Core Power Distribution

The Model 412 PWR uses several control mechanisms. The first is the control cluster, consisting of a set of 25 hafnium metal rods coimected by a spider and inserted in the vacant spaces of 53 of the fuel assembhes (see Fig. 6). The clusters can be moved up and down, or released to shut down the reactor quickly. The rods are also used to (/) provide positive reactivity for the startup of the reactor from cold conditions, (2) make adjustments in power that fit the load demand on the system, (J) help shape the core power distribution to assure favorable fuel consumption and avoid hot spots on fuel cladding, and (4) compensate for the production and consumption of the strongly neutron-absorbing fission product xenon-135. Other PWRs use an alloy of cadmium, indium, and silver, all strong neutron absorbers, as control material. 

Fission counters are used extensively for both out-of-core and in-core measurements of neutron flux in nuclear flux in nuclear reactors. In out-of-core situations, they monitor the neutron population during the early stages of power ascension when the neutron flux level is very low. For in-core measurements, fission counters are used for flux mapping (and consequently, determination of the core power distribution). They are manufactured as long thin q lindrical probes that can be driven in and out of the core with the reactor in power. Typical commercial fission counters for in-core use have diameters of about 1.5 mm (0.06 in), use uranium enriched to at least 90 percent in as the sensitive material, and can be used to measure neutron fluxes up to 10 neutrons/(m s) [10 neutrons/(cm s)]. 

Parametric studies were performed in which core excess reactivity was related to uranium-235 and boron-10 loading and metal to water ratio. The merits of two different control arrays were studied and critical stuck rod configurations established for start-up and mid-life cores. Power distribution in the core was measured. A presentation of typical SM-2 start-up core data follows ... 

RCCA ejection accidents caused by mechanical failure of a control rod mechanism pressure housing, resulting in the ejection of an RCCA and drive shaft. The consequence of this mechanical failure is a rapid positive reactivity insertion together with an adverse core power distribution, possibly leading to localised fuel rod damage. 

The distribution of burnable absorbers must result in a radial core power distribution in line with the assumptions of the safety case. 

The eapability to aceept ramp load changes at 5 -percent power per minute while operating in the range of 15-pereent to 100-percent of full power without reactor trip or steam dump system actuation, subject to core power distribution limits. 

The feedwater is distributed and mixed with the recirculating saturated water discharged from the steam separators and dryers to provide subcooling at the inlet to the jet pump or internal/ external pump to prevent cavitation and to have a uniform temperature mixture entering the reactor core to prevent an asymmetrical core power distribution. 

During commissioning, channel measurements were made at various reactor powers using the inlet flow meters and quality meters. At zero power, l.e., with no steam quality, checks were made of the channel flows as measured by the inlet and outlet Venturi meters respectively, and where they did not agree within 5, those channels were excluded from the subsequent analysis of core power distribution. In addition certain of the channel Instruments had developed faults and could not be repaired at this stage because access is only available during shutdown. Nevertheless the instrumentation in 77 out of the... 

Figure 7. Representative LOFT core power distribution.

Eigure 4.4 illustrates the horizontal power density distribution through the vertical center of the core. The peak power density at the center of the core divided by the minimum power density at the center of the fuel tubes near the vertical faces of the core boundary is 2.3. The peak-to-average core power distribution was determined to be 2.09. 

Limits on the power distribution of the core and margins to these limits must be established to preclude fission product release from the fuel due to fuel and cladding failure. In pressurized water reactors (PWRs) the ultimate limit is the limit on the departure from nucleate boiling ratio (DNBR), which quantifies how close the core is to experiencing fuel melting. Inherent to the DNBR determination are core power distribution parameters such as assembly average powers and hot channel factors (HCFs). Since these parameters help make up the DNBR, limits placed on the DNBR can be translated into limits on these power parameters. 

The core bumup calculations are also carried out in a 1/4 symmetric core geometry as shown in Fig. 2.20 [9]. The macro-cross section sets of the fuel assemblies are allocated according to the cycle number of the fuel assemblies (first cycle, second cycle, and third cycle), insertion or withdrawal of the control rods, and coolant and moderator densities. These fuel assemblies are surrounded by light water with some stainless steel smeared to model the reflectors. The macrocross section sets are allocated for each fuel element volume and renewed as the bumup proceeds. Each fuel element is further divided into calculation meshes to evaluate neutron flux distributions. The three-dimensional core power distribution is obtained by evaluating the power density for each calculation mesh. This means... 

