A History of Research and a Review of Recent Developments

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