12.106. Before considering fission product transport, mention should be made of the physical barriers in reactor systems to the escape of radio­activity. The first barrier is the fuel material itself, which in the case of uranium dioxide retains the solid fission products and inhibits release of the volatile radionuclides. The fuel rod cladding is the second barrier. During service, the cladding does develop small pinholes and cracks, which allows some radioactivity to escape into the cooling water. The third bar­rier, the primary coolant system boundary, contains the normally small amount of radioactivity in the circulating coolant, which is continuously monitored. The final physical barrier is the containment structure. How­ever, as we discuss shortly, certain chemical and physical processes along the transport path also inhibit the fission product release.

8.42. Standards and codes have played an important role in engineering practice for many years. The American Society of Mechanical Engineers Boiler Code had its beginnings in the nineteenth century, for example. Presently, a large body of standards developed under the auspices of the respective engineering professional societies, including the American Nu­clear Society, are coordinated by the American National Standards Insti­tute (ANSI). However, the American Nuclear Society maintains the In­formation Center on Nuclear Standards (ICONS) for all nuclear standards, including those developed by other societies.

Federal regulations, guides, and periodicals

8.43. A great deal of technical information is provided in the regulatory literature. Title 10 of the Code of Federal Regulations (10 CFR) is devoted to nuclear energy and consists of a number of parts. For example, Part 20 (10CFR20) deals with the standards for protection against radiation. The various parts of the Code of Federal Regulations, which have the force of law, are supplemented by Nuclear Regulatory Guides. These are advisory and are coordinated in some cases with engineering society standards and codes. There are several hundred published guides divided into ten cate­gories. They are revised periodically.

8.44. The U. S. Department of Energy publishes several periodicals and newsletters. For example, Nuclear Safety is a technical progress review issued four times per year.

Introduction

9.109. Since energy must be removed from the core by the flow of the coolant, some well-known flow fundamentals are reviewed here. We re­strict our attention to semiempirical methods that have been used for many years to solve practical problems. In a fluid flowing in a pipe or “channel,” shear forces between fluid particles and the wall and between the particles themselves result in friction that must be overcome by pumping. Hence, we will first examine the flow pressure drop.

10.36. The design procedure for a reload batch of fuel assemblies should accomplish the general objective of achieving minimum energy-generating costs within licensing and utility planning constraints. In practice, the re­sponsibility for the several aspects of the design process may be divided among several groups. For example, in a typical utility, one group may have the primary responsibility for plant scheduling, including refueling outages, and establishing energy generation requirements. Fuel procure­ment and economic analysis are likely to be the responsibility of a second group, while in-core nuclear analysis and reload assembly design would be accomplished by a third group.

10.37. Initially, a preliminary core reload design is prepared by the third group to meet cycle energy needs that have been specified by the first group and economic guidelines provided by the second group. In this preliminary step, which is likely to involve all three groups, the batch size and enrichments are selected. After agreement, subsequent analyses and design are pursued primarily by the third group. We will concentrate on the activities of this third group.

11.15. Various regulations limit allowable exposure from reactor ef­fluents and from waste packages. For example, in 10 CFR 50, Appendix I, to meet ALARA program (§6.63) objectives, the annual above-background dose or dose commitment from liquid effluents in unrestricted areas from all pathways of exposure is limited to 3 mrem to the total body or 10 mrem to any organ. The gaseous effluent total body annual dose limit is 5 mrem. Radioactive iodine is particularly important with the annual dose or dose commitment from it or particular deposits limited to 15 mrem to any organ of a person in an unrestricted areas. Note that ALARA guidelines are more restructive than exposure standards, as given in §6.67.

11.16. Radioactive exposure regulations also limit the concentration of radionuclides in gaseous and liquid effluents at the outer boundary of the plant site, that is, the limit of public access. These are listed in 10 CFR 20, Appendix B, and may be considered as the maximum permissible con­centrations (MPCs). They take into account the manner of entry of each radionuclide into the body, the biological and radioactive half-lives, and the dose effects. The concentrations have been calculated to be consistent with the dose limit of 0.1 rem/yr for members of the public that was established in 1991.

11.17. Rules for controlling radioactive materials in effluents are es­tablished both by the NRC and the Environmental Protection Agency (ЕРА). EPA regulations are found in Title 40 of CFR. For example, 40 CFR 190 limits the dose from the uranium fuel cycle to the public to 25 mrem/yr. Licensing requirements for land disposal of radioactive wastes are given in 10 CFR 61. However, it should be recognized that such values change with time. Therefore, current references should be consulted.

