Simple Model of the World Trade Center Fireball Dynamics.
Simple Model of the World Trade Center Fireball
Baum, H. R.; Rehm, R. G.
Combustion Institute, Symposium (International) on
Combustion, 30th. Proceedings. Volume 30. Part 2.
July 25-30, 2004, Chicago, IL, Combustion Institute,
Pittsburgh, PA, Chen, J. H.; Colket, M. D.; Barlow, R.
S.; Yetter, R. A., Editor(s)(s), 2247-2254 pp, 2005.
combustion; World Trade Center; fireballs; flame spread;
fluid mechanics; safety; equations; conservation; heat
release rate; velocity field; mathematical models;
computational fluid dynamics
An analytical model of the initial expansion of a
fireball is presented. The model is based on an exact
solution of the low Mach number combustion equations in
the form initially proposed by the authors. The
equations consist of the conservation of mass, momentum,
and energy with an isobaric equation of state. The heat
release rate is a prescribed spherically symmetric
function characterized by a flame expansion velocity, a
flame brush thickness that increases with time, and a
heat release rate per unit surface area. The
introduction of a prescribed heat release rate obviates
the need for an explicit turbulence model. Thus, the
inviscid forms of the conservation equations can be used
in the analysis. The velocity field is decomposed into a
spherically symmetric expansion field and a solenoidal
component determined by the buoyancy induced vorticity
field. The expansion field together with the induced
pressure rise and temperature fields are spherically
symmetric. However, the buoyancy forces induce vorticity
where the temperature changes rapidly and break the
spherical symmetry of the velocity field. The solution
is used to study the initial expansion of the fireballs
generated in the attack on the World Trade Center south
tower. Video images are used to estimate the expansion
rate of the fireball. This information, when combined
with the analysis, leads to an estimate of the fuel
consumed in the fireball that is independent of any
assumptions about either the initial fuel distribution
or the state of the building following the crash.