Nuclear Engineering

Basic Design Aspects of a Fission Reactor

In these two lectures I am going to discuss various components of a fission reactor, their structures and basic design aspects. The fundamental design aspect of a nuclear fission reactor involve following components (Fig. m3.2) in a reactor:
A reactor core, Moderation stage, Reflector covering the core region, Coolant and energy removal, Radiation shielding and Overall control system.
Let us know the role of individual components of the reactor and their basic design aspects:

Reactor core (S1):

In active core region, the fission chain is sustained and most of the energy of fission is released as heat. The core contains the nuclear fuel, consisting of a fissile nuclide and often a fertile material in addition. Among various reactor fuels, here we will discuss about uranium as a fuel material. The percentage of U is only 0.001 or less and hence extraction of metal would appear to be uneconomic.


FIGURE m3.2Schematic of a nuclear fission reactor and various components.


The uranium to be used as a reactor fuel must be especially free from elements having appreciable cross-section for neutron capture. Most uranium ores contain about 1.5 to 10 lb of U₃O₈ per ton, i.e., roughly 0.1 to 0.5 % of U, and these are concentrated by a chemical process². The ore is first leached with acid or alkali (sodium carbonate) depending on its nature. The uranium can be precipitated from the leach solution in one-way or another, but it has generally been found most satisfactory to remove the uranium by solvent extraction or ion-exchange techniques. Partially enriched uranium, containing from 1 to 5 % U-235 used as a fuel, is separated from its isotopes by the gaseous-diffusion method. In this method, isotopes of different molecular weights are separated through a porous barrier due to their different diffusion rates. The barriers used in the uranium separation process contain hundreds of millions of pores per square inch, the average pore diameter being about two-millionth of an inch. Based on the diffusion rate, which is inversely proportional to the molecular weight, a separation factor s.f. is defined in the following manner:

Where M (heavy) and M (light) are the molecular weights of the heavier and lighter isotopic diffusion species, respectively. For the separation of the isotopes of uranium by diffusion, the gaseous compound employed is hexafluoride, UF₆. This substance is a solid at ordinary temperatures, but it has relatively low sublimation temperature, so that it vaporizes readily. Taking uranium hexafluoride as the diffusion gas, M (heavy) is (238) + (6 x 19) = 352, whereas M (light) is (235) + (6 x 19) = 349. The theoretical separation factor is consequently,


The theoretical enrichment factor² defined as s.f. – 1, is therefore 0.0043 for U-235 in UF₆. A nuclear reactor cannot be used to release energy continuously unless the critical mass of the particular fuel, shape etc. is exceeded. For this reason, the power reactor must include extra fuel, and so it must obviously have excess reactivity to an appreciable extent at the time it commences operation.


Moderator (S2):


Most of the fissions result from the absorption of slow neutrons, and hence the presence of a moderator is must. The function of the moderator is to slow down the high-energy neutrons liberated in the fission reaction, mainly as a result of elastic scattering. The best moderators are materials consisting of elements of low mass number with low neutron capture probability. Examples of moderator are ordinary water, heavy water (deuterium oxide), beryllium oxide, carbon (as graphite), and hydrocarbons. For a given moderator material, there is a cross section, σ_s, for neutron scattering by collision, and a cross-section, σ_a for neutron absorption. A parameter known as slowed down parameter, ξ² can be deduced from kinematics⁴:

where A is the atomic mass number. This can also be defined as

where E = energy before collision and E₀ = energy after collision. Moderating ratio (M.R.) can be defined as

The relative amounts and the nature of the fuel and moderator determine the energies of the most neutrons causing fission. Detailed graphitization process of petroleum coke and its use as moderator can be found in the literature.^1,3


Reflector (S3):


Reflector is a material placed around the reactor core (that contains the fuel and the moderator), which prevents neutrons from escaping the reactor core. Therefore, reflector decreases the loss of neutrons from the core by scattering back many of those, which have escaped. Hence, the use of a reflector results in a decrease in the critical mass of the fissile nuclide. Good moderators are good reflectors in case where core contains moderator to slow down the neutrons. On the other hand, when it is required that most of the fissions should be caused by neutrons of high energy, the presence of moderating material must be avoided; the reflector then consists of a dense element of high mass number. For a thermal reactor, heavy water, beryllium (or its oxide), or graphite is generally used for this purpose. As many neutrons get reflected back from the reflector, the leakage of neutrons is reduced, which results in the decrease of the critical mass of fissile material as compared to bare reactor. In addition to decreasing the volume and mass of the critical core, the reflector also plays a role in the increase of the average power output of the reactor for a given mass of fuel and peak neutron flux. Because of the return of neutrons to the core by the reflector, the flux near the boundaries will be much greater than in the absence of a reflector, resulting in an increase of average neutron flux over the whole core, and hence the average power output for a given flux. The spatial distribution of neutrons for bare and reflected reactors is shown in Fig.m3.3.

