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Values for reactivity effects are required both for transient safety analysis and for control requirements during normal operation. Reactivity effects of importance in fast reactor design and safety include (1) effects of dimensional changes in core geometry, (2) the Doppler effect, (3) effects of sodium density changes or loss of sodium, and (4) long-term reactivity loss from fuel burnup.The reactor control system must compensate for these reactivities during normal operation and provide sufficient margin to handle off-normal situations.We begin this chapter with a review of the reactor kinetics equations (Section 6.2). We then proceed to discuss adjoint flux and perturbation theory (Section 6.3) since these are needed for an understanding of reactivity effects. Kinetics parameters β and l, the effective delayed neutron fraction and the neutron lifetime respectively, are then discussed and the differences in these values between fast and thermal reactors are presented (Section 6.4). Sections 6.5 through 6.7 cover the first three categories of reactivity effects. Section 6.8 is addressed to reactivity worth distribution, and the final section discusses the control requirements for a fast reactor. A detailed discussion of the fourth category of reactivity, that associated with fuel burnup, will be delayed until Chapter 7, although sufficient information will be summarized in this chapter to define the control requirements. Reactor KineticsReactor kinetics equations for both fast and thermal reactors are identical. However, point kinetics approximations can be used more effectively for fast reactors than for thermal reactors because fast reactors are more tightly coupled neutronically. Tighter coupling implies that the neutron flux is more nearly separable in space and time, which is a necessary condition for point kinetics approximations to be valid. Fast reactor safety codes to date have therefore generally employed point kinetics. 1 Inevitably, as commercial fast reactors reach the 1,000-2,000 MWe range, and particularly if they employ heterogeneous cores, problems involving space-time kinetics will arise. Such considerations, however, are beyond the scope of this text.

Two different techniques, the Particle Image Velocimetry (PIV) and the Shadow-Image Velocimetry (SIV) techniques have been used to capture detailed two-phase bubbly flow experimental data. The PIV has provided a two-dimensional velocity field of the liquid phase for analysis of the continuous phase. The SIV has utilized to reconstruct the bubble shape and velocity of the dispersed phase in three-dimensions.