We have discussed the time behavior of the neutron flux and reactivity feedbacks. Now it is time for the the thermal side of things. The point kinetics model describes how much energy is produced in the fuel, but we also need a model for how the energy is transported within the fuel, through the fuel cladding and into the coolant. To figure it out we need models for heat conduction through the fuel and cladding, heat transfer to the fluid through convection, properties of the fluid at different temperatures and pressures and so on. This blog post will deal with the heat conduction in the pellet and through the cladding.
Advanced test reactor Foto: Matt Howard, Source: Wikimedia Licens: Creative Commons Attribution-Share Alike 2.0 generic
Its time for some more fun with reactor kinetics, in the last post we ended by looking at the point kinetics equation with one group of delayed neutrons. In this post as I promised we will talk about reactivity feedbacks. To brush up your memory, reactivity is defined as:
Nuclear reactors contain tons of fissile material and nuclear bombs contain only kilograms of fissile materials, so why does one of them explode with enough force to flatten a city but the other doesn't? I will pull out some latex skillz and geek it out with equations to describe the physics behind whats in nuclear engineering is called reactivity excursions or RIA (Reactivity Insertion Accident). The level of these blog posts will be such that an interested and fairly math savy person can understand and calculate these kind of things on their own.
Castle Romeo photo: United States Department of Energy, Source: Wikimedia
The issue of recriticality in the damaged reactors at Fukushima pops up every now and then (a few examples link1, link2, link3, link4). Perhaps it is worth taking a look at what recriticality means, how likely it is and what it would mean if the cores goe critical. These posts will contain some maths and give some insight into basic reactor physics. Despite what most people think it is actually quite easy as long as one can follow the solution of some simple differential equations.
We will look at two different cases, in the first case the core has melted completely and is as a molten puddle or bed of "gravel" at the bottom of the vessel. In the second case the fuel rods are still mostly geometrically intact while the control rods have melted. If I have energy I might throw in a section about criticality in spent fuel pools as well at the end. We start with the completely molten core because it is easier and highlights all the relevant physics.
What exactly is criticality?
Fission is a reaction whereby a incoming neutron hits a nucleus, the nucleus then has a certain probability (depending on the energy of the neutron, what nucleus it is etc) of splitting into two roughly equally large pieces and in the process emit 2-3 new neutrons. Those neutrons can in turn hit new nuclei that causes more fissioning and voila, we have a chain reaction. If we assume we have a system where nothing is happening and we send in a burst of neutrons, those neutrons, that we will call the first generation, will cause an initial amount of fission reactions that produce a second generation of neutrons which goes on to create a third generation etc. Criticality is simply defined as the ratio between a subsequent generation with the one preceding it, it is usually designated by the letter K. Continue reading A look at recriticality during meltdown, part 1