9.82. Heat transfer to gases is treated in much the same way as for ordinary fluids such as water, and convection heat-transfer coefficients can be predicted by means of the correlation in equation (9.36). For many gases, including helium, carbon dioxide, and air, Pr is approximately 0.70, and so equation (9.36) reduces to

Nu — 0.020Re0 8.

The marked differences in physical (especially thermal) properties result, however, in some important general differences in heat-transfer behavior between gases and liquids. For example, the thermal conductivity of helium gas at atmospheric pressure is only about a third that of water although it is enhanced by an increase in pressure. In considering the transport of heat away from the heated surface by the fluid, the specific heat of the latter is important. Here again, an increase in the gas pressure is advantageous; there is a density increase accompanied by a corresponding increase in the heat capacity per unit volume.

9.83. In so-called high-speed flow, where the gas velocity is greater than about 0.2 that of sound (§9.129), certain special effects occur that influence the temperature driving force for convection heat transfer. For example, “aerodynamic heating” results from the frictional effects in the boundary layer, and kinetic energy considerations (stagnation effects) lead to a dif­ference between flowing and “at rest” conditions. For such matters, heat — transfer texts should be consulted [7].

10.12. Following enrichment, the uranium hexafluoride is shipped to the plant of a fuel assembly vendor, where it is converted on-site to oxide. Fuel fabrication is a highly automated process with the need for close quality control to meet exacting specifications. Uranium dioxide powder having the proper characteristics is first prepared, then formed into pellets using ceramic techniques. Adherence to close dimensional tolerances is obtained by grinding. They are then inserted into clad tubing which had been previously prepared. The various components making up the finished fuel assembly (§§7.168, 13.23) are then brought together using standard fabrication procedures.

10.109. An extensive program of safeguards has been established in the United States to prevent the theft of “special nuclear material” defined as plutonium, uranium-233, or uranium enriched in uranium-235, and partic­ularly of “strategic” special nuclear material, consisting of plutonium, ura­nium-233, or uranium enriched to more than 20 percent in an amount equivalent to more than 5 kg of uranium-235. The importance of the latter lies in the fact that it could be used for the illicit production of a nuclear explosive. The safeguard regulations apply to all stages of the fuel cycle, including fuel fabrication, power generation, fuel reprocessing, storage, and transportation. Broadly speaking, however, two situations are consid­ered: material at fixed sites and material during transportation.

10.110. At fixed sites, special nuclear material must be held within a “protected area” with multiple physical barriers. Access to the area is controlled and unauthorized entry is prevented by monitoring systems with alarms. Continuously operating communication systems provide contact with local law-enforcement authorities.

10.111. During transportation, special nuclear material is probably more vulnerable to diversion than at any other time. All shipments, which may be by road or rail, must be accompanied by armed guards, and regular communication must be maintained with the shipper of the material. Trans­portation of special nuclear material could be minimized if nuclear reactors, fuel fabrication plants, and spent-fuel reprocessing facilities were in close proximity. However, single fuel fabrication and reprocessing plants would meet the requirements of more reactors than are likely to be constructed in a particular area. Consequently, even under the best conditions, some transportation of special nuclear material could not be avoided.

10.112. Additional protection against the diversion of special nuclear material is provided by a comprehensive program of internal material con­trol and accounting. This program is designed to detect any loss and to take timely action should such a loss occur. In the United States, the Nuclear Regulatory Commission operates an inspection and enforcement program which includes supervision of material control and accounting. Although the overall costs of the safeguards program are substantial, they are expected to increase the cost of nuclear power by no more than a few percent.

10.113. The International Atomic Energy Agency (IAEA) conducts a broad safeguards program to enforce adherence to the Treaty of the Non­proliferation of Nuclear Weapons (NPT) which has been signed by over 100 nations. An inspection program features accountancy, containment, and surveillance. Material accountancy utilizes various sophisticated in­struments to assay the amount of fissile material present to supplement ordinary “bookkeeping.” “Containment” includes various measures such as locks and seals to assure that material has not been tampered with between inspections. By “surveillance” is meant an inspection program to keep track of material flows.