Introduction

12.32. The purpose of the engineered safety features is to prevent or limit the escape of radioactivity to the environment in cases of a highly unlikely transient or accident that is too severe to be accommodated by the reactor protection system alone. The major engineered safety features are: (1) the emergency core-cooling system to supply water to the reactor core in the event of a loss-of-coolant accident, (2) the containment vessel (or structure) to provide a barrier to the escape to the environment of radioactivity that might be released from the reactor core, (3) the cleanup system for removing part of the radioactivity and heat that may be present in the containment atmosphere, and (4) hydrogen control to prevent for­mation of an explosive hydrogen-oxygen (air) mixture in the containment.

12.130. The modeling of various aspects of reactor system behavior is the objective of a large number of safety-related computer codes. Also, by assembling specialized codes into related modules, it is common practice to provide a description of system behavior following a spectrum of dis­turbances and accidents of varying degrees of seriousness. Since modeling methods are continually being updated and many are proprietary, our primary purpose here is to provide orientation and describe some typical approaches.

12.131. Modeling methods may be classified by their intended appli­cation.

1. Licensing requirements. Licensing codes, which are primarily thermal — hydraulics in nature, confirm the protection provided by LWR emergency core cooling systems.

2. Modeling as an integral part of design procedures. Design codes provide “best estimate” or “realistic” predictions. They, too, normally model thermal — hydraulics behavior, although some deal with containment response.

3. Severe accident analysis. Analysis complements risk assessment and source term development activities.

Many codes, particularly those in the second category, have been de­veloped by reactor vendors and are proprietary. Others have been devel­oped with government or utility support. Some codes serve more than one application. Each of these general modeling categories are considered in the following sections.

9.28. Heat transmission by convection, which is usually concerned with the transfer of heat across a solid-fluid interface, involves macroscopic motion of the fluid. In free convection, the motion is a consequence of the buoyant forces generated in the fluid due to temperature differences within it. In forced convection, on the other hand, the fluid is moved by mechanical means, e. g., by a pump. When applied to heat removal in reactors, two aspects of convection heat transmission must be considered; there is, first, transfer of heat from the material which is being cooled, e. g., the fuel element, to the coolant; and, second, the transport of this heat, usually in sensible form, by flow of the coolant from one point in the system to another. Fluid flow is thus an important problem, as will be seen later, in the study of reactor cooling systems.

9.29. The fundamental equation of convection heat transfer, for both free and forced motion of the fluid, is the so-called Newton’s law of cooling, which may be written as

q = hAhAt, (9.9)

where q is the rate of convection heat transfer to or from a surface of area Ah when the temperature difference is At. The quantity h, defined by equation (9.6), is commonly called the heat-transfer coefficient and is ex­pressed in units of W/m2 • K. It should be noted that equation (9.9) applies to convection heat flow 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 At.

9.30. Although the value of h is dependent upon the physical properties of the fluid medium, it is also a function of the shape and dimensions of the interface, and of the nature, direction, and velocity of the fluid flow. Thus, the heat-transfer coefficient is a property of the particular system under consideration. Another factor which determines h is the exact def­inition of At, i. e., the temperature difference between the surface and the fluid. Whereas the surface temperature of the solid is uniquely defined, that of the fluid is subject to several arbitrary definitions. The latter is usually taken as the “mixed-mean (or bulk) fluid temperature” tm given by

where p, cp, and v are the density, specific heat, and flow velocity, re­spectively, of the fluid, and Af is the cross-sectional (or transverse) flow area of the fluid. The value of the heat-transfer coefficient in any given circumstances can be determined experimentally, but for design purposes, the general practice is to use results predicted by means of various theo­retical and semiempirical expressions (see §9.78 et seq.).

9.31. By slight rearrangement, equation (9.9) can be written in the Ohm’s law form

l/hAh

so that, as before, q and At are analogous to current and potential differ­ence, respectively, but VhAh now represents the thermal resistance to convection-heat transfer. Thermal circuits can thus be constructed with one or more stages of thermal conduction combined with convection for the solution of problems involving both types of heat transfer, as will be shown in the succeeding paragraphs.

