Page 120 - Fundamentals of Magnetic Thermonuclear Reactor Design

104 Fundamentals of Magnetic Thermonuclear Reactor Design

result for the tokamak as a whole) is found using the superposition principle.
This algorithm enables a fourfold decrease in the computer memory allocated
when solving problems with integral–differential problem formulation that
implies dense matrices.
The TYPHOON and TORNADO codes contain special post-processing
modules to obtain outputs for the periodicity element Ω .

A general solution of the form
j tot = j + j ;
2
1
B tot = B + B + B ;
2
ext
1
j ×
f tot = f + f + 1 B + j × B , 1
2
2
1
2
where j and j , j are the eddy current total and partial densities, B is
tot
2
1
tot
the total field, B and B are partial fields due to eddy currents, B is the
2
ext
1
external field, f is the Lorentz force total density, and f = j × (B + B ),
ext
tot
1
1
1
f × (B + B ) are components of the Lorentz force total density. Subscripts
2
ext
2
jtot=j +j ;Btot=B +B +Bext;ftot=f 1 1 and 2 denote partial components determined when solving the two prob-
1
2
1
2
+f +j ×B +j ×B , lems mentioned.
2
2
1
2
1
In some cases, one can apply the superposition principle to widened an-
gular sectors up to 180 degrees to obtain a general solution. If the sector is
regular, the problem dimensionality is reduced that allows the use of a refined
FE meshes.
The TYPHOON code allows volume forces to be transformed to a set of
equivalent nodal loads. Then, the TYPHOON output files can be used directly
as inputs for a subsequent stress analysis.
4.4.4 3D Computational Models
The conducting shell concept is unsuitable for a mathematical description of
massive conductive structures, such as the divertor and blanket modules. In this
case, a 3D solid-body simulation is required. As with other numerical models, a
3D model has limitations associated with the mesh approximation for the initial
stages of modelled EM transients. That is why additional models need to be
developed. For example, a perfect conductor model is applicable to evaluate a
field outside a conducting structure in the analysis of the initial stage of an EM
transient when the skin effect is pronounced. Within certain approaches, local
models are capable of providing an adequate assessment of EM response of the
structures.
The code TORNADO enables the analysis of EM transients in massive
solids. The code uses four types of FEs: eight-node hexahedra, six-node
triangular prisms, five-node pyramids, and four-node tetrahedra. Equations
are solved in terms of the three-component electric vector potential P and