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14 декабря, 2021

While the US programme was based on the Th cycle, the British programme (UKAEA and CEGB) has been based almost exclusively on low enriched uranium. The UKAEA programme was started in 1969 in Winfrith with lattice parameter measurements at room temperature in an undercritical system using the NESTOR reactor as a neutron source.

The central part of the HECTOR reactor was later used for measurements up to 427°C.<16) Various reaction rates have been measured and calculated for the NESTOR experiments with tubular pins and teledial fuel. The discrepancies in relative conversion ratio (RCR), 238U/235U fission ratio (FR) and Pu/U fission ratio range from 0.5 to 3% for WIMS calculations, slightly higher for simplified Dragon methods.<17_21) The HECTOR experiments were rather difficult to analyse because of the marked heterogeneity in composition and temperature.

There appeared to be a tendency to overestimate the magnitude of the negative temperature coefficient.1221 In a phase II of the UKAEA programme cross-pin and cross-block power and damage distributions and thermal spectrum characteristics have been measured in hexagonal block geometry in the ZENITH-I reactor. The experiments have been repeated at 400°C to check the effect of temperature on the measured distributions and control-rod worths. These experiments were terminated in June 1971. Like in the HECTOR case, there was a tendency to overestimate the negative temperature coefficient and the spectral changes at the core-reflector boundary were rather poorly calculated.

In a phase III the cold ZENITH-II reactor has been used for measurements on block to block and cross core distributions, three-dimensional effects on a large core, effect of absorbers, burnable poisons, non-uniform enrichment, Pu02/U02 fuelled blocks, control-rod worths and interactions, local criticality situations/23’24’

Compared to other reactor types, high-temperature gas-cooled reactors have a higher degree of safety. Sudden introductions of large amounts of reactivity are not possible in the foreseeable design. In the following paragraphs various types of accident will be analysed: the list includes all accidents foreseeable with the present designs, but any new design may carry with it new sources of accidents which will have to be analysed from case to case. In the evaluation of the consequence of the accidents it is very important to take into account the initial state of the system. The maximum temperatures reached during an accident vary considerably according to the initial power. Accidents at zero-power in a cold core seldom lead to dangerous temperatures if adequate safety equipment provides for a properly timed scram. In the analysis of the accidents occurring at power operation it is important to find the worst moment in which the accident can occur. This means considering the time when the fission product concentration leads to the worst temperature coefficient and when the configuration of the control rods already inserted in the core reduces to a minimum the reactivity effects of the insertion of the remaining rods. Very important in this respect is the Xe concentration which strongly influences the temperature coefficient and is dependent on the load diagram. In the following list we have in part followed the classification of accidents given by Stewart and Merrill,<25> limiting our analysis to the accidents which are of interest for the reactor physicist.

Control rods are often classified according to their function. Thus it is possible to distinguish:

1. Regulating rods used for automatic control.

2. Shim rods used for compensating slow reactivity changes (e. g. burn-up).

3. Safety rods used for scram.

In many cases it is not possible to distinguish the control-rod functions because the same rods are used for the functions described in points 2 and 3. This is done in order to limit the total number of control rods, in all cases in which it is not explicitly required that some safety rod remain always out of the reactor, even in the shut-down cold condition.

According to their absorbing properties control rods can be classified as black and grey. A black rod absorbs practically all neutrons impinging on its surface; if this is not the case the rod is grey. This definition applies normally to thermal neutrons: no rod is completely black for neutrons of very high energy. Grey rods can be used when highly absorbing rods would disturb too much the neutron flux distribution. This is especially important for the rods compensating the excess reactivity, because they are most of the time inserted in the core.

The use of grey rods increases the total number of rods needed to meet the given requirement, and leads therefore to higher costs and mechanical complications. Grey rods are needed in reactors with very strict temperature limitations, but cannot be considered as absolutely necessary in HTRs.

The control-rod blackness is dependent on the composition and thickness of the absorbing material. Grey rods can be simply made of steel, while black rods consist normally of an absorbing part of B4C or borated steel canned in steel or other alloys.

