4.1 Heat Ratings and Coolants

The fast reactor core is typically much smaller than a thermal reactor system with the same heat output, since there is no requirement for a moderating material. Much higher heat ratings result from the size of the core, and the problem of removing heat from the system becomes a major design problem.

In order to provide more heat transfer surface for the heat removal pro­cess, the fuel is subdivided more than it is in a thermal system. Pins will have characteristically about half the diameter of the thermal reactor. Figure 4.1 illustrates the difference in size of fuel pin lattice and core be­tween a 1000 MWe PWR and a 1000 MWe LMFBR (7).

The fast reactor is very small with 10 times the volumetric PWR heat rating. Thus an extremely efficient coolant is required for heat removal from the very close lattice that is inherent in the fast reactor.

In order to illustrate the main variables of interest in the sodium fire representation, the following model is worth discussion. The model com­prises heat balance equations for the pool, flame, and the room, respectively, and mass balance equations for the sodium and the oxygen content of the room. The model is not a spatially distributed one; therefore the heat transfer from the room to ambient temperatures outside is necessarily crude. Nevertheless it does give reasonable results for large pools.

The pool loses heat to the vault walls at temperature Tv but gains heat from the flame at temperature Tt. Figure 4.26 shows the assumed configura-

+ See Hines et al. (33) and Humphreys (34).

Sodium pool Pool wall heat

mass Mp losses h4 (Tp-Tv)

Fig. 4.26. Model for calculation of containment pressures following a sodium pool fire.

tion of the pool lying in a pit at the bottom of the room with a flame above it. Heat transfer rates are shown between the various components. Thus the pool heat balance equation is

MpCp dTpjdt = h3(Tt — Гр) — Л4(ГР — Tv) (4.41)

The flame heat balance equation includes no heat capacity term, but it does include a heat production term based on the rate of burning of the sodium mass

— 6H dM^/dt = hi(Tf — Гг) — ht(Tt — Гр) (4.42)

The room heat balance includes heat received from the flame and that given up to the ambient temperatures T& outside the walls.

MA dTJdt = — Лх(Гг — rr) — h2(Tt — Г.) (4.43)

And finally the mass balance for oxygen depends directly on how much sodium is used; that is,

dM0Jdt = A dM^Jdt (4.44)

The mass of sodium burned depends on the concentration of oxygen, and it is proportional to the square root of the absolute temperature as shown.

This is an experimental correlation.

dMNJdt = —AcM0% (7V + 273.2)1/2 (4.45)

Finally the pressure in the room, according to the ideal gas law, is

Pt = k{Tt + 273.2) (4.46)

In the preceding equations, 8H is the heat of combustion (4850 Btu/lb), and c is a coefficient to make the units correct in the burning equation. The heat of combustion is based on an initial burning rate of 5 lb/hr-ft2 and has a value of 0.17-10~10 in cgs units. The heat transfer coefficients are all of the order of 10~4A’ cal/cm2-sec-°C, where A’ is the surface area of interest.

This model does not allow for the effect of a throat above the fire or for blanketing of the fire by the oxide the fire produces. It does not include time lags to account for nonimmediate mixing of the heat in the room or the pool, although this could be included by using a spatially distributed model. It naturally does not have enough nodes for more than illustrative accuracy. Nevertheless, very similar models are used in the sodium fire codes (see Appendix).

Figure 4.27 shows typical results that are obtained from such a model. After the fire is initiated by allowing contact between sodium and air, the temperature, and therefore the pressure in the room, rises rapidly to a peak where there is a balance between the heat input and that lost through the walls of the room. After this peak, due to lack of oxygen, the temperatures

slowly diminish. The time scale is long, the maximum pressure of 20 psia not being attained in this case for 5 hr. Also shown is a parametric case in which the room volume was doubled.

The pressures resulting from the sodium fire may in certain cases set the design pressures for the containment building (34) if nothing worse than this fire could be envisaged. The sodium and its combustion products may of course be slightly radioactive and the smoke is caustic.

The burning rate in the above model was based on a proportionality with the concentration of oxygen and the square root of the absolute temperature, as predicted by experimental work and theory. The square root accounts for the relative velocity of the sodium and oxygen molecules. If the reaction takes place in the pool, then the expression of Eq. (4.45) can be used, but if the reaction actually takes place in the flame, then the concentration of sodium molecules also ought to be included in the expression.

burning rate = c’AM0tM-si(Tt + 273.2)1’2 (4.47)

Some codes, instead of assuming a semiempirical burning rate of this kind, actually calculate the chemical balance at each point in time from the re­action between available sodium and oxygen molecules. This approach is more useful in spray calculations.

