An alternative approach is to map out the whole of the vessel internal volume as a hydrodynamic system with a two-dimensional mesh, then to represent the hydrodynamic equations of motion in each mesh node, to apply the proper boundary conditions, and to insert a pressure-temperature distribution in the core. The system can then be used to calculate the relaxa­tion of these pressures and temperatures as a function of time in each mesh.

A series of such representations has been prepared by ANL (27a, b, 28a). These codes use the pressure-temperature distribution calculated from an energy release code such as MARS or VENUS and describe the con­sequences by means of a Lagrangian mesh that deforms with time.

The equations used in each mesh node are

where q, r, z, p, and E are the density, radial and vertical accelerations, the pressure, and the internal energy of the fluid, respectively. The initial vol­ume and density are V and q0, while v is the deformed volume element.

Figure 5.10 shows a series of illustrations starting from an undeformed mesh of half the reactor system in which the left-hand boundary is con­sidered a line of symmetry. Successive illustrations show how the mesh is deformed as a result of a sharp pressure distribution input to the mesh in the core region only. The pressure waves can be seen moving outward as a

function of time until they contact the vessel walls first in a radial direction and then the bottom head. Figure 5.11 shows the pressure profile at the core center in an axial direction. The pressure, initially peaked, can be seen to relax into two peaks moving up and down, the one moving up being atte­nuated by a plenum above the core on the right, while the one moving down is held up temporarily at the vessel bottom before this finally ruptures, to relieve the pressure build-up against it. Figure 5.12 shows the radial pressure profile and the shock front moving toward the vessel wall in a radial direc­tion.

The Lagrangian mesh deforms in the code and to retain finite difference accuracy it is necessary to rezone when the mesh gets somewhat deformed. This rezoning is a matter of experience and at present it is time consuming,

being nonautomatic. The code has several deficiencies which are all gradually being remedied. However, it has been successfully compared to a British experiment in which a 2 oz charge of RDX/TNT 60/40 was detonated in water inside a 2-ft diameter pressure vessel. The agreement of REXCO calculated pressure values at the vessel boundary with the experimentally observed values is good (within 20%) (28b).

Two principal versions of the code exist, REXCO-H and REXCO-I, one being the basic code and the other including inelastic deformation of vessel walls. So far no heat transfer is included in the mesh and the model is only good for the start of an excursion following the energy release. It is therefore an excellent method of calculating radial damage, but (as is shown in the next section) for the prediction of a sodium hammer ejection above

the core, heat transfer is now of importance and therefore the hydrodynamic code has to be linked to a further hammer heat transfer representation.

In principle it is to be expected that a full hydrodynamic model with heat transfer should eventually do away with the need to consider chemical explosive work.

The chemical explosive methods are, as we have seen, pessimistic. There-

Fig. 5.11. Pressure profiles along core vertical centerline at various times after start of the pressure pulse. Times are shown in microseconds. [Courtesy of Argonne National Laboratory (27a).]

Fig. 5.12. Pressure profiles along core horizontal axis at various times after the start of the pressure pulse. Times are shown in microseconds. [Courtesy of Argonne National Laboratory (27a).]

fore, if they predict that a vessel will rupture, a doubt whether this will be true still lingers. However, if they predict that a vessel will not rupture then we can be confident that this is so. A 2-in. vessel with a 10-fit radius would not rupture under an explosion of 250 MW-sec if 12% strain were acceptable (Table 5.12) by this analysis. However for the same case, a more realistic evaluation of the strain would show it to be less than 1%.