wall protrusion height <strong>and</strong> D is the<br />
duct diameter. Fashbaugh used the equation<br />
t=0.016+0.00491(h/D) 1/2 +0.258(h/D),<br />
(5.30)<br />
<strong>and</strong> for a side-on entrance A(1)=1.1398, A(2)=1.24. The linear relationship<br />
between p te/p ts <strong>and</strong> M s from experiments is shown in Figure 5.15. The code<br />
has been shown to give good agreement with tests for the decay <strong>of</strong> shock<br />
pressure with distance along a duct, <strong>and</strong> for the effects <strong>of</strong> a sudden increase in<br />
the cross-sectional area <strong>of</strong> a duct.