From these ICRP recommendations the AEC has set regulatory limits for the United States. These are derived from Federal Radiation Council interpretations of ICRP values.

These are set for radioactive levels due to normal nuclear plant operation and for operational transients which might be expected to occur and also for radioactive levels following accident situations. These two sets of regulatory limits are embodied in Section 10 of the Code of Federal Regula­tions (8), Part 20 and Part 100, respectively,+

a. 10 CFR 20. This limits the exposure of individuals to radiation in restricted areas during normal operation of the plant.

(1) For the whole body, head and trunk, active blood forming organs, lenses of the eyes, and gonads: 1.25 rem/quarter.

(2) For the hands and forearms, feet and ankles: 18.75 rem/quarter.

(3) For the skin of the whole body: 7.5 rem/quarter.

A greater exposure than this may be incurred only if:

(1) During any calendar quarter the dose to the whole body does not exceed 3 rem; and

(2) the dose to the whole body when accumulated does not exceed 5(N — 18), where N is the age of the individual.

+ See Note added in proof on p. 325.

b. 10 CFR 100. This limits the exposure of individuals to radiation follow­ing an accident. The site will have two boundaries inside which lie an exclu­sion area and a low population zone, respectively. These boundaries are detailed in Section 5.2.1. The Federal regulations limit radioactivity at these boundaries in the following way.

(1) Whole body dose to an individual at the boundary of the exclusion zone during the two hours following the incident shall not exceed 25 rem.

(2) The thyroid dose at the same point shall not exceed 300 rem.

(3) The whole body dose to an individual located at the boundary of the low population zone during the whole passage of the cloud (assumed to be 30 days) shall not exceed 25 rem.

(4) The thyroid dose at the same point shall not exceed 300 rem.

(5) A distance limitation is set around the plant so that population centers of more than 25,000 persons are not involved (see Section 5.2.1).

The fast reactor contains plutonium and the 10 CFR 100 accident limits do not yet provide limits for ingested plutonium. In fact plutonium is an extremely long-lived (120-yr half-life)+ bone seeker so that any ingested plutonium will give the individual a continuous dose throughout his life­time. At present, limits of plutonium release are governed by ICRP limits on radiation exposures to the general public of 1.5 mrem/yr (9). Assuming a 50-year lifetime, and that ingested plutonium stays with the carrier for life, then a total of 75 mrem in any one exposure would seem an upper limit. The AEC has yet to set such a regulatory limit for plutonium.

The 10 CFR 20 limits are essentially the ICRP ones slightly undercut by taking the maximum annual permissible dose levels and dividing by four for the quarter’s dose. The 10 CFR 100 doses are higher than these because of the much lower probability, and therefore frequency, of occurrence.

These limitations are, as following sections will show, met by the contain­ment design bases with considerable safety margin. However, actual plant releases prove, in practice, to be as much as two orders of magnitude lower than even the design values for operational releases. Accidental releases have been insignificant.

An alternative approach is to map out the whole of the vessel internal volume as a hydrodynamic system with a two-dimensional mesh, then to represent the hydrodynamic equations of motion in each mesh node, to apply the proper boundary conditions, and to insert a pressure-temperature distribution in the core. The system can then be used to calculate the relaxa­tion of these pressures and temperatures as a function of time in each mesh.

A series of such representations has been prepared by ANL (27a, b, 28a). These codes use the pressure-temperature distribution calculated from an energy release code such as MARS or VENUS and describe the con­sequences by means of a Lagrangian mesh that deforms with time.

The equations used in each mesh node are

where q, r, z, p, and E are the density, radial and vertical accelerations, the pressure, and the internal energy of the fluid, respectively. The initial vol­ume and density are V and q0, while v is the deformed volume element.

Figure 5.10 shows a series of illustrations starting from an undeformed mesh of half the reactor system in which the left-hand boundary is con­sidered a line of symmetry. Successive illustrations show how the mesh is deformed as a result of a sharp pressure distribution input to the mesh in the core region only. The pressure waves can be seen moving outward as a

function of time until they contact the vessel walls first in a radial direction and then the bottom head. Figure 5.11 shows the pressure profile at the core center in an axial direction. The pressure, initially peaked, can be seen to relax into two peaks moving up and down, the one moving up being atte­nuated by a plenum above the core on the right, while the one moving down is held up temporarily at the vessel bottom before this finally ruptures, to relieve the pressure build-up against it. Figure 5.12 shows the radial pressure profile and the shock front moving toward the vessel wall in a radial direc­tion.

