The first operation, which is seldom directly performed by the reactor designer, consists in the preparation of the nuclear libraries for the codes for spectrum calculations, starting from the basic data of the ENDF/B type.

The proper reactor design usually starts with zero-dimensional optimization calcula­tions for the equilibrium condition. Later space-dependent calculations for the equilib­rium condition are performed including control rods, temperature coefficient, heat — transfer and dynamics calculations. The running-in strategy is then defined and the above calculations are repeated for different stages of the running-in period.

The type of approximation needed in order to obtain sufficient accuracy without waste of computing time will have to be chosen for each of these steps by the designer. This choice is based sometimes on comparison with experiments, but most frequently on numerical experiments. This means that in order to check whether an approximation is sufficient for a certain type of calculation, the designer tries a higher approximation in one typical case. If the difference is sufficiently small the approximation can be considered as sufficient. This can be done for most types of numerical approximations: number of energy groups, space dimensions, mesh points, order of an S„ approxima­tion, size of time steps etc. Obvious limits to this procedure are posed by computer capacity and costs, but it is often possible to simplify the problems in these tests (e. g. the number of energy groups necessary for a two-dimensional calculation is tested on a one-dimensional test case). It must be remembered that not always the next higher approximation gives better results, but it is sometimes necessary to test on even higher approximations (e. g. a two thermal group calculation is not necessarily better than a one thermal group calculation, so that the test may require four or more thermal groups). Another typical numerical experiment consists in checking the method being studied with a Monte Carlo calculation.

The advantage of numerical experiments is that they are cheaper than actual experiments, and enable the designer to check one single approximation at the time, without involving the global error due also to other approximations and inaccuracies in the data. Obviously these analyses are only thoroughly performed when high comput­ing costs are involved, whereas in simpler cases higher approximations are used. This may lead to what can be easily considered a waste of computing time, but overall economic considerations may indicate that it is often cheaper to perform a sophisti­cated calculation instead of spending days in analysing which simplification can be tolerated without loss of accuracy.

In order to illustrate the practical use of the methods and codes described in this book, we give here some schematic flow diagrams of the most frequently performed reactor calculations.

The Sequence of Reactor Design Calculations

Estimate of core composition

Spectrum-averaging cross section codes

		Improve estimate " of fuel cycle ~ characteristics
Zero-D codes to define equilibrium cycle		Fuel cycle cost code

First estimate of equilibrium fuel cycle characteristics

і Broad group cross sections

Estimate of equilibrium fuel cycle composition

Attractive fuel cycle

♦_____ .

І-D codes to refine knowledge of equilibrium cycle

Firm definition of attractive equilibrium fuel cycle-fuel management scheme and core composition

Final estimates of core composition and fuel cycle cost for a given fuel management strategy

Fig. 16.1. Information flow diagram for fuel-cycle calculations (to estimate composition and power cost for a given fuel management scheme).*0

Figure 16.1 gives the flow diagram of a typical sequence of fuel-cycle calculations for the equilibrium and the running-in period, as established by General Atomic. w

A similar scheme for pebble-bed reactors is described in Fig. 16.2. Possible flow paths for burn-up and kinetics calculations are shown in Figs. 16.3 and 16.4m while Fig. 16.5 gives a possible way of designing the control-rod system.

All these flow paths are only indicative and change from establishment to establish­ment according to the computer codes being used, and to the peculiarities of the reactor under consideration.

Various computer codes have been mentioned in the course of the preceding chapters. It is not within the scope of this book to give a complete list of the codes which can be used for HTR calculations. Abstracts of the codes for nuclear calcula­tions, whose distribution is not restricted, are published regularly by the NEA Computer Programme Library of Ispra, and by the Argonne Code Center for US users.

Range of parameters (C./U, T, P) a change of the optimum case Fig. 16.2.

Estimate of core composition

Spectrum-averaging cross­section codes

2-D X-Y calculations

—- f—-

Reactivity and power distributions for use in radial zoning studies, radial peaking factor estimates, etc., as a function of time

1-D radial calculation

Reactivity and power distributions for use in radial zoning studies, radial peaking factor estimates, etc., as a function of time

1-D axial calculations

Reactivity and power distributions for use in axial zoning designs, rod movement estimates, axial peaking.

factor estimates, etc., as a function of time

Fig. 16.3. Information flow diagram for conventional core depletion calculations.

Fig. 16.4. Possible flow diagram for control rod calculations.

Estimate of core composition and system temperature Fig. 16.5. Information flow diagram for kinetics calculations (to estimate core power versus time).’11

Some particular attention must be paid to the recent development of modular systems which permit a considerable authomatization in the sequence of many reactor calculations without the need of a separate data manipulation for each single calcula­tion. These systems allow the execution of a sequence of codes (modules) with various paths which may be selected at run time, and provide for exchange of information between these modules. This exchange of information is obtained writing and reading from a collection of the data (interface) which are produced or required by the operation of a module and are available for use by other modules.® The use of modular systems results in a saving of both manpower and computer time.

In the HTR field efforts in this direction started in the past with the development of coupled burn-up and spectrum codes (e. g. MAFIA’41) to which later transport codes have been added (VSOP<5>), but these cannot be properly called modular systems. The peculiarity of modular systems lies in the possibility of changing the path of the calculation at the will of the user. A typical example is given by the WIMS-E scheme’6’ which was originally a code for spectrum calculations’7’ and has now evolved to a system including almost all codes needed for a complete core calculation (see Table 16.1). The modules available in WIMS-E are listed in Table 16.1 with a brief description of their functions. The names of these modules are usually those of previously existing codes with the letter “W” added at the beginning.

This scheme is now the basis of most HTR calculations in Britain. Another modular system developed by UKAEA is COSMOS which is mainly intended for fast reactors, but has already been used for HTR calculations’8’ because it can perform three­dimensional burn-up calculations using its three-dimensional diffusion module TIGAR.