Temperature Effect of Reactivity

Abstract

In Chap. 2, it was assumed that effective multiplication coefficient k _eff and reactivity ρ do not depend on reactor power n, and the point reactor kinetics equations were solved. Their solutions are applicable to the reactor having almost zero power or zero number of neutrons. It is called the “zero-power reactor” and its reactor temperature does not change. In the actual reactor, however, when its number of neutrons numbers (or its power) changes, the temperature of the reactor changes and therefore, the k _eff and ρ values change. These changes affect reactor power. This reactivity change is called the temperature effect of reactivity. The reactivity changes with reactor temperature and moderator density, etc. The reactor power changes with the reactivity. Therefore, this reactor power change is called the reactivity feedback effect.

An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-4-431-54195-0_12

Chapter 3 Exercises

• 1. The reactor with a negative temperature coefficient −α[Δk/k/ °C] and a large heat capacity C[kcal/ °C] is operated in a steady state. Add the reactivity δk[Δk/k] stepwise and complete the following tasks.

  • (a) Calculate the temperature increase until the neutron flux reaches the maximum level.

  • (b) Calculate the neutron flux at the maximum level.

  • (c) Draw the transient time change of neutron flux ϕ and temperature (T °C).

Assume the following:

• <1> Delayed neutrons can be ignored.

• <2> The heat generated after the stepwise reactivity addition is not removed to the outside, but it is used to increase the core temperature only.

• <3> The transient change is small and occurs around k = 1.

• <4> The initial neutron flux is ${\varphi_0}$, the neutron lifetime is l(s), the conversion factor between the neutron flux and heat is A (kcal/neutron flux * s).

  (Question 3.3 from the 11th examination for license of chief reactor engineers of Japan)