The Lagrangian mesh deforms in the code and to retain finite difference accuracy it is necessary to rezone when the mesh gets somewhat deformed. This rezoning is a matter of experience and at present it is time consuming,

being nonautomatic. The code has several deficiencies which are all gradually being remedied. However, it has been successfully compared to a British experiment in which a 2 oz charge of RDX/TNT 60/40 was detonated in water inside a 2-ft diameter pressure vessel. The agreement of REXCO calculated pressure values at the vessel boundary with the experimentally observed values is good (within 20%) (28b).

Two principal versions of the code exist, REXCO-H and REXCO-I, one being the basic code and the other including inelastic deformation of vessel walls. So far no heat transfer is included in the mesh and the model is only good for the start of an excursion following the energy release. It is therefore an excellent method of calculating radial damage, but (as is shown in the next section) for the prediction of a sodium hammer ejection above

the core, heat transfer is now of importance and therefore the hydrodynamic code has to be linked to a further hammer heat transfer representation.

In principle it is to be expected that a full hydrodynamic model with heat transfer should eventually do away with the need to consider chemical explosive work.

The chemical explosive methods are, as we have seen, pessimistic. There-

Fig. 5.11. Pressure profiles along core vertical centerline at various times after start of the pressure pulse. Times are shown in microseconds. [Courtesy of Argonne National Laboratory (27a).]

Fig. 5.12. Pressure profiles along core horizontal axis at various times after the start of the pressure pulse. Times are shown in microseconds. [Courtesy of Argonne National Laboratory (27a).]

fore, if they predict that a vessel will rupture, a doubt whether this will be true still lingers. However, if they predict that a vessel will not rupture then we can be confident that this is so. A 2-in. vessel with a 10-fit radius would not rupture under an explosion of 250 MW-sec if 12% strain were acceptable (Table 5.12) by this analysis. However for the same case, a more realistic evaluation of the strain would show it to be less than 1%.

As the fuel temperature increases, the motion of the fertile atomic nuclei increases and the width of the absorption resonances increases (although the height decreases to keep the area constant). This occurs mainly below 20 keV. The thermal reactor resonance escape factor p is reduced and, in combination with the flux distribution, this results in a change in reaction rates giving a decrease in reactivity [Eq. (1.1)]. Thus, for a fuel temperature increase, the reactivity decreases — so that afuei is negative.

However the opposite happens for 239Pu because, on absorption, fission may occur in the plutonium and the reactivity increases. Here afuel may be positive. Thus the actual Doppler coefficient is determined by a competi­tion between the two effects and it depends on the isotopic concentrations of 239Pu and 238U and their relative proximities. The plutonium effect is generally small.

The usual calculated values are approximately 10-5 8k j к and are designed to be negative. The coefficient is the main safety parameter of a design as we shall see in later sections.

The Doppler coefficient (afuei or dkffidT) in current liquid-metal fast breeder reactor designs varies as Г-1, so the Doppler coefficient is very often quoted in terms of the value of T dkeS/dT, the Doppler constant.

1.4.1.1 Moderator Coefficient in a Thermal Reactor

In a thermal reactor, 238U is a l/v absorber in which the absorption cross section decreases as the inverse of the square root of the energy of the neutrons. However the absorption in 235U falls off faster than this and the absorption for 239Pu falls off more slowly than this as the energy increases (Fig. 1.12).

Thus, in a plutonium dominated system, the coefficient is usually positive but is very small in magnitude, whereas in a 235U dominated system the coefficient is negative, but any value can result from this competition process.

However, the temperature of the system also has other effects which cannot be neglected: as the temperature and the energy E increases, the diffusion length increases, giving more leakage in small cores; the relative absorption in the fuel (/ = Е{ие1/1!л) increases for fine structure changes and the control rod effectiveness increases. These changes give, respectively, negative, positive, and negative contributions to a system temperature coefficient.

Thus the final moderator coefficient is very much a matter of balance and can either be positive or negative. It depends critically on the config­uration and makeup of the design.

Such flow failures also disturb the primary system and the flows in the secondary and tertiary circuits would be calculated from hydraulic balances and pump characteristics in the same way as previously discussed. How­ever, the disturbances are exhibited in the primary system as thermal changes due to a decrease in heat removal capability. Thus the core first experiences a rise in inlet temperature. As thermal disturbances, these effects will be discussed in Section 2.4.