FIGURE m3.3 Thermal neutron flux distributions in bare and reflected reactors


Coolant and energy removal (S4-S6):


The major portion of the heat generated in the core is due to the kinetic energy of the fission fragments, which usually manifests itself as heat release in the fuel elements. Heat is also produced from the slowing down of neutrons and beta particles, and the absorption of various gamma radiations. The heat so generated in a reactor is removed by circulation of suitable coolant and transported to heat exchanger. Examples of coolants are liquid water, liquid sodium, some organic compounds, and gases of air, carbon dioxide, helium etc. The choice of coolant, arrangement of fuel and coolant and method of heat removal are the primary considerations while designing a reactor. This is based on the engineering knowledge of heat transfer, hydrodynamics, and thermal stress etc. There are three general mechanisms whereby heat is transferred from one point to another, namely, conduction, convection and radiation. In conduction process, heat is transferred from one point to another by molecular interaction without any macroscopic displacement of matter. The flow of heat is governed by the Fourier equation

Where q is the heat per unit time conducted along x direction through a plane of area A normal to this direction, and at a point where the temperature gradient is dt/dx. K is the thermal conductivity with unit Cal/(sec)(cm²)(⁰C/cm). Thermal conductivity is a physical property of the medium through which the heat conduction occurs. Considering k to be independent of temperature, the above equation can be integrated for unidirectional heat flow by conduction in a slab of constant cross section

Where t₁ and t₂ are temperatures at two points whose coordinates are x₁ and x₂ respectively. Replacing t₁-t₂ by Δt, the temperature difference and x₁-x₂ by L, the length of the heat-flow path the above equation can be written as

This expression is analogous to Ohm’s law, I = V/R; hence the quantity can be defined as thermal resistance for a conductor. The temperature difference Δt is analogous to potential difference V.

The convection process occurs due to the macroscopic motion of the medium, and is generally concerned with the transfer of heat across a solid-fluid interface. In free convection, the motion is influenced by the buoyant forces generated in the fluid due to temperature differences within it. In forced convection, on the other hand, the fluid is displaced by mechanical means, e.g., by a pump. The fundamental equation of convective heat transfer for both free and forced motion of the fluid is

Where q is the rate of heat transfer to or from a surface area A_h when the temperature difference is Δt. The quantity h is commonly known as heat-transfer coefficient or unit thermal conductance. The above equation applies to convective heat flow equation in either direction, i.e., from solid to fluid or from fluid to solid; the actual direction of the flow depends, of course, upon the sign of Δt. Rearranging the above equation, we get,

defining 1/hA_h as the thermal resistance of the convective heat transfer. As far as heat transfer is concerned, one can consider thermal circuits consisting of different stages of thermal conduction and convection. Let us first take an example of an infinite slab of finite thickness with no internal heat source (Fig. m3.4).


FIGURE m3.4 Heat conduction in infinite slab with convection boundaries

It is considered that heat is transferred at both faces by convection, and heat transfer coefficients are h_a and h_b respectively. Total thermal resistance of this thermal circuit can be written as¹

where A is the heat flow area and U is the overall coefficient of heat transfer having same dimension of heat transfer coefficient. Rate of heat flow for this system is

or

The idealization of an infinite slab is a good approximation to real (finite) systems. In many cases coolant circuit has cylindrical or components of various other shapes. The simplest coolant circuit for heat-removal in a reactor is the direct-cycle one in which the coolant is passed once through the reactor and then to a sink. Sometimes river water is used as a coolant, and after passage through the reactor it returns to the river, which acts as a sink. In some cases, air is used as a coolant and the atmosphere as a sink. These systems, although simple in principle, are not without problems. River water must be purified before using it as coolant, and provision must be made for preventing the discharge of the radioactive air or water to the surroundings. For better control over the radioactive pollution, a secondary coolant system in conjunction with primary coolant circuit must be used. Heavy water, for example, is a desirable coolant from the standpoint of its nuclear properties, but due to its high cost, a secondary coolant, e.g., ordinary water, is required to transfer the heat to the sink. Finally, steam is produced from hot coolant and is converted to the mechanical energy of the turbine for production of electricity (S8).

Nuclear Engineering

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Basic Design Aspects of a Fission Reactor

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