The core thermal-hydraulic calculations are based on the single channel analysis model. On the other hand, the three-dimensional core power distribution is obtained by COREBN for the calculation mesh described in Fig. 2.20 [9]. In the core thermal-hydraulic calculations, the neutron flux calculation mesh of the COREBN is assumed to compose a fuel channel group. The fuel channels in this fuel channel group are assumed to be identical. 

In the case of the Super LWR core, design, the X-Y-Z three-dimensional core calculation model is essential. It is a thermal-spectrum core with large heterogeneities. Not only the neutron flux but also the special dependences of the coolant temperature and density are large. These parameters may also be largely affected by the local insertions of control rods. The core characteristics also depend on the bumup distributions, which ultimately depend on the core power distributions, control rod patterns and fuel replacement patterns. In order to consider these parameters in the design, the three-dimensional core calculation model is required. 

The COREBN code does not have the coupling function. Hence, the bumup calculations for one cycle of the core operation is divided into a number of bumup steps. Within each bumup step, the neutronic and thermal-hydraulic calculations are coupled by the core power and density distributions (within each bumup step, the coolant density distribution is assumed to be constant). These calculations are repeated until the core power distribution and the density distributions are converged. Once the convergence is obtained, the bumup step proceeds to the next step. For the coupling calculations, the macro-cross section sets of the fuel assemblies are prepared for different coolant and moderator densities and these are interpolated by bumups. 

Cluster type control rods are designed to control the excess reactivity as well as to control the core power distributions during operation. The control rods should also be capable of bringing the core to a cold shutdown state with a sufficient margin. The shutdown margin of the core is evaluated after designing the equilibrium core and all design parameters are determined. 

The control rod patterns are determined for each of the 15 bumup steps of the equilibrium cycle (cycle bumup exposure of 0-14.8 GWd/t). Figure 2.54 [9] shows the control rod patterns for the equilibrium core (1/4 core symmetry). Each box represents a fuel assembly and the value in the box represents the control rod withdrawn rate out of 40. A blank box represents a fuel assembly with control rods completely withdrawn. While the control rod patterns are adjusted at every 1.1 GW/t throughout most of the cycle, the fine adjustment of the control rod pattern at a cycle bumup of 0.22 GWd/t is necessary to compensate for a rapid drop of BOC excess reactivity. The excess reactivity drop is relatively fast with respect to the bumup at BOC because of the initial build up of xenon gas and other fission products. The concentration of xenon reaches eqmlibrium shortly after operation commences and from there, the rate of the excess reactivity drop becomes lower and almost constant. The control rod patterns are determined by considering control of the core power distributions while keeping the core critical. The radial core... 

Radial Core Power Distributions and Radial Core Power Peaking Factor... 

Fig. 2.55 Radial core power distributions (I/4 symmetric core). (Taken from doctoral thesis of A. Yamaji, the University of Tokyo (2005) [9]j...

These calculated results imply that with an appropriate core design, suitable radial core power distributions to achieve a high outlet temperature can be obtained. The design parameters of main concern here are the fuel loading patterns, the coolant flow rate distributions (orifice designs), and the control rod patterns. 

The above relationships assume that the maximum power point always appears in the maximum power fuel assembly. Such an assumption may be acceptable when the core power distribution is relatively smooth, and it seems to be acceptable for the Super LWR core design as far as the three-dimensional core calculation results are concerned. 

The bumup profile of the density reactivity coefficient of the equilibrium core is shown in Fig. 2.61 [9]. Although the calculation methods used in this chapter are not accurate enough to state the precise density coefficient values, the tendency of the density reactivity coefficient to decrease with the cycle bumup exposure can be seen. This decreasing trend is due to the increase in the core average density with the bumup from about 0.50 g/cm at the BOC to about 0.57 g/cm at the EOC. The gradual increase of the core average water density can be explained by the gradual shift of the axial core power distribution from the bottom peak to the top peak towards the EOC. As the axial power distribution shifts to the top peak, the axial... 

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