2.2 Reactivity Perturbations

Reactivity perturbations have very much the same effect in any of the three reference systems except that the feedback coefficients may differ in value and sign. In all cases the reactivity disturbance is first noted as a rise in power and fuel temperatures and later by a rise in coolant temperatures. The Doppler coefficient is therefore most important in curtailing the transient.

Knowing something of the failures which might occur and something of the response of the system to the accidents, it is important to classify the accidents according to:

(a) Probability. This is impossible to do exactly at present and engineer-

TABLE 3.3 (continued)

° See Budney (6).

ing judgment is used. As failure statistics improve, then it may be done for some of the plant components.

(b) Severity. This is a calculated severity with experimental confirma­tion where possible.

Light water reactors (LWR) also use accident classifications that range from those accidents and occurrences which are expected frequently (minor perturbations in reactivity or single failures of control elements) to those which are never expected to occur but which are nevertheless chosen as a design basis because their consequences are so severe (major pipe break, ejection of a control rod).

An accident classification may tie the probability and severity of the consequences together, without reference to criteria for the design of the plant. A more logical classification is proposed which in general may be applied to any nuclear system.

A reactivity addition accident that involves high addition rates attaining prompt criticality might arise from rapid voiding of the central assemblies of the LMFBR, an ejection of a control rod in some way, fuel slumping following local melting, or even from mechanical compaction of the fuel in a high-pressure fast reactor depressurization.

The improbability of these initiators is discussed in Section 5.4. It is sufficient to say that each could occur mechanistically, and therefore should be the subject of further study. These events could give reactivity addition rates in the range of from $ 5/sec to $ 200/sec (see Table 5.6).

Fermi is a 200 MWt reactor cooled by upward flowing sodium from three loops. The vessel is enclosed in a guard tank with a bottom inlet entering from a downcomer inside the guard tank. Figure 4.35 shows a cross section of the reactor vessel.

The uranium-molybdenum fuel is clad in zirconium. The fuel and cladding are integral, being coextruded. The blanket is stainless steel clad sodium — bonded fuel. The assemblies are rigidly held together in a birdcage with grids 2 in. apart. The core is mechanically restrained and compacted toge­ther with an upper plate and spider to hold down and bring the assemblies together. This restraint was due to the uncertainty about the EBR-I stability during the Fermi design period. The addition of further grids to help with the stiffening gave an extra pressure loss and caused a derating of the plant from 300 to 200 MW.

The control rods are sodium-cooled tubes of boron carbide. They are spring assisted to 2 g and slowed after insertion by a dashpot.

The assembly was equipped with a filter inside the inlet, but there was no protection against overall blockage. Inside the vessel there is a conical flow guide which doubles as a melt-down molten fuel deflector. It sits above a melt-down delaying system composed of zirconium-plated steel plates. Outside the vessel there is a graphite-lined catch pan.

A Offset handling mechanism — <L Rotating, plug

Thermal shield-

Blsupport assembly

Subassembly transfer pot

Transfer

rotor

container

Prevailing Wind Variation. Prevailing surface winds in the region surrounding the Hypothetical Site blow from the south through west quadrant at speeds varying from 4 to 15 miles per hour throughout the year. There are no large daily variations in wind speed or direction. Observations of wind velocities at altitude indicate a gradual increase in mean speed and a gradual shift in prevailing wind direction from southwest near the surface to westerly aloft.

Frequency of Temperature Inversions. Surface-based atmospheric inversions occur fre­quently during summer and early fall nights with clear skies and low wind speeds. These inversions are destroyed quickly by solar heating. Inversions occurring during winter or spring are more likely to extend into the daytime. Inversions occur most frequently when the winds blow from the south. Unstable weather conditions usually occur with winds from the north or west.

Stagnation periods with steady light winds and a high frequency of inversions are most probable from August to October. A persistent inversion with its base between 1000-4000 feet; wind speeds less than 5 miles per hour below 5000 feet; and clear skies which permit the formation of surface based inversions at night are characteristic of these periods. The annual average percentage of time with inversions is 48 percent. A survey of United States climatology records indicates that 50 percent of total annual time with inversions is a representative national average.

Frequency and Severity of Disturbances. A maximum wind velocity of 100 mph has been recorded at the site.

Snow Load. 30 psf shall be used for snow loading.