Introduction
A nuclear reactor is an engineered system for allowing a controlled nuclear chain reaction to take place to provide a source of heat. The level of heat production may be set at any level from almost zero in reactors designed to study reactor physics, to very intense sources of heat for electric power production. Since the fission reaction, which is the basis of the chain reaction and provides the source of heat, was discovered in 1938, there have been an enormous number of reactor designs, most of which have never been built, involving diversity in the form of the fuel, in the heat transfer medium to take heat away from the active region and in the layout of the engineering structures and components. Applications range from electricity production to district heating, from space propulsion to industrial heat, from semiconductor production to medical radioisotopes and from peaceful civilian applications to military weapon material production.
This entry is concerned with applications which generate large amounts of heat and therefore present problems of heat transfer both in normal operation and in upset conditions. The high capital cost of nuclear reactors has tended to push power density to levels as high as possible to optimize the revenue or other benefits of the plant and has necessitated large programs of experimental and theoretical development in heat transfer. The entry will describe the basic elements of reactor physics, describe the most important types of reactor and then list some of the issues of heat and mass transfer which have to be addressed.
Reactor Physics
In boilers using fossil fuel, the heat derives from chemical reactions which involve the electrons in the outer region of the atoms. In a nuclear reactor, the reactions take place within the nucleus of the atoms and the energy release per event is about 2 × 107 bigger than in a chemical reaction such as the oxidation reaction of combustion.
Nuclei can react with neutrons in one of three ways: scatter, capture or fission; it is a question of chance which reaction will occur. The probability of occurrence of each reaction is measured by its neutron cross section which can be thought of as the average diametric area of the nucleus as seen by a traveling neutron. However, these cross-sections are strong functions of the relative velocity between the neutron and the nucleus and have different values for the different types of reaction.
In scatter, the nucleus does not change but its motion may be changed in direction and velocity or in vibrational amplitude and frequency if it is bound in a lattice. At the same time, the neutron velocity and its direction will be changed in a manner analogous to the way in which a billiard ball slows down and changes direction when it collides with another ball. In capture, the neutron is absorbed into the target nucleus, the nucleus increases its mass by one unit and may become radioactive. In the case of absorption into Uranium 238, and after two rapid stages of radioactive decay, Plutonium 239 is formed. This is called breeding since fissile isotopes (those capable of undergoing fission) are produced to replace those being used up in fission. Isotopes which can be used for breeding are called fertile isotopes and the most important ones are Uranium238, giving Plutonium 239, Plutonium 240 giving Plutonium 241 and Thorium 232 giving Uranium 233. Neutrons can be captured to some degree by almost all the materials which go to make up the reactor as well as in the fuel materials.
In fission, the target nucleus absorbs the neutron and then splits into normally two unequal size pieces, the fission products. The two pieces move apart at high velocity and it is this kinetic energy which provides most of the nuclear heat. In addition, between two and three neutrons are emitted at high velocity from the fission process. These take part in further neutron reactions including fission, and hence a chain reaction can occur. If on average one, and only one, neutron leads to a further fission, the reactor is said to be in a steady state at constant power. If there is not a perfect balance, the power level will either increase or decrease and a balance is established by moving absorbers into the reactor core or by adjusting the net leakage of neutrons from the core. A reactor in which the balance is maintained at a constant level is said to be critical.
Only isotopes of Uranium, Plutonium and other higher man-made isotopes are able to support fission. Properties of the most important fissile isotopes are given in Table 1. Cross-sections are given both for thermalized neutrons (2200 m/s), appropriate for thermal reactors and for fast neutrons, appropriate for fast reactors.
Table 1. Cross section in barns (10−28 m2) and neutron yields of fissile isotopes for both thermal and fast reactors
Neutrons are emitted from the fission process with an energy of about 2.5 MeV. In the fissile isotopes, the cross-section for fission is highest at the low neutron energies typical of neutrons scattering in thermal equilibrium with the surrounding atoms. Hence materials called moderators are provided within the lattice to slow the neutrons down by elastic scatter. The most effective moderators are those having nuclei with a low mass to maximize the energy loss per collision, with a high cross-section for scattering and with a low cross-section for absorption to avoid excessive neutron losses. The most suitable ones are hydrogen in the form of water, deuterium in the form of heavy water, carbon in the form of graphite and beryllium. Table 2 gives data on the key properties of moderators. The moderating ratio is the ratio of energy loss to absorption and should be high. Light water is not the best moderator in this sense but it has been used more than the others because of its ready availability and low cost.
Table 2. Moderator properties
Criticality in a reactor is a question of obtaining a balance between fission, absorption and leakage from the sides of the reactor core. Increasing the size of the reactor decreases the surface area to volume ratio and hence reduces the fraction of neutrons which leak out compared to those that undergo fission or absorption in the volume of the core. From this is derived the concept of critical size.
Fission and absorption are accompanied by very high radiation levels from which people and equipment have to be protected by massive shielding. Radiation also causes structural materials to become radioactive and causes radiolasis in water. The gases from the latter may have significant effects on heat transfer.