12.3. The prevention of the release of harmful amounts of radioactivity beyond the site boundaries has become the most important objective in the design and operation of nuclear power plants. Although our indus­trialized society has become accustomed to other types of hazards, a public sensitivity to the effects of radiation has played a strong role in the ac­ceptability of nuclear power plants. This has been so although the actual risks to public health have been substantially less than those from the burning of fossil fuels [1].

12.4. The present generation of nuclear power plants in the United States and many other countries now have numerous design features that make the risk of harmful accidental release of radioactivity to the public extraordinarily low. These features have evolved not only through con­servative design, but also by continued analysis and research on the nature of postulated accidents. The design and operation of nuclear power plants are also strictly regulated to assure public safety. In fact, regulatory re­quirements have an important role in establishing the level of safety or risk that is acceptable. Therefore, throughout this chapter, we will mention relevant regulatory considerations, as appropriate.

12.5. In the United States during the 1970s, the ordering of new nuclear power plants ceased, primarily because of economic factors and uncertainty regarding long-time regulatory requirements. A contributing economic fac­tor was the added cost of many new safety-related features. In addition, public acceptance was eroded by the Three-Mile Island accident in 1979, and further reduced by the Chernobyl accident in 1986. Since there will be a need to construct new plants to meet energy requirements, substantial efforts have been made during recent years to develop advanced “next — generation” designs that will have passive safety features and be economical to construct. Improvements in regulatory procedures have likewise re­ceived attention.

12.6. Our purpose in this chapter is to describe the many aspects of reactor safety, including accident analysis. Design features can best be understood in light of postulated accident scenarios. Also, with this back­ground, the advantage of future plant passive features can be examined.

12.110. The fission product elements react chemically with each other and with other substances during the course of an accidental release from the fuel. These reactions affect the transport characteristics of the radio­nuclides that concern us. A starting point is to consider the reactor fission product inventory, which consists of nearly 40 different elements. Various tabulations and computer codes such as ORIGIN-2 [8] are available to provide these data. However, it is important to remember that chemical reaction rates depend on the amount of element present, not just the amount of a radioactive isotope. Therefore, the inventory must include all the isotopes. A typical PWR element inventory is given in Table 12.1. Based on their reactivity with oxygen, it is convenient to classify the elements into eight groups: the noble gases, halogens, alkaline earths, tellurium, noble metals, rare earths, elements with refractory oxides, and stable fis­sion product elements.

12.111. The general chemical behavior of the elements in the various groups as they occur in the fuel, in the water coolant of a LWR, and in the containment is summarized as described below.

9.4. As background for the thermal-hydraulics aspects of reactor design, it is helpful to consider the path of energy transport from the thermody­namic viewpoint. In a nuclear power plant, heat flows from the fuel ele­ments to a coolant, then perhaps to a secondary coolant, as in a PWR, to form steam. Work is done by expanding the steam in a turbine. The turbine exhaust steam is then condensed and recycled. Heat extracted during the condensation process is rejected to the environment. Thus, we have a movement of energy from the heat generation at high temperature in the fuel elements progressively downward on the temperature scale until the environment is reached. Along the way, a portion of the original energy is converted to useful work by a steam expansion in the turbine that is almost thermodynamically reversible. However, at each heat flow step, an irreversible temperature “drop” is needed to accomplish the heat transfer at a practical rate. As we shall see, this temperature difference acts as the driving force for the thermal transport rate process.

9.5. The thermodynamic efficiency of the conversion to work is im­proved if the heat input from the steam to the turbine is at as high a temperature as possible and the heat rejection in the condenser is at as low a temperature as possible. Since the “high” temperature in a water — cooled reactor is usually limited by materials and pressure considerations, and the “sink” or rejection temperature by environmental and other fac­tors, the irreversible temperature “drops” required for heat transfer be­tween these two limits must be expended carefully by the thermal system designer.

Design Methods

9.6. Engineers have used design methods describing the transfer of heat and the movement of fluids for many years. In a typical reactor core, the transport of heat from the fuel to the moving coolant involves the traditional processes of conduction and convection. Further steps in the thermody­namic energy path described above also involve the behavior of fluids in motion, particularly the effects of a second phase, as is produced by boiling. Over the years, a substantial body of literature has been developed de­scribing the principles relevant to thermal system design. Early, largely empirical design methods have been supplemented by models having some theoretical basis. Finally, the general availability of powerful computers has made a reasonably sophisticated description of transport processes practical for design purposes.