9.138. In order to provide a basis for reactor design, certain operating conditions, averaged over both the volume and lifetime of the core, must first be specified for the reactor to operate at the desired power level. In principle, the appropriate core specifications, such as number, dimensions, and arrangement of the fuel rods of a given type, coolant-flow rate, tem­perature distribution, etc., could then be computed to meet the require­ments. In practice, however, the situation is complicated by the fact that the ideal specifications cannot be met precisely. For example, the dimen­sions, density, and enrichment of the uranium dioxide fuel pellets may vary slightly, and so also may the dimensions and spacing of the rods and the thickness of the cladding. Consequently, the actual heat flux, temper­ature, and other parameters at various locations in the core may differ considerably from the specified (or nominal) values.[13]

9.139. A fundamental requirement in reactor design is to ensure that, in spite of such unavoidable variations from average values which are inherent in reactor design, e. g., nonuniform neutron flux distribution, there shall be no point in the core where certain limiting parameters are exceeded during operation under normal conditions. Two important limiting oper­ating parameters (or constraints) are the critical heat flux (§9.98) and the fuel temperature.1 A critical heat flux, even locally, can result in a boiling crisis accompanied by an increase in surface temperature, which could lead to cladding failure.

9.140. A principle that has been useful in reactor design is to relate the nominal (or average) performance to the maximum value that can be expected anywhere in the core. To this end, each of several relevant design specifications is assigned an adjustment or correction factor which repre­sents the ratio of the maximum to average values of such parameters as heat flux, coolant-flow rate, and enthalpy rise that would result from the most probable variations in the given specifications. The various factors are then combined in a suitable manner to yield the overall ratio of the maximum to average values of a particular operating parameter. The con­straints mentioned must then apply to the maxima determined in this manner.

10.73. The conditions under which breeding is feasible will be developed shortly, but for the present it is sufficient to state that a breeder will usually consist of a core, containing both fissile and fertile species, surrounded by a blanket initially containing only the fertile species. Fissile nuclei are then produced from the fertile nuclei in the core and also in the blanket by neutrons which have escaped from the core.

10.74. Bearing the foregoing in mind, the breeding ratio defined by equation (10.10) can be represented by

І ф2?г1і1е dV + І ф2£егШе dV

. J core./blanket

BR (at a given time) = ————- ^———————————— , (10.13)

ф(2г + 2c)fissile dV

J core

where and are the macroscopic fission and capture cross sections, respectively, for the indicated species, and dV is a volume element. (The destruction of fissile nuclei in the blanket is neglected.) By integrating over the core and blanket volumes, the breeding ratio is an average over the whole reactor system. It is to be understood that the neutron spectra are different in the core and blanket systems. As noted earlier, equation (10.13) refers to a particular time, at which the values of ф and S are applicable.

10.75. It will now be assumed that all the neutrons leaking from the core will eventually be utilized for breeding by capture in the blanket. This assumption is fairly reasonable since some neutrons are formed by fission in the blanket to compensate for neutrons lost in parasitic (nonbreeding) processes and by escape. If the total breeding ratio is divided into two

since T) is equal to v/(l + a) by equation (2.57).

10.76. The fission cross section ratio does not vary significantly with neutron energy; hence, an indication of the effect of neutron energy on the potential for external breeding (or conversion) is given by the corre-

sponding value of r| — 1. Approximate data for several energy ranges are quoted in Table 10.1, and general trends (omitting fine structure) are shown in Fig. 10.8. It is seen that only in a comparatively fast neutron spectrum (>0.1 MeV) is t) — 1 sufficiently greater than unity to make plutonium — 239 breeding practical. Breeding of uranium-233 from thorium-232 should be theoretically possible, although with a smaller efficiency, in a thermal spectrum as well as in a fast spectrum.

10.77. The internal (or core) breeding ratio is given by

ф^егШе dy

where 1/(1 + a) = t]lv by equation (2.57). It is seen from Table 2.9 that the highest values of ті/v arise in a fast-neutron spectrum for all three fissile species. Hence, the internal breeding ratio is largest in such a spectrum. Apart from its contribution to the total breeding ratio, internal breeding has an important bearing on fuel-cycle costs since fissile material produced in the core can be utilized directly without the necessity of going through reprocessing and fabrication stages. It is apparent from equation (10.15) that the internal breeding ratio for a given fertile-fissile nuclide system depends on the core composition, since this determines the macroscopic cross-section ratio. For example, an increase in the ratio of fertile to fissile atoms in the core would lead to an increase in the internal breeding ratio. There is a general decrease in breeding ratio as the core is diluted with inert material because of spectral softening which results in a greater par­asitic capture of neutrons in inert diluents.