Fast and Thermal Reactors
The use of moderators reduces the neutron energy to levels where the fission cross-section is very high. One of the consequences of this is that the amounts of fissile isotopes as indicated by their enrichment can be quite low (few %). A critical reactor in which all reactions take place at high neutron energies can still be obtained if the enrichment is high enough. Such a reactor is known as a fast reactor since fission takes place before thermalization; fast reactors are built without moderator. The advantage of this mode of operation is that the number of neutrons from each fission is higher than in low energy or thermal fission and a higher proportion of the spare neutrons can be absorbed in fertile materials. More fissile material can be produced than is burnt in fission; the stock of fissile material for use in further reactors increases with time and is recovered by reprocessing. Since this allows for ultimate use of the fertile U238, which constitutes 99.3% of uranium mined from the earth, the potential power production per tonne of uranium ore can be increased by a factor of over 60 by use of fast reactors as compared to thermal reactors.
In the early stages of development of the nuclear power program, the benefits of breeding were thought to be so important that reducing the doubling time, the time taken to produce enough surplus-bred plutonium to allow the commissioning of a second fast reactor, was a prime design consideration. This called for compact reactor cores with a very high power density. To cope with the heat transfer requirements without introducing significant moderation, liquid metals (usually Na, Na/K and in some proposals Pb or Bi) have been used as coolants.
Main Reactor Types
Fuel
In most reactors, the fuel elements are in the form of metallic tubes filled with fuel material either in the form of metal rods or ceramic pellets. The most common ceramic is uranium dioxide or a mixture of uranium and plutonium oxides. Other ceramics are nitrides and carbides. Ceramics were chosen in preference to metallic forms because of their superior properties under irradiation, particularly in their dimensional stability. They do, however, have the disadvantage of low thermal conductivity, resulting in high center temperatures, and high specific heat resulting in a large amount of stored energy which can produce problems in some emergency loss of coolant conditions.
High temperature gas cooled reactors have all-ceramic cores. The fuel is in the form of small (approx. 0.5mm) spheres coated with layers of graphite and silicon carbide. These spheres are normally embedded in a graphite matrix which in turn is moulded into rods or spheres and covered in a further layer of graphite.
Water cooled reactors
These are the most widely adopted designs for power production with over 400 in operation in 1994. Ordinary water is used as both moderator and coolant and the same water serves both purposes. From Table 2 it is seen that the absorption cross-section of water is relatively high compared with the other moderators and this leads to a close spaced lattice of fuel rods to reduce the water content. High water velocities are required to remove the heat. Typical fuel rods have a diameter of around 10 mm with UO2 pellets in a cladding of Zircaloy, an alloy of zirconium.
There are two forms of water reactors, Boiling Water Reactors (BWR) and Pressurized Water Reactors (PWR). BWRs operate at a pressure of 7 MPa and generate steam by boiling within the reactor core. The core is contained within a steel vessel which also contains steam separators and dryers in its upper region. Steam passes directly to the turbine. Water may circulate through the core by natural circulation, or, more usually be directly or indirectly pumped. Some designs, for example, have jet pumps around the core which are driven by high pressure pumps taking only a fraction of the total core flow outside the vessel.
In a PWR, the pressure is raised to 15 MPa by an electrically heated pressurizer to prevent boiling in the reactor core at its operating temperature of around 310°C. Water is pumped into the pressure vessel, down an annular downcomer, up through the core and out to a steam generator. The latter may be of the inverted U-tube type or be a once-through steam generator. Variants of the PWR may be of the integral type with the steam generators and pumps, if provided, within the pressure vessel.
Water reactors are provided with safety systems designed to prevent overheating of the core and release of radioactive material from the core, in case of reasonably conceivable accidents short of failure of the main pressure vessel. In the unlikely event of failure of one of the main coolant pipes in a PWR, for instance, most of the core water inventory could be lost in a few seconds. Large accumulators are provided to reflood the core before it overheats. There are also pumped systems designed to supply sufficient water flow to the vessel at high and low pressure. To provide adequate reliability allowing for failure of these systems to operate on demand, they are duplicated up to four times to provide redundancy. Analysis of heat and mass transfer during emergency conditions presents some very challenging problems.
Demonstrable safety requires that consideration is given to failure of all the safety systems. A Containment structure is provided to contain the steam released from the most serious possible failure of the pipe systems and to contain the fission products which may be released from overheated fuel. These are large buildings, in some cases (particularly for BWRs and some integral PWRs) provided with a pressure suppression system, and with further provision for the ultimate removal of heat. Many designs, particularly the smaller ones, make use of natural convection and heat conduction to avoid the need for reliable redundant emergency electricity supplies.
