{"id":15660,"date":"2017-10-19T17:39:37","date_gmt":"2017-10-19T17:39:37","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=15660"},"modified":"2022-11-01T08:21:20","modified_gmt":"2022-11-01T08:21:20","slug":"power-distribution-conventional-reactors","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/power-distribution-conventional-reactors\/","title":{"rendered":"Power Distribution in Conventional Reactors"},"content":{"rendered":"

It should be noted the flux shape derived from the diffusion theory<\/a> is only a hypothetical case in a uniform homogeneous <\/strong>cylindrical reactor at low power levels (at \u201czero power criticality<\/strong>\u201d). We have implicitly assumed that the core consisting of thousands of fuel and control elements, coolant, and structure can be represented by some effective homogeneous mixture. This is a very strong assumption<\/strong>\u00a0because it does not take into account the heterogeneity of a core.<\/p>\n

See also: Diffusion Equation \u2013 Finite Cylindrical Reactor<\/a>.<\/p>\n

\"Solution<\/a>
Solution for the finite cylindrical homogenous reactor.<\/figcaption><\/figure>\n

Heterogeneous Core<\/h2>\n

\"heterogeneous-core-min\"<\/a>Most of PWRs<\/a> use uranium fuel<\/strong><\/a>, which is in the form of uranium dioxide<\/strong>. Uranium dioxide is a black semiconducting solid with very low thermal conductivity. On the other hand, uranium dioxide has a very high melting point and well-known behavior. The UO2<\/sub><\/strong> is pressed into pellets, and these<\/strong>\u00a0pellets are then sintered into the solid.<\/p>\n

These pellets<\/strong> are then loaded and encapsulated within a fuel rod (or fuel pin) made of zirconium alloys due to their very low absorption cross-section<\/a> (unlike stainless steel). The surface of the tube, which covers the pellets, is called fuel cladding<\/strong>. The collection of fuel rods or elements is called the fuel assembly<\/strong>. The fuel assembly constitutes the base element of the nuclear reactor core<\/a>. The reactor core (PWR type) contains about 157 fuel assemblies\u00a0<\/strong>(depending on a reactor type<\/a>). Western PWRs use a square lattice arrangement, and assemblies are characterized by the number of rods they contain, typically 17\u00d717<\/strong> in current designs. The enrichment of fuel rods is never uniform. The enrichment is differentiated in the radial direction but also axial direction. This arrangement significantly influences the power distribution.<\/p>\n

Russian VVER-type<\/strong> reactors use a fuel characterized by their hexagonal arrangement but is otherwise of similar length and structure to other PWR fuel assemblies.<\/p>\n

\n

Flux Distribution<\/h2>\n

In commercial reactor cores, the flux distribution is significantly influenced by:<\/strong><\/p>\n

\"flux<\/a>Heterogeneity of fuel-moderator assembly.<\/strong> The core\u2019s geometry strongly influences the spatial and energy self-shielding<\/strong><\/a> primarily in heterogeneous reactor cores. In short, the neutron flux<\/a> is not constant<\/strong> due to the heterogeneous geometry of the unit cell. The flux will be different in the fuel cell<\/strong> (lower) than in the moderator cell<\/strong> due to the high absorption cross-sections of fuel nuclei. This phenomenon causes a significant increase in the resonance escape probability<\/strong><\/a> (\u201cp\u201d from the four-factor formula<\/a>) compared to homogeneous cores.<\/p>\n

Reactivity Feedbacks.<\/strong> At power operation<\/strong> (i.e., above 1% of rated power), the reactivity feedbacks<\/a> cause the flattening<\/strong> of the flux distribution because the feedbacks acts stronger<\/strong> on positions where the flux is higher<\/strong>. The neutron flux distribution in commercial power reactors depends on many other factors such as the fuel loading pattern<\/strong>, control rods position, and it may also oscillate within short periods (e.g.,, due to the spatial distribution of xenon nuclei). There is no cosine and J0<\/sub> in the commercial power reactor at power operation.<\/p>\n

\"Power<\/a>
In commercial reactor cores, the flux distribution is significantly influenced by many factors. There is no cosine and J0 in the commercial power reactor at power operation.<\/figcaption><\/figure>\n

Fuel Loading Pattern. <\/strong>The key feature of PWRs fuel cycles<\/strong> is that there are many fuel assemblies<\/strong> in the core. These assemblies have different multiplying properties<\/strong>\u00a0because they may have different enrichment<\/strong> and different burnup<\/strong>. Generally, a common fuel assembly contains energy for approximately 4 years of operation at full power<\/strong>. Once loaded, the fuel stays in the core for 4 years, depending on the design of the operating cycle. During these 4 years, the reactor core has to be refueled. During refueling, every 12 to 18 months, some of the fuel \u2013 usually one-third or one-quarter of the core<\/strong> \u2013 is removed to the spent fuel pool<\/strong>. At the same time, the remainder is rearranged to a location in the core better suited to its remaining level of enrichment. The removed fuel (one-third or one-quarter of the core, i.e., 40 assemblies) must be replaced by fresh fuel assemblies<\/strong>.<\/p>\n

Many different loading patterns have been considered, with the general conclusion that more energy is extracted from the fuel when the power distribution in the core is as flat as possible. In principle, these loading strategies may be divided into two categories:<\/p>\n