The control-rod effectiveness can be increased by making them black also at higher energy. This can be obtained with a very high,0B concentration, or using additional epithermal and fast absorbers like Eu, Dy, Hf, Gd or In. The amount of absorber contained in a control rod must be sufficient to ensure sufficient absorbing properties for the required time of operation.

13.2. Control-rod configuration

It is important to program the control-rod movement in such a way as not to distort too much the power and temperature distribution. Because of this reason it is better to avoid the bank movement of the control rods, which would strongly disturb the axial flux distribution. The best solution is to have only the regulating rods half inserted, while the other rods are either fully inserted or extracted. As soon as the regulating rods have moved too far from the core centre some other rod would be moved in order to bring again the regulating rods to their position of maximum effectiveness.

It is very important to know the curve of control-rod worth as function of its insertion depth (so-called “S-curve” because of its S-shape). This curve depends on the axial flux and material distribution of the reactor and on the control-rod configuration. Very important is the number of rods being moved at the same time. A bank movement of many rods tends to shift the power towards the other end of the reactor shifting then also the S-curve. Figure 13.1 shows the S-curve for one rod, once moving the rod alone and once moving it as a bank with other rods.

The shifting of the S-curve is also important to determine the effective delay of the counteraction to accidents. If a high effectiveness is reached only at deep insertion, this results in a bigger delay.

The control-rod effectiveness is highly influenced by their relative configuration. If rods are too near to each other the flux depression due to one rod reduces the effectiveness of the other (mutual shadowing). The control rods should be distributed as homogeneously as possible in the core. Local concentration of control rods in one part of the core tends to shift the power toward other reactor zones, thus producing hot spots and reducing the control-rod effectiveness. Especially with grey rods it is possible to use them for power flattening depressing the power in large reactor zones, or simply in the surrounding of freshly loaded fuel elements.

Fig. 13.1. S-curve: effectiveness of a control rod as a function of its insertion depth. |

In the same period of time a series of room-temperature critical experiments on the zero energy HITREX reactor have been performed at the CEGB Berkeley Nuclear Laboratories.

The HITREX-I core had a prismatic HTR lattice containing fuel of two types— teledial and annular—in a zone 2 m high of twenty-seven hexagonal blocks (399.5 mm across flats) surrounded by graphite reflectors. The measurements involved: reactivity, axial buckling, power distribution, fine structure effects, thermal spectrum distributions (Pu/U ratio), graphite damage (Rh reaction rate), control-rod worths. The theoretical evaluation has been performed with the WIMS-E modular scheme. Reaction rate distributions show a very good agreement between calculations and experiments, with a mean deviation of less than 1%. Also the prediction of the thermal flux within the central block is very well described by the analysis method. The major discrepancy between experiments and analysis is an underprediction of reactivity of about 1.5% Дk/k. It is likely that some 0.3% of this discrepancy is due to poor treatment of steel absorbers. The relative conversion ratio (RCR) in the annular fuel appears to be overestimated by 3.5%. This could result in an underestimate of up to 0.5% k/k in core reactivity/25"28’ An independent evaluation performed by the Dragon Project129’ based on 123 groups S4 cell calculations with the XSDRN code00’ overpredicts reactivity by about 1.5% Дk. An HITREX-2 series of experiments has been started, based on integral fuel blocks. It is also foreseen to heat a single block column up to 400°C.<3I)

The optimization of the high-temperature reactor fuel cycles leads always to rather undermoderated cores. As a consequence an introduction of water has a positive effect on reactivity. However, it is in most cases possible to design the system so that the water entering the core is limited to a very small amount.

In many cases it is not possible to have an ingress of liquid water into the hot core. The water will be vaporized in the high temperature ducts before reaching the core.

If the introduction of liquid water into the core cannot be absolutely excluded it is also possible to poison the water of the secondary system with a strong neutron absorber.

This is not necessary in big systems where only the introduction of steam is possible and the resulting Ak is limited to a few per mill. In this case the greatest damage is not caused by the power excursion, but by the corrosion due to chemical reaction of water with the core materials. An evaluation of the power excursion is made evaluating the maximum rate of insertion of water into the reactor and calculating its reactivity worth. The group constants for reactivity calculations in presence of water must be obtained from codes able to deal with neutron moderation in water (spectrum calculations based on multi-group diffusion theory, like in the MUPO code, cannot be used in this case).