Gas reactors
Gas reactors have a graphite moderator and use gas for heat removal to a steam generator normally of the once-through type. Most of the operating gas cooled power reactors are in the UK. The early ones use a finned Magnox cladding and CO2 coolant. The natural uranium fuel is in the form of metal rods 2.5 cm in diameter. Graphite has a small neutron absorption cross-section but the atoms of carbon are less efficient than the hydrogen in water for neutron slowing down. The spacing between each fuel element is about 20 cm with a 10 cm channel for coolant. The Advanced Gas Cooled Reactor (AGR) is a later design still using CO2 but at a temperature permitting the production of superheated steam at a temperature and pressure typical of modern coal fired plant. This requires the use of stainless steel cladding and enriched ceramic fuel. The fuel element is in the form of a cluster of pins of smaller size than the Magnox reactors and the cladding is ribbed to improve heat transfer.
A further advance in gas reactor technology is the High Temperature Reactor (HTR). The coolant gas is Helium and the fuel is the all-ceramic type described above. It is possible to reach temperatures of 950°C enabling HTRs to be used as a heat source for some high temperature industrial processes.
Heavy water reactors
These usually have heavy water moderator and usually use a separate flow of heavy water as coolant. The properties of heavy water permit the use of natural UO2, clad in Zircaloy as fuel. The fuel bundles and coolant are contained in an array of pressure tubes insulated from the main body of the moderator by a gas gap and a second tube known as the calandria tube. There are header arrangements at each end of the pressure tubes which are normally horizontal. There are systems for the injection of water in emergencies. There is a second heavy water reactor type which has boiling light water coolant with vertical calandria tubes. Steam is separated from the circulating water in a steam drum and then passes directly to the turbine.
Water cooled graphite moderated reactors
Like the heavy water reactors, these are pressure tube reactors. The pressure tubes are vertical and very long. Boiling takes place within them and there are large external steam drums. The stations which have been built do not have a containment structure but do have a pressure suppression pool underneath the reactor itself.
Fast reactors
These use highly enriched fuel and, in most designs, liquid metal coolant. This allows them to operate at near atmospheric pressure, eliminating many of the problems of pressurized loss of coolant accidents which have to be considered in other designs. There are both loop type and integral type designs in which the core, the coolant pumps and the primary heat exchangers are contained in a single vessel filled with liquid metal. Since it is undesirable for there to be any chance of water interacting with the primary coolant in the event of a steam generator leak, there is an intermediate heat transfer loop to link the primary heat exchangers with the steam generators using liquid metal as the heat transfer medium.
Other reactor concepts
Over the years of reactor development, there have been a very large number of combinations of fuel type, coolant, moderator, pressure vessel or pressure tube, operating temperature and pressure and power output. Reactors have been designed for use on land, to power ships and submarines and in space to provide electric power as well as to provide the driving force for rocket propulsion. There have been reactors operating with a liquid salt fuel, which was directly pumped to a heat exchanger, and reactors with gaseous fuel for use in space.
Heat and Mass Transfer Issues—Normal Operation
In normal operation, the prime concern is to remove the heat generated from the fuel with a margin for failure large enough to allow for expected transients in the local power level. Excessive margins result in economic penalty through the provision of, for example, unnecessary pumping power or unnecessary downrating of the plant. Failure means failure of the fuel cladding by melting, chemical reaction with the coolant or physical weakening of the material. A good knowledge of the heat transfer coefficient under all operating conditions, coupled with an ability to calculate the resulting fuel and cladding temperature including the effects of the gap between the fuel and the cladding, is required. The gap clearance changes with irradiation due to dimensional changes in the fuel and cladding and due to the build up of fission product gases within it, which changes its conductivity. With liquid coolants, it is necessary to avoid a crisis in heat transfer associated with the phase change to vapor. In nonboiling systems, this is the point of departure from nucleate boiling (DNBR) and in boiling water reactors it is the critical heat flux (CHF) in both cases where the cladding surface becomes dry and is only cooled by water vapor as opposed to water or a water/steam mixture.
Heat and Mass Transfer Issues—Emergency Conditions
It is necessary to determine what would happen to the reactor, and particularly to its fuel, in the event of failure of the heat transfer systems, whether by electrical failure or by mechanical failure of equipment or rupture of the piping. Failure of large diameter pipes, such as the main coolant ducts in a PWR which have a diameter approaching 1m, results in massive turbulence and rapid ejection of much of the primary coolant. In making the reactor safety case, it is normally assumed that all the fluid is ejected, a very pessimistic assumption that may lead to over-design of safety injection systems. Following the cooling which occurs during this rapid Blowdown phase, the fuel may dry completely and experience a rapid heatup from the decay heat. Subsequent introduction of water causes the fuel to quench with an advancing quench front along its length. Efforts are being made (through 1994) to develop the methods and supporting data needed for a best estimate approach, rather than a pessimistic one. The calculation problem in gas reactors is less severe since there is no phase change.
Prolonged failure of the coolant systems may allow the fuel to melt and form a molten pool, either within the reactor vessel or piping system or below it, having melted through the vessel wall. This introduces new issues in heat transfer as water is introduced to cool the molten pool. There will also be release of gaseous fission products and radioactive aerosols which are carried through the duct systems by steam flows and will be deposited at various points within the reactor vessel and piping and, for the material which escapes through the rupture, within the containment. It is important to know how much of this material is available from any possible failure in the containment system.