9.7. Since it is not our purpose here to treat the principles of conductive and convective heat transfer from the beginning, readers who have not been introduced to this area are advised first to consult an elementary text. Of importance is the concept of a rate process and the role of a mathe­matical representation of the conservation of mass, energy, and momentum in the description of such processes. With this background, we are then able to introduce the highlights of nuclear reactor thermal-hydraulics. Dis­cussions of sophisticated analysis methods are beyond the scope of this book but are available in standard sources [1].

9.8. Our objective here is merely to provide a picture of energy trans­port considerations in a reactor system using simple analysis methods. Such methods may be useful for preliminary design or scoping, but appropriate computer codes are needed for subsequent more detailed design. However, it is important to recognize that every method has a level of confidence or range of error that should be identified by the user.

9.116. In a flowing fluid there will be changes in pressure due to changes in velocity resulting from gradual or abrupt changes in flow area. Such pressure changes are usually considered in terms of the velocity head, defined as u2/2; the pressure corresponding to a head H is essentially equal to Яр.[9] Since u2 is generally high for turbulent flow, the pressure losses accompanying changes in cross-sectional area of fluid conduits may be very significant. In general, for abrupt expansion (Fig. 9.16A) or contraction (Fig. 9.16B), the pressure change Дp due to the loss of head ДЯ, which occurs in either case, can be represented by

q//Z

Д/7 = pAff(expansion) = Ke —^ Д/7 = pAtf(contr action) = Kc^-,

where ux and u2 are the upstream and downstream (smallest pipe) veloc­ities, respectively; the value of К, the loss coefficient, depends on the conditions.

9.117. For abrupt expansion,

where Dx and D2 are the pipe diameter upstream and downstream, re­spectively. For expansion into a large reservoir, D2 is large, and Ke becomes virtually unity. The loss of head is then almost equal to ul2.

9.118. For abrupt contraction, the value of Kc varies with the ratio D2!Dl in the following manner:

D2!Dx 0.8 0.6 0.4 0.2 0

Kc 0.13 0.28 0.38 0.45 0.50

For the case of inlet from a very large reservoir, D2IDl approaches zero, and Kc is then approximately 0.5; the corresponding loss of head is u2/4. It should be understood that these results apply only to cases of abrupt expansion or contraction. The loss of head decreases if the fluid exit is rounded, making the change less abrupt. Where the exit is tapered so that the included angle is 7° or less, the losses will usually be negligible.

Example 9.9. Estimate the pressure loss due to contraction and ex­pansion of coolant as it enters and then leaves a channel between the fuel rods considered in Example 9.8.

The coolant undergoes sudden contraction and expansion as it enters and leaves the channel, respectively, from or to a header or manifold of large cross section. The loss of head upon entering the channel, i. e., upon contraction, may then be taken as 0.5u2/2, where u2 is the velocity of the coolant in the channel. Similarly, upon leaving the channel, the loss is ujl2, where ux is also the velocity of the coolant in the channel. The total loss of head upon entry and exit is thus 1.5w[10]/2, where и is the velocity of the coolant in the channel, i. e., 5.40 m/s (Example 9.8). The pressure loss is equal to the loss of head multiplied by the density of the coolant; hence,

Pressure loss =
(1.5)(5.40)2(691)
= 1.5 x 104 Pa.

9.119. Additional contraction and expansion losses are introduced in the flow channels between long fuel rods by spacer grid assemblies which support the fuel rods at intervals along their length. Loss coefficients for such a special geometry can best be determined by experiment. However, for an order of magnitude estimate of the effect, a loss of one velocity head for each spacer grid may be assumed to account for both contraction
and expansion. The pressure loss is thus roughly pw2/2 per grid. In Examples 9.8 and 9.9, the loss for six grids would be about 6 x 104 Pa.

9.120. Losses in pipe fittings, due to changes in direction, e. g., in el­bows, curves, etc., or to contraction in valves, can also be expressed in terms of the velocity head, e. g., Кги2/2. The factor Kx may range from 0.25 or less for a gradual 90° curve or a fully opened gate valve, to 1.0 for a standard screwed 90° elbow, or as high as 10 for a fully opened globe valve.[11]

10.44. A number of considerations are clear to the experienced reload core designer. Although some of these have previously been mentioned, a summary here may be helpful. The feed batch size, cycle length, and discharge burnups are related by material balance requirements as illus­trated in Example 10.1.