Because of the high absorption localized in a geometrically small zone, the diffusion approximation is not suited to treat properly the neutron distribution in the vicinity of a control rod. The use of transport theory is required, but a full space-dependent transport calculation over the complete core is not usually within the capability of the available computers, and not even necessary, so that various simplifications are needed.

The control-rod cell must be in any case calculated with a transport theory code, whereas the whole reactor is calculated with few-group diffusion theory codes. Two possibilities are available. The control rod can either be simulated by a “non-diffusion region” at whose boundary is given an extrapolation length obtained from the transport calculation, or the control cell can be poisoned with a diffused poison giving the same neutron absorption as the control rod.

The first type of approximation may lead to better results, especially in the flux distribution, but requires a high number of mesh points to treat with sufficient accuracy the flux gradient near the control rods. In this case the cross-section of the control rod has to be simulated using the mesh points of R-9 or X-Y geometry; it is important to have the same absorbing surface as in the real rod, trying not to distort the shape too much.

The problems posed by the calculation of the extrapolation length for “non-diffusion regions” have been dealt with in § 5.5.

The second approximation is used for less detailed calculations (e. g. in the diffusion part of space-dependent burn-up codes), or when the number of control rods is very high. This method becomes rather unreliable when control rods are in the vicinity of zone boundaries (e. g. between core and reflector) or when the rods are few and unsymmetrically distributed.

When hexagonal fuel elements are treated with a diffusion theory code based on hexagonal geometry this method of cell poisoning may be the only way of representing control rods. A transport theory calculation is performed (usually with S„ methods) over the control-rod cell and for each group an absorption cross-section, equivalent to the control rod, is calculated. The control rod is then represented by a uniformly distributed “control poison” whose cross-section as a function of energy is established in such a way that in each group the poison absorbs the same number of neutrons as the control rod. In practice this poison can always be represented by a 1/u absorber with appropriate energy-dependent, self-shielding factors. These self-shieldings take into account the fact that while the cross-section of a 1/u absorber continuously increases with decreasing energy, a control rod cannot be more than black, so that a saturation is reached after which the absorption does not increase. Instead of distributing it homogeneously over the cell it is also possible to concentrate the control poison on a smaller region. This solution is used to represent a ring of control rods with a so called “grey curtain”.

In this way the three-dimensional problem representing a ring of equally spaced control rods can be treated in a two-dimensional RZ geometry. This sort of representation is adequate if a high number of control rods is present in the ring. In this case the concentration of control poison in the curtain must be obtained iterating in a diffusion calculation. The poison concentration is varied until keff is the same as that obtained by a detailed calculation with a more exact representation of the control rods (e. g. an R6 calculation where control rods are calculated as non-diffusion regions).

If more control-rod rings are present, this procedure may have to be repeated for each ring.

When some of the control rods are partially inserted at different depth a threedimensional code is needed to describe accurately the problem. Codes of this type are now available for big computers, but the high calculation time and sometimes the difficulty of having access to big computers limits the use of three-dimensional codes. On the other hand, three-dimensional diffusion codes with a limited number of mesh points are not giving more information than properly used two-dimensional codes. Fully inserted control rods can be easily calculated in R-в or X-Y geometry.

Partially inserted rods can be calculated in RZ geometry using some approximation. A central control rod can be calculated exactly. If control rods are ordered in rings, so that many rods are on the same radius, they can be simulated with a grey curtain.

Another possibility first proposed by Kalnaes’” consists in the simulation in R-Z geometry of a number of control rods vertically inserted at the same radius with a proper number of horizontal control-rod rings (“piston rings”) of equal radius, whose axial spacing is chosen in such a way that the total length of rod in the reactor remains the same. In this case partial insertions can be calculated. All these methods are valid if a sufficient number of rods is inserted in the core.

