Kinetics of Circulating-fuel Reactors

J. A. Fleck, Jr., Theory of Low-power Kinetics of Circulating Fuel Reactors with Several Groups of Delayed Neutrons, Brookhaven National Laboratory, BNL 334 (T-57), April, 1955 The Theory of Circulating Reactor Kinetics at Low Power, BNL 1933, Apr. 13, 1954 also, Kinetics of Circulating Reactors at Low Power, Nucleonics, 12, 11 (1954). 

J. A. Fleck, Jr., The Temperature-dependent Kinetics of Circulating Fuel Reactors, Brookhaven National Laboratory, BNL 357 (T-65), July, 1955. 

Note that the function has been used throughout. It is of interest to mention that the set (9.246) constitute the relations used by Ergen, Weinberg, and Welton in their studies of the kinetics of circulating-fuel reactors. These studies place emphasis on the stability aspects of the nonlinear set (9.246) and include the extension of the present theory to account for the effects of alternate fuel paths through the core with different transit times as well as the effects of delayed neutrons. 

Fli ck, Jr., Theory of Low Power Kinetics of Circulating Fuel Reactors with Several Groups of Delayed Neutrons, US. UC Report RNL-334, Hrookhaven National Lahoi atory, April 1955. 

Another interesting conclusion which may be drawn is that the kinetic behavior of a circulating-fuel reactor (within the limits of the present model) may be described in terms of an equivalent stationary-fuel system in which the fractions of the delayed neutrons < jS,-, the actual delay fractions. To demonstrate this we determine the excess reactivity for the circulating-fuel system. By this we mean the reactivity over and above that required for criticality at any specified circulation velocity. This is the quantity to — a>circ. From (9.217) and (9.218) we obtain... 

This calculation has been performed by F. G. Prohammer, Note on the Linear Kinetics of the Circulating Fuel Reactor," Oak Ridge National Laboratory, Y-FlO-99, Apr. 22, 1952. 

W. K. Ergen, Kinetics of the Circulating-fuel Nuclear Reactor, J. Appl. Phyi. 25(6), 702-711 (June, 1954). 

The effective delayed neutron fraction ( Seff) represents an important reactor kinetics parameter. In circulating-fuel systems, because of the delayed neutron precursor drift, the Seff calculation requires special techniques. The coupled neutronics/CFD simulations represent a necessary step for the accurate calculation of the effective delayed neutron fraction in the MSFR (Aufiero et al., 2014). Fig. 7.3 shows the distributions of the prompt (right) and delayed (left) neutron sources obtained in OpenFOAM and adopted to calculate fieti in the nominal MSFR conditions. 

As shown in Table 4.2, large break LOCA events involve the most physical phenomena and, therefore, require the most extensive analysis methods and tools. Typically, 3D reactor space-time kinetics physics calculation of the power transient is coupled with a system thermal hydraulics code to predict the response of the heat transport circuit, individual channel thermal-hydraulic behavior, and the transient power distribution in the fuel. Detailed analysis of fuel channel behavior is required to characterize fuel heat-up, thermochemical heat generation and hydrogen production, and possible pressure tube deformation by thermal creep strain mechanisms. Pressure tubes can deform into contact with the calandria tubes, in which case the heat transfer from the outside of the calandria tube is of interest. This analysis requires a calculation of moderator circulation and local temperatures, which are obtained from computational fluid dynamics (CFD) codes. A further level of analysis detail provides estimates of fuel sheath temperatures, fuel failures, and fission product releases. These are inputs to containment, thermal-hydraulic, and related fission product transport calculations to determine how much activity leaks outside containment. Finally, the dispersion and dilution of this material before it reaches the public is evaluated by an atmospheric dispersion/public dose calculation. The public dose is the end point of the calculation. 

The AHTR reactor core physics, general core design, and fuel cycle are similar to those of the proposed General Atomics Gas-Turbine Modular Helium Reactor (GT-MHR). The low-power-density graphitemoderated core also has the long neutron lifetime, slow kinetics, and thermal neutron spectrum characteristic of the proposed GT-MHR. The molten salt (Fig. 3) flows through the reactor core to an external heat exchanger (to provide the interface for the H2 production system), dumps the heat load, and returns to the reactor core. The molten salt can be circulated by natural or forced circulation. 

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