Methods for Determining the Energy Release in Hypothetical Reactor Meltdown Accidents Page: 77

                                
CHAPTER VI

TWO-DIMENSIONAL AND NON-UNIFORM EFFECTS
The methods of Chapters III, IV and V were restricted to situations
which can be described by, or at least approximated by, a spherical
uniform homogeneous core. It is believed that such a model is adequate
for many interesting cases. However, the hypothetical excursions are
generally supposed to result from meltdown of the reactor core, and it
is not difficult to visualize fuel configurations from meltdown which
cannot be well represented by a uniform homogeneous sphere. To study
the non-spherical configurations we here develop a procedure for solving
the equations (using the basic method of analysis of Chapter II) in two-
dimensional cylindrical geometry.
There are two principle new effects which arise in non-spherical
non-uniform situations. The equation of state (17) predicts that for a
given energy input per unit mass the pressure in a high density region
may be much higher than in a low density region. This means that the
reactivity effects produced by expansion of high density material can,
in some cases, shut the reaction down before there is any significant
Pressure produced in the low density region.
The second new effect when non-spherical geometries are con-

sidered is that it is possible that the maximum of the reactivity distribu-
tion and the maximum of the pressure distributions may not occur at the
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