Example 10.1. A PWR rated at 3000 MW(th) has a core consisting of 193 assemblies, each containing 450 kg of uranium (as oxide). If a plant capacity factor[17] of 0.8 is assumed, approximately what fraction of the core must be discharged per year if a burnup of 30 GW • d/t is achieved? Staggered batch loading is used.

Energy generated per year = (3 GW)(365)(0.8) = 876 GW • d

Reactor inventory = (193)(0.45) = 87 tonnes U

Energy generated per reactor inventory before discharge

= (30)(87) = 2610 GW • d

Core lifetime = —— = 3 years 876

If an annual refueling is assumed, one-third of the core would be discharged each year. For a 12-month operating cycle yielding a burnup of 10,000 MW • d/t (864 GJ/kg), should the discharge burnup be increased from a nominal 30,000 MW • d/t to 40,000 MW • d/t, the feed batch size would be reduced from one-third to one-fourth of the total core assemblies.

10.45. The feed enrichment must be high enough to provide the reac­tivity needed for the planned burnup cycle length. However, when de­signing a loading pattern, careful management of the fresh fuel assemblies is needed to avoid local power peaks. Power peaking may be looked upon as a result of the reactivity contributions of adjacent assemblies. Thus, it is helpful to balance the reactivity of fresh or once-burned fuel in interior or “inboard” positions with neighboring depleted fuel assemblies.

10.46. In practice, compromises are likely to be needed in the adjacent assembly reactivity balancing procedure as a result of limitations on po­sitions available. The use of solid burnable absorbers is then necessary to suppress the local power peaks selectively. However, such use of burnable poisons should be minimized. One approach that provides additional flex­ibility in locating fresh assemblies is to divide the fresh assemblies into two subbatches, each with a different enrichment. Since the use of a split batch permits assigning a lower enrichment to those assemblies that will even­tually be discharged after several operating cycles with lower-than-average exposure for the batch, there is some saving in fuel cycle costs.

10.47. The selection of assembly positions and determination of burn­able poison loading are carried out in conjunction with core neutronic modeling calculations to determine the acceptability of candidate patterns. However, an alternative promising approach is to develop an extensive data base of loading patterns which include appropriate specific design parameters. A computer search isolated from neutronics methods can then select a desirable pattern [12].

11.27. Chapter 10 was devoted to the management of fuel loaded into the core. We determined that the proper design of reload cores is essential for economical reactor operation. However, for every fuel assembly loaded into the core, one must be discharged and subsequently properly managed. Although discharged fuel no longer affects operation, its high radioactivity necessitates special provisions for temporary storage and shipping to a central facility. In many countries, the fuel assemblies are “reprocessed” to separate the fission products from useful fuel nuclides that can be re­cycled. However, in the United States, this option is not being pursued. Therefore, the assemblies must be stored either temporarily or permanently in a suitable facility. Since the assemblies are highly radioactive, they must be shipped in special shielded containers and if stored permanently, suitably packaged to preserve their integrity for thousands of years.

11.28. The technology of packaging discharged fuel so that it can safely be stored permanently has been satisfactorily developed. However, in the United States, political and legal issues have delayed the implementation of permanent repository arrangements. Unfortunately, the delay has led to some public misconception that the technical challenges have not been met. A related public perception problem has evolved as a result of un­satisfactory provisions made for storage of weapons program waste during World War II and for a decade thereafter. In the late 1980s, the need for cleanup at great expense became evident and received a great deal of publicity. Public confidence in the ability of the government to manage commercial reactor wastes safely was thereby diminished. A related com­plication has been the “NIMBY” (not in my backyard) syndrome. This refers to a general public unwillingness to accept the siting of many types of essential facilities, particularly those involving any form of waste, within their own geographical unit, which may be a city, county, or state.

11.29. An important consequence of the delays is the need to provide temporary storage of spent-fuel assemblies either at the reactor site or
elsewhere. Although there are technical solutions to permanent storage problems, the challenge is to implement them. Our objective is to con­centrate on the technical principles involved and to describe some of the options under consideration.

