Page 119 - Fundamentals of Magnetic Thermonuclear Reactor Design

Simulation of Electromagnetic Fields Chapter | 4 103

relative errors in mechanical stress estimation when compared to currents
and fields.
The MFR’s complex geometry and the great number of conductive struc-
tures, electrical contacts and structural gaps affecting the distribution of cur-
rents inevitably calls for global computation models that are difficult to imple-
ment, even with state-of-the-art computation techniques. This is particularly
the case with the vacuum vessel and in-vessel components, the thermal shield
and the cryostat, which exert strong EM forces on one another and on other
reactor systems.
The growing complexity of an object of interest makes the use of the shell
approach and the TYPHOON code feasible and justifiable. One example is a
model of the ‘vacuum vessel–thermal shield–cryostat’ (VV + TS + CR) con-
ductive structures linked with each other as a whole (see Appendix A.4.2).
In the developed shell model, the total number of triangular FEs describing a
40-degree regular sector of ITER is ∼120,000. This is equivalent to a system
of ∼60,000 equations relative to node unknowns. Such a model provides for a
desired computational accuracy for the entire range of stresses caused by the
EM transients (Appendix A.4.2).
Let us compare the shell model with, for example, a 3D FE ANSYS
model that describes massive solids and would provide the same approxi-
mation. ANSYS [35] utilises the differential formulation and magnetic
vector potential. ANSYS modelling implies a number of requirements to
be met. First, several variables have to be found at each node of a mesh.
Second, the gaps between conducting structures must be filled with 3D FEs
of small volumes, typically. Third, boundary conditions for a field at the
external boundary of a computation domain must be fulfilled. The impor-
tant point here is that the space outside the reactor must be also filled with
FEs. If these requirements are met, the problem dimensionality is around
7
(4–8) × 10 at least.
To spare the computational resources, different types of symmetry inher-
ent for tokamaks (e.g. cyclic symmetry, mirror symmetry and mirror asymme-
try) are applied. For each type of symmetry, a minimum angular sector (10–20
degrees typical for MFR) is specified. For example, a minimal rotationally
symmetric sector Ω is bound by planes  = ± , where  is an angular co-
s

ordinate on the tokamak toroidal circumference. As a periodic structural ele-
ment, this sector can be subdivided into subdomains that are mirror symmetric
with respect to plane  = 0. We take one of the computational subdomains,
Ω or Ω − , to solve two independent problems with differing field/current
+
symmetry conditions. One problem deals with EM transients due to varia-
tions of poloidal fields, and the other concerns toroidal fields. A spatial field
distribution and eddy current/Lorentz force densities are determined for each
of the problems. Then, a general solution for the periodicity element Ω (as a
