Essay Example on Maintaining Constant Fission Reaction in Nuclear Reactor Systems

Introduction

The needed situation for a steady, continuous fission series reaction in a nuclear reactor system involves a response in which each fission prompts another one. The minimum condition entails the respective nucleus experiencing fission reaction to generate, typically, a neutron that results in the splitting chain reaction of another core. Besides, the reaction rate within the system must remain constant (Saracco et al., 2019). The purpose of this paper involves the examination of reactor safety concerning effects of temperature and behavior of fossil products in nuclear reactions.

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Infinite Medium Multiplication Factor

The infinite medium multiplication factor refers to the ratio of the neutrons generated by the chain reaction in one neutron production to the number of neutrons missing through raptness in the previous neutron creation. Infinite medium equation: k = neutron generation from fission chain reaction in one neutron production neutron absorption in the former neutron production. The temperature difference in a fission system prompts alterations in the atomic reaction rates and the moderator thickness, and subsequently, in the infinite medium multiplication factor. The temperature reliance on the multiplication factor is essential concerning the transient conduct of the nuclear reactor (Saracco et al., 2019). The multiplication factor correlates with nuclear criticality safety challenges and requires assessment because it entails a significant impact on the approximation of functional fission balance. The outcome involves either a positive or negative reaction series, creating a modification in the reactor power. With a rise in temperature, the absorption characters widen, thereby growing the absorption of a neutron, so the resonance leakage possibility reduces and contributes negatively to the temperature constant in the infinite medium multiplication influence.

Example

A temperature variation in a functioning reactor causes a change in power-a power-level rise results in more nuclear reactions, and subsequently greater liberation of heat energy. As the average temperature increases in the reactor, the coolant and the moderator enlarge, and its density reduces. The moderator becomes less efficient due to the decreasing molecules per unit volume. The neutrons slow down, and leakage in the reactor increases, and negative reactivity rises in the reactor.

Migration Area and Geometric Buckling

The migration area or square of the migration length (M2) equal to a sixth of the square of the mean length between the neutrons' natal point and its absorption (Liu et al., 2020). The distance moved by fast neutrons during control and the length covered by thermal neutrons in the course of fission in a chain reaction plays a significant role in the reactor system due to their impact on the critical size and influence on the neutron leakage. The migration area equation: (M2) = L2 +LS2, where L2 refers to the diffusion length, and LS2 refers to the Fermi age or the slowing-down length. The rate of fission discharge amplified with time under controlled temperature and fluidity (Liu et al., 2020). The increase in the rate of fission discharge due to high temperatures involves a mixture of decay and pore movement developments (migration area). High-temperature reactors have higher safety standards than other reactors. From the example above, an increase in temperature results in the moderator becoming less efficient in decelerating the neutrons and leakage increases. The PNL decreases from an increase in temperature according to the following equation: PNL=11+M2B2 , where M2 refers to the migration area. Besides, Keff decreases according to the six factor formula creating an increase in negative reactivity. Thus: keff=11-r , where rho refers to the reactivity.

Geometric buckling refers to the quantity of neutron escape from the fission reaction system. In contrast, material buckling refers to the variation between neutron reaction with the fuel and the neutron generation (Ray et al., 2017). Geometric buckling equation: Bg2 = [(k/ k) - 1]/ L2. The acute buckling temperature of FG radioactive elements relates to the nonlocal limit, solid structure, and material geometrical factors. Temperature significantly impacts on the design aspect in particular fission reactions. An increase in temperature results in a reduction in the geometric buckling since there exist a rise in thermal tensions. Geometric buckling also changes from extreme cold or hot temperatures. Furthermore, from the previous example: PNL=11+M2B2 , where B2 refers to the geometric buckling.