It is also important to treat properly the layers of structural material, or voidage around the control rods. This is usually done in the transport calculation and included in the extrapolation length used in the diffusion codes (which must be given for the outermost boundary of all the above-mentioned layers). A limited empty volume around a control rod can increase its effectiveness because the neutron density in the gap tends to be more constant than if the gap were filled with core material, thus reducing the “bottleneck” effect (see ref. 3, p. 626). This name is given to the reduction in absorption in cylindrical geometry as compared with plane geometry due to the shrinking of the area available to the neutrons as they diffuse towards the absorber.

Depending on the moderation ratio, also graphite layers can increase the control-rod effectiveness by increasing the thermal flux in its vicinity.

The control-rod worth depends also on the diffusion length of the surrounding medium, and therefore on the fuel loading. A higher diffusion length increases the effectiveness by increasing the area influenced by the control rod. In the calculation of the control-rod holes when the rods are extracted. Filling the holes with material as is usual with diffusion codes leads to an overestimate of the control-rod worth, which has to be assessed (e. g. Behrens and Benoist methods, §8.10). to be assessed (e. g. Behrens and Benoist methods).

Like the reactivity requirement Дkr the control-rod effectiveness Дke is also calculated as a difference of two static calculations, one without rods and one with fully inserted rods, omitting those which are not supposed to be available or which fail to enter the core.

The determination of Дke (and in general of all reactivity differences) requires great consistency in the two calculations out of which the difference is made. The type of approximation and the spatial meshes must be the same, otherwise numerical differences could alter the result.

The control-rod efficiency calculations should be performed for the cold unpoisoned reactor because this is the condition posing the most stringent requirements on the control system. Both calculations of Дkr and Д/с* involve an uncertainty which may be

assumed to be of the order of 5-10%. The shut-down margin Afce-Afcr must be wide enough to cover this uncertainty.

A series of experiments on low enriched HTR fuel was started in 1970 at Cadarache on the MARIUS reactor at room temperature and on the CESAR reactor at temperature up to 450°C. The first MARIUS experiments have been performed on a configuration with a lattice of hexagonal cells of 61 mm diameter with a 90-mm triangular pitch. The programme covered buckling and spectrum measurements at 3.5% enrichment, measurements with the PCTR method at 1.1% enrichment and measurements on teledial fuel/32"35’ The agreement with calculations performed with the APOLLO code was very satisfactory with differences in reactivity of the order of 0.1—0.3%/36’ Oscillations of Pu samples in the CESAR reactor have been performed in 1973 at room temperature, 200°C and 400°C.<37’38’ A new series of experiments on fuel blocks of General Atomic design with Th fuel cycle is planned in MARIUS for 1975/391

This accident can be caused by a fault of the operator or of the control system. The number of control rods which can be moved simultaneously is limited for safety reasons. For the same reason is limited the maximum speed of withdrawal. The maximum rate of insertion of reactivity is determined by the operational requirements, and in particular by the Xe override. The control system must be able to compensate the rate of increase of Xe after a power reduction, even in the most unfavourable configuration. This requirement can be fulfilled by moving more rods at a lower speed or one rod only at higher speed. In the case of accidental withdrawal, it must be assumed that the maximum number of control rods which can be moved simultaneouly are withdrawn at the maximum speed, and that their configuration is the one giving the maximum reactivity increase. In the study of this configuration the insertion depth and the effect of other control rods which may be inserted in the reactor must be considered, as well as the burn-up stage of the fuel elements surrounding the control rods.

When a scram occurs it may be necessary to suppose that one of the rods, at least, involved in the accident does not respond to the signal and continues to move out of the core. The maximum withdrawal speed is usually the one foreseen for reactor operation, but in some cases a higher speed may be possible. Rods inserted from below the core can fall out of the reactor, and the gas pressure in the reactor may shoot a rod out. Usually proper mechanical design can insure that these events are either impossible or extremely improbable.

While the control-rod insertion must be as quick as possible in order to be able to shut-down the reactor after an accident with minimum delay, the extraction speed must not be greater than that which is necessary for flexible operation. This is done in order to reduce the maximum rate of reactivity insertion in case of accidental withdrawal of a rod. Usually the maximum extraction speed is required to compensate the loss of reactivity due to 135Xe build-up after a power reduction, considering the control-rod pattern giving the minimum possible worth.

