Figure 1.17 shows the basic blocks of the closed loop—the kinetics, the thermal representation, and the feedback from thermal effects. An added xenon feedback is included to indicate how the thermal reactor xenon poisoning arises directly from flux changes. (Note also that the delayed neutrons contribute to the calculation of the flux only through the kinetics block.)

Further feedback lines can be added to this basic reactor core closed — loop model. They might arise from the control and protective system, and the figure shows the flux and excess outlet temperature trip lines as indica­tive of this type of feedback. External influences also play their part; here control and coolant flow changes might disturb the state of the system.

Indeed as we have seen, the coolant inlet temperature is the reference temperature for the system.

This basic feedback loop is added to in different ways for each different reactor type.

a.

Boiling water reactor {BWR). Figure 1.18 now shows the closed-loop model for the BWR. The circuit between coolant outlet and inlet is closed by a primary loop which includes the steam drum. The time delay between outlet and the drum is shown as r3 and the subsequent delay to the inlet plenum is denoted by r4. Conditions in the steam drum depend on a rep­resentation of how much boiling is occurring in the core and what the outlet quality is and also on what steam load is extracted from the drum to

drive the turbine. Thus this model also requires a turbine representation and its return make-up lines to the steam drum. Notice also that the boiling in the core contributes a feedback reactivity to kefr. The closed loop is an example of a direct cycle system.

b. Pressurized water reactor {PWR). The circuit (Fig. 1.19) is very slightly altered by the addition of another secondary circuit as the PWR does not have boiling and must generate the steam for the turbine in a heat exchanger

(steam generator). It is an example of an indirect cycle system in which the steam drum and turbine are in the secondary cycle.

c. Liquid metal fast breeder reactor (LMFBR). Figure 1.20 shows that yet another circuit has been added between the secondary of the heat exchanger and the steam generator. This is an insulator between the primary radioactive sodium coolant and the water in the steam cycle. Now no xenon feedback exists.

External plant items in these loops will all be represented by thermal balance equations in as much complexity as the particular problem requires. The representation of the steam generator is difficult outside the normal operating range, because the boiling boundaries can shift so rapidly with steam collapse and water flashing into steam. The turbine, too, is particular­ly difficult since its transient behavior is largely unknown. Delays in the circuits must be included in the representations since they have a critical bearing on the stability of the system and these delays are variable, depend­ing as they do on the circuit flows.

It is possible to simplify models, depending on the investigation to be made. If, for example, a rapid reactor core variation is the phenomenon under consideration, it will be adequate to assume that the inlet temperature is constant (as it must be for a circuit time). This will allow the secondary and tertiary circuits to be neglected. If a secondary flow perturbation is to be investigated for its effect on the core, then it will be adequate in some circumstances to assume constant steam generator boundary conditions (in the LMFBR) and so obviate the need for representing the turbine and its feedwater line.