Neutron kinetics equations

Summary of neutron kinetics equations reactor power... 

She heat transfer and neutron kinetics equations were standard. (See Section 7 8) Delayed neutron constants were characteristic of fuel exposed to 1000 IM)/T Safety r strengths of 20 kO and 60 x 10" considered. 

Measurements of subcriticality relative to the effective delayed neutron fraction can be made by calibrating a reference fine control rod by means of asymptotic period measurements following rod withdrawal, or by inverse kinetics analysis of the reactor power response following rod drop or rod withdrawal (fitting the response using the delayed neutron kinetics equations).There are imcertainties in total delayed neutron yields and in the time dependence of delayed neutron emission, the accuracy of this reactivity scale being estimated to be 5%. 

Point neutron kinetics equations with six delayed neutron precursor groups are employed to calculate the transfer functirm from reactivity to core power. 

To determine physical and heat engineering SRU parameters, a calculated study of potential emergency situations related to water penetration into the core was performed. Mathematical description of the processes was based on dot description of both the neutron kinetics and the equations for heat transfer in the storage facility container (under such container SRU arranged within steel cup with frozen alloy was understood). 

When it is not possible to use the standard kinetic equations, the emergent neutron energy cannot be calculated from the scatter angle. The nuclear data library provides secondary energy laws in these instances as follows ... 

The problem is separable for a bare homogeneous reactor. However, only the case of a step input of reactivity, i.e., the case of a constant value of p, is easily solved. In this case, the kinetic equations are readily reduced to a second order (for the case of one delayed neutron group) homogeneous linear differential equation with constant coefficients. For an input of positive reactivity two solutions arise, of the form and where o>i > 0 and 0)2 < 0. The first solution controls the persisting exponential rise of the flux, where it is recalled that T = l/o>i is the reactor period, and the second solution which rapidly becomes small is called the transient solution. 

The kinetics equations for the thermal neutron flux used in the present study are of the same form as those of the preceding section except for being somewhat less general. They are written in the form... 

The spectrum of thermal neutrons is characterized by an equilibrium of the neutrons kinetic energy with that of the surrounding moderator. Like for any gas the speed distribution can be described by the MaxweU equation ... 

TWINKLE is a multidimensional spatial neutron kinetics code, whieh is patterned after steady-state codes currently used for reactor core design. The code uses an implicit finite-difference method to solve the two-group transient neutron diffusion equations in one, two, and three dimensions. The code uses six delayed neutron groups and contains a detailed multi-region fuel-clad-coolant heat transfer model for calculating point-wise Doppler and moderator feedback effects. The code handles up to 2000 spatial points and performs its own steady-state initialisation. Aside from basic cross-section data and thermal-hydraulic parameters, the code accepts as input basic driving functions, such as inlet temperature, pressure, flow, boron concentration, control rod motion, and others. Various edits are provided (for example, channel-wise power, axial offset, enthalpy, volumetric surge, point-wise power, and fuel temperatures). 

In the absence of delayed neutrons, the kinetic equations in the Fuchs-Nordheim model are ... 

So far we have assumed that the appropriate jS value to use in the kinetic equation is simply the total fraction of neutrons that is delayed. In fact, because the energies of the delayed neutrons are much lower than those of the... 

Neutronic characteristics of MSRs have been explored in the literature. Flow effects were considered when calculating the effective multiplication factor and fast neutron, thermal neutron, and delayed neutron precursor distribution of the liquid-fuel MSR based on the multigroup neutron diffusion equation and delayed neutron precursor conversation equation (Zhang et ah, 2009b Cheng and Dai, 2014 Zhou et ah, 2014). Spatial kinetic models were developed for better neutronic analysis of the MSRs (Zhang et ah, 2015 Zhuang et ah, 2014). 

The point kinetic equations formulated by reactivity (p) and neutron generation time (A), are as following dn P - P... 

To facilitate modeling of the metal fuel used in KALIMER, several reactivity models are modified in SSC-K code. For neutronic calculations, SSC-K uses point kinetic equations with detailed reactivity feedback from each channel. Reactivity effects are required both for transient safety analysis and for control requirements during normal operation. Reactivity changes are calculated for control rod scram, the Doppler effect in the fuel, sodium voiding or density changes, fuel thermal expansion, core radial expansion, thermal expansion of control rod drives, and vessel wall thermal expansion. Figure 5 shows the components of reactivity feedback considered in the KALIMER core. The effect of fuel expansion becomes more significant when metallic fuel is used. 

The reactivity in point kinetics equations depends on time-dependent average fuel temperature and time-dependent distributions of coolant and moderator density, and hence this model couples reactor neutronics with thermal-hydraulics. This model receives the fuel temperature distribution from the fuel rod heat transfer model and the coolant density distribution and moderator density distribution from the two thermal-hydraulic models. Then, it generates the power distribution to the fuel rod heat transfer model. 

In this section our object is to survey the most general existing criteria which, if satisfied, imply that any solution of the point kinetics equations (1) tends to the equilibrium value sLSt- oo, regardless of the initial conditions. We are thus interested in criteria sufficient for asymptotic stability in the large. We first include the delayed neutrons in the treatment and begin by presenting the results available on the n-temperature model, which is, of course, a particular case of Eqs. (1). The kinetics equations may then be written in the following form ... 

The three methods for measuring reactivity in a nuclear reactor are the inverse multiplication method, the positive-period and rod-drop methods based on reactor kinetics equations, and the pulsed neutron technique. This experiment will acquaint the participant with the latter technique. The pulsed neutron technique has two advantages over the others. The first is that large negative reactivities can be measured with good accuracy. Secondly, the method obtains its own calibration at delayed critical, relating the prompt-neutron decay constant to the reactivity of the system. 

For simplicity of calculations, most of the large system codes consider the point kinetics model assuming the overall buckling to be almost constant during the transient. The parameters used in these equations such as delayed neutron fraction, prompt neutron life time, delayed neutron precursor concentration, etc. are defined taking into account some phenomena formally neglected during the derivation of the point kinetics equation. An improvement to the... 

The simplest model of time-dependent behavior of a neutron population in a reactor consists of the point kinetics differential equations, where the space-dependence of neutrons is disregarded. The safety of reactors is greatly enhanced inherently by the existence of delayed neutrons, which come from radioactive decay rather than fission. The differential equations for the neutron population, n, and delayed neutron emitters, are... 

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