The problem is strictly related to the definition of the number of control rods which can be extracted at the same time from the core. The required rate of reactivity insertion can be given with one rod at a relatively high speed, or more rods at a lower speed. For safety reasons it is better to restrict to a minimum the number of rods being extracted at the same time, but the simultaneous movement of more than one rod may be necessary in order to avoid too high a speed for one single rod, and thus too strict mechanical requirements (high speed and high positioning accuracy).

The accuracy with which a position can be reached and the minimum possible movement determine the accuracy with which the critical point can be reached. These requirements are, of course, stricter for each rod if more rods are being operated simultaneously. The accuracy with which criticality can be attained determines the accuracy with which a constant reactor temperature can be assured. This is not an important problem as long as the temperature coefficient is sufficiently negative, but if the temperature coefficient is zero or positive a small inaccuracy in reaching the critical control-rod position can lead to strong temperature variations. In this case, if the critical position can only approximately be reached, the temperature can only be kept within the desired limits by a continuous movement of the control rods (making the reactor continuously slightly over — and then undercritical). Consequently this relates the positioning accuracy to the frequency of the control-rod movement.

It must also be considered that one or more rods can fail to enter the core. If control-rod mechanisms can be inspected during operation it must be assumed that the rods being inspected are not available for shut-down.

The reactor must be kept undercritical even without the missing rods, which must be assumed to be the most effective ones. The criticality of a reactor in which some control rods are locally missing is sometimes improperly called “local criticality”. The reactivity released by the extraction of these missing rods must, of course, be subtracted from the control-rod effectiveness.

If the region in which control rods fail to enter is sufficiently large and has a high k* (e. g. fresh fuel) it might be difficult or even impossible to keep the reactor undercritical simply adding more rods in the surrounding regions. This problem is strongly dependent on the к» of the region considered, so that it is usually only important in the cold unpoisoned condition. This means that if control rods fail to enter a region large enough for local criticality, the reactor can be shut down, but after cooling down and Xe decay it may start up again. The power would then automatically stabilize itself to the level whose temperature corresponds to criticality. In this normal case of negative temperature coefficient local criticality is not an accident with serious consequences, but makes a normal reactor shut-down impossible. It must be noted that if we consider the region without rods as an independent critical reactor, this would have a very high leakage because of its small size, and consequently a large negative temperature coefficient.

The problem of avoiding local criticality poses a restriction on the permissible control-rod pattern. Calculations about local criticality are usually performed in R-в geometry. It is better to represent control rods as non-diffusion regions, at least in the vicinity of the region without rods, because the use of equivalent diffuse poisons calculated for an infinite lattice is questionable in this case. It is important to calculate the complete reactor (e. g. 360° in R-в geometry). A calculation on a 180° geometry with (for symmetry reason) twice as many missing rods does not necessarily give the double excess reactivity than a 360° calculation. The reason is that if there are two completely independent critical regions the reactor has the same kcf! as with only one critical region (two critical reactors are as critical as one critical reactor).

The CESAR facility in Cadarache has been transformed to load in its centre fuel of the pebble-bed type (~ 10,000 elements) with 3.5% enriched uranium/41’ Some comparisons between theory and calculations are given in refs. 42, 43 and 44. The relative conversion ratio was calculated with an error of 3%, spectral indices could also be calculated with good accuracy. Control-rod measurements on a single and a pair of rods could be recalculated with errors of the order of 1.5% of the rod worth.

A pebble-bed critical facility for high-temperature reactors (KAHTER) started operation in July 1973 at KFA Jiilich<45) with the scope of measuring effects which are peculiar of pebble-bed reactors (effect of upper air gap between core and reflector, effect of filling factor, etc.). The criticality of all configurations of the KAHTER facility have been calculated within errors of 0.3% in Д к Ik. The agreement between theoretical and experimental control-rod effectiveness lies within 2.5% for the central rod and within 5% for the reflector rods/46’ Also in Jiilich Th resonance integrals have been measured by means of a lead spectrometer in fuel compacts containing coated particles. The discrepancy between theory and calculations is of the order of 1 to 3%.<48)

Other minor contributions came from the RB-2 reactor—Bologna/49 50’ IRI (Interuniversity Reactor Institute, Delft)15” and CCR Ispra/52’53’