The behavior of Fission Products in the Primary System In Case of Severe Accidents

At intermediate temperatures, oxidizing environments only discharge volatile and inert gases. Both the fuel and casing can swell. Cladding shields the fuel to produce a fuel pin and may result in deformation. Usually, the gap between the fuel and the cladding gets filled with helium gas to provide better thermal contact between the fuel and the casing. During chain reactions, the quantity of gas inside the fuel pin can improve due to the formation of inert gases like xenon and krypton. If a loss-of-coolant accident (LOCA), such as Three Mile Island or a Reactivity Initiated Accident (RIA) like Chernobyl or SL-1, happens, then the temperature of this gas rises. As the fuel pin gets sealed, the stress on the gas increases according to the formula PV= nRT and may become deformed and explode the cladding (Stacey, 2018). Corrosion and irradiation can change the characteristics of the zirconium alloy typically utilized as cladding, causing its brittleness. Therefore, experts do not recommend experiments using non-irradiated zirconium alloy tubes.

The heating of pellets results in some of the radioactive elements getting lost from the nuclear of the pellet. If xenon rapidly escapes the pellet, then the quantity of 134Cs and 137Cs existing in the gap between the fuel and the cladding improves (Pontillon et al., 2017). When the zirconium alloy tubes holding the pellet get broken, then a greater liberation of cesium happens. 134Cs and 137Cs gat formed through various forms, and therefore, the two cesium isobars occur at several parts of a fuel pin. The gaseous xenon and iodine elements can diffuse out of the pellet and into the gap. The xenon can degenerate to the stable cesium isotope. The discharge kinetics of FPs get hastened through oxidizing conditions. Besides, the general liberation of particular FPs depends on the oxidizing reducing environments.

Vaporization from fuel shells entails the regulation mechanism of discharge for the less volatile elements, such as strontium, yttrium, niobium, zirconium, rhodium, and molybdenum. Other less volatile species include technetium, ruthenium, barium, palladium, cerium, neodymium, lanthanum, and praseodymium. The liberation of radioactive elements from the damaged fuel shaft involves a two-step procedure that entails conveyance via the fuel medium and vaporization into the gas torrent rolling past the rod. The rate-limiting step governs the release kinetics (Stacey, 2018). The initial technique entails a slow process for the volatile elements, while the second one becomes rate-limiting for the non-volatile radioactive species. The vaporization discharge of non-volatile nuclear reactions from the fuel relies on the partial vapor stress of the fission products and the mass transfer from the fuel surface into the carrier gas stream. As a result, the mass transfer happens first through atomic diffusion in the fuel matrix, and then vaporization from the fuel surface.

References

Liu, Z., Smith, K., & Forget, B. (2020). Calculation of multi-group migration areas in deterministic transport simulations. Annals of Nuclear Energy, 140, 107110. www.sciencedirect.com/science/article/pii/S0306454919306206

Pontillon, Y., Geiger, E., Le Gall, C., Bernard, S., Gallais-During, A., Malgouyres, P. P., & Ducros, G. (2017). Fission products and nuclear fuel behaviour under severe accident conditions part 1: Main lessons learnt from the first VERDON test. Journal of Nuclear Materials, 495, 363-384. www.sciencedirect.com/science/article/pii/S0022311517303380

Ray, D., Kumar, M., Bhadouria, V. S., Saraswat, S. P., & Munshi, P. (2017). A study of transverse buckling effect on the characteristics of burnup wave in a diffusive media. www.indico.iync2020.org/event/6/papers/141/files/348-IYNC_final_dipanjan.pdf

Saracco, P., Chentre, N., Abrate, N., Dulla, S., & Ravetto, P. (2019). Neutron multiplication and fissile material distribution in a nuclear reactor. Annals of Nuclear Energy, 133, 696-706. www.sciencedirect.com/science/article/pii/S0306454919303627

Stacey, W. M. (2018). Nuclear reactor physics. John Wiley & Sons. www.books.google.com/books?hl=en&lr=&id=NzlJDwAAQBAJ&oi=fnd&pg=PR23&dq=geometric+buckling+in+fission+reaction&ots=TxL54Zcfwo&sig=HcyBbXyGZpudZ_TH1CltN4X06Ro