1 NUEN 301 Exam 2, 2008 – Morning Section [points] [15] 1. Write down the one-speed steady-state diffusion equation with appropriate boundary conditions for a cubical homogeneous reactor surrounded by vacuum. Don’t try to solve the problem – just write it down completely enough that you could give it to a mathematician and she could solve it. [15] 2. A large commercial power reactor is critical and operating at a steady-state power level of 1 GW? Operators quickly insert several control rods, making the reactor very subcritical. They do not do anything else. Sketch the reactor power as a function of time, putting labels and marks on your graph. Point out and describe interesting features of the graph, as if you were explaining to a bright high-school student how a reactor works. Some of your explanation should be qualitative and some should talk about the actual functional form of P(t). In particular, be quantitative about how long it takes for the power to drop from one level (say 1 MW) to a lower level (say 100 kW). 3. A neutron detector next to the reactor at the Nuclear Science Center shows a linear increase in the neutron population as a function of time for several minutes, with the reactor operating at very low power. [10] a) Is the reactor critical, subcritical, or supercritical? Explain your answer. [5] b) Is there a source present or not? Explain your answer. 4. Someone solved a two-region slab-geometry diffusion problem with the following characteristics: for 0<x<a: DF, Σa,F, νΣf,F, for a<x<b: DM, Σa,M, νΣf,M, He found the following solution: φ(x) = A cosh x / LF( ), 0 ≤ x ≤ a,C exp x / LM( )+ E exp − x / LM( )+ G , a ≤ x ≤ b.⎧ ⎨ ⎩ (1) According to this solution and according to diffusion theory: [10] a) At what net rate per unit area are neutrons crossing from region “M” to region “F” across the surface at x=a? [10] b) At what net rate per unit area are neutrons crossing from region “F” to region “M” across the surface at x=a? [10] 5. a) Approximately how many fuel pins are in a commercial PWR? Approximately what are the dimensions of each pin (diameter and length)? [10] b) If such a reactor is operating at 3 GW thermal power, approximately what is the average linear heat generation rate of a pin (energy per unit pin length per unit time)?2 6. For this question, assume that a reactor remains at a low enough power level that there is no feedback. [5] a) If the reactor is source-free and slightly supercritical (small positive reactivity), what is the functional form of P(t) if you look at it several seconds after the reactor became supercritical? [5] b) If there were no delayed neutrons, what would be the answer to question (a)? [5] c) Do delayed neutrons make a difference in a slightly supercritical reactor? Explain this, using your answers to (a) and (b), as if you were teaching a high-school student about delayed neutrons. [5] EXTRA. Repeat question (1) but include energy dependence instead of assuming one-speed