12.45. Containment structures for PWRs vary to some extent from plant to plant, but they are commonly cylindrical (roughly 37 m diameter) with a domed top (overall height some 61 m). They are usually made of rein­forced concrete, about 1.07 m thick, with an internal steel liner, roughly 38 mm thick. As shown in Fig. 12.3, the entire primary coolant system is enclosed as well as elevated injection tanks.

12.46. A spherical design is shown in Fig. 12.4. Compared with a cy­lindrical design of equivalent free volume, the spherical configuration pro­vides additional operating floor area and efficient placement of auxiliary and maintenance activities. An in-containment refueling water storage tank (IRWST) shown in the figure provides water for both safety injection and severe accident core debris cooling. Sphere diameters vary from about 40 m for a 2600-MW(t) plant to about 60 m for a plant rated at 3800 MW(t). Corresponding free volumes are about 57,000 and 96,000 m3, respectively.

12.47. If there were to be a complete loss of coolant, nearly all the heat content of the coolant and fuel prior to the accident would be released to the containment atmosphere. The volume and strength of the structure are such that it can withstand the maximum containment temperature and pressure that would be expected from the steam produced by the flashing of all the water in the primary circuit and from the effects of the ECCS. Typically, the calculated maximum pressure would be about 280 kPa(g); the containment structure is thus designed to withstand 310 kPa(g) and is tested at 350 kPa(g). At the design pressure, the leakage rate should not

exceed 0.1 percent of the containment volume per day. Spherical contain­ments may be designed for pressures as high as 500 kPa(g).

Example 12.1. Consider a large PWR with a total primary system coolant inventory of 350,000 kg at 15.5 MPa(a) and 320°C. If the contain­ment free volume is 57,000 m3, make an initial approximation of the mag­nitude of the pressure load on the containment following a loss-of-coolant accident.

As a first step, let us determine the amount of steam produced if the final pressure is “guessed” as 200 kPa(a) (about 2 atm). From the steam tables, the specific enthalpy of the subcooled coolant water prior to blow­down is 1462 kJ/kg. At 200 kPa, the specific enthalpy of the saturated liquid is 505 kJ/kg and the latent heat of vaporization is 2202 kJ/kg.

The steam produced would then be approximately

350,000(1462 — 505)
2202

The corresponding specific volume is

57.000

152.000

This corresponds to a pressure of 500 kPa(a), which we use as a second trial. Then, using new properties, the steam produced would be

350,000(1462 — 640)
1922

The new specific volume is then 0.38 m3/kg, which is relatively unchanged. Considering that the total pressure is made up of the partial pressures of air and steam, the gage pressure is roughly 5 atm. However, other effects must be considered in an actual calculation. Thermal energy absorbed by the components, building, and injected water must be considered as well as the heat input by fission product decay. A pressure in the neighborhood of 3 atm is then likely to result.

12.48. In order to cool the containment atmosphere and reduce the pressure by condensing part of the steam after a loss-of-coolant accident, water would be sprayed through nozzles near the top of the structure. The water, which collects in the containment sump, can be recirculated through
the heat exchangers of the residual-heat removal system (§12.29) to provide continuous cooling of the containment atmosphere.

12.49. The containment sprays also serve to remove some of the radio­activity from the atmosphere. Sodium hydroxide or alkaline sodium thi­osulfate in the water facilitates the removal of radioiodines which are generally the determining factor in the environmental hazard that would result from a large radioactive release (§12.160 et seq.). In some PWR installations, the radioactivity level in the containment atmosphere would be reduced by using blowers to circulate the air through iodine absorbers and particulate filters.

12.50. A special type of PWR containment system makes use of an ice condenser to reduce the interior pressure. Instead of the usual steel-lined concrete structure, the steel liner (or shell) is separated from the outer concrete (or shield) building. The annular space between the liner and the concrete, above the level of the reactor vessel, contains cells filled with refrigerated borated ice. In the event of a loss-of-coolant accident, con­densation of the released steam by the ice would limit the pressure in the containment. Consequently, the structure may be designed for a pressure of only 69 kPa(g) and it can have a smaller volume than a conventional PWR containment building. Some fission products would also be removed in the condenser. Furthermore, the borated water formed by the melting ice would collect in the containment sump and would be available for core cooling.