Reactor Kinetics and Point Kinetics

We apply the concept of convergence acceleration, also known as extrapolation, to find the solution of the reactor kinetics equations (RKEs). The method features simplicity in that an approximate finite difference formulation is constructed and converged to high accuracy from knowledge of the error term. Through the Romberg extrapolation, we demonstrate its high accuracy for a variety of imposed reactivity insertions found in the literature. The unique feature of the proposed algorithm, called RKE/R(omberg), is that no special attention is given to the stiffness of the RKEs. Finally, because of its simplicity and accuracy, the RKE/R algorithm is arguably the most efficient numerical solution of the RKEs developed to date.

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TRANSIENT EXPERIMENTS IN ZED-2 TO INVESTIGATE THE IMPACT OF LEAKAGE ON REACTOR PHYSICS PHENOMENA

AECL Nuclear Review ◽

10.12943/anr.2014.00032 ◽

2015 ◽

Vol 4 (1) ◽

pp. 67-73

Author(s):

M.B. Zeller ◽

J.E. Atfield

Keyword(s):

Neutron Transport ◽

Measurement Techniques ◽

Critical Conditions ◽

Reactor Physics ◽

Validation Data ◽

Reactor Kinetics ◽

Static Measurement ◽

Transient Experiments ◽

Point Kinetics ◽

The Impact

This paper describes an experimental approach where reactor kinetics experiments are used to study reactor physics phenomena that are normally investigated using static-measurement techniques. This approach provides validation data relating to these phenomena for a range of core reactivities, rather than only providing data at critical conditions. Sub-critical and super-critical transient measurements were performed in the ZED-2 reactor. The transients were analyzed using a point kinetics model to derive the reactivity states that induced the transients. The reactor physics phenomenon of interest for the current study is Coolant Density Induced Reactivity. Initial measurements were performed using an air-cooled (i.e., voided) ZED-2 lattice; the measurements were then repeated using the same lattice cooled with light water. These measurements yielded reactivity values for both coolant conditions in the lattice for a range of super-critical and sub-critical states. This investigation avoids the inherent assumption of static-measurement analyses that the bias in predicting criticality for the two coolant conditions is identical to the bias in predicting the phenomenon of Coolant Density Induced Reactivity itself. The measured reactivity values are compared with calculations employing the 3-D stochastic neutron transport reactor code MCNP.

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Coupled Reactor Kinetics and Heat Transfer Model for Fluoride Salt-Cooled High-Temperature Reactor Transient Analysis

Volume 5: Student Paper Competition ◽

10.1115/icone24-60728 ◽

2016 ◽

Author(s):

Xin Wang ◽

Kathryn D. Huff ◽

Manuele Aufiero ◽

Per F. Peterson ◽

Massimiliano Fratoni

Keyword(s):

Heat Transfer ◽

High Temperature ◽

Heat Transfer Model ◽

Transfer Model ◽

Monte Carlo Code ◽

Fluoride Salt ◽

Neutron Lifetime ◽

Delayed Neutrons ◽

Reactor Kinetics ◽

Point Kinetics

Coupled reactor kinetics and heat transfer models have been developed at the University of California, Berkeley (UCB) to study Pebble-Bed, Fluoride-salt-cooled, High-temperature Reactors (PB-FHRs) transient behaviors. This paper discusses a coupled point kinetics model and a two-dimensional diffusion model. The former is based on the point kinetics equations with six groups of delayed neutrons and the lumped capacitance heat transfer equations. To account for the reflector effect on neutron lifetime, additional (fictional) groups of delayed neutrons are added in the point kinetics equations to represent the thermalized neutrons coming back from the reflectors. The latter is based on coupled multi-group neutron diffusion and finite element heat transfer model. Multi-group cross sections and diffusion coefficients are generated using the Monte Carlo code Serpent and defined as input in COMSOL 5.0.

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Simulation of IAEA Reactivity Initiated Transient Benchmarks Using Reactor Dynamics Code “REDAC”

Journal of Nuclear Engineering and Radiation Science ◽

10.1115/1.4045394 ◽

2020 ◽

Vol 6 (3) ◽

Author(s):

Vivek A. Kale ◽

Obaidurrahman K.

Keyword(s):

Peak Power ◽

Channel Model ◽

Neutron Generation ◽

Energy Agency ◽

Reactor Kinetics ◽

Power Peak ◽

Tightly Coupled ◽

Safety Parameters ◽

Fast Transients ◽

Point Kinetics

Abstract This paper presents the analysis of reactivity initiated transients in an idealized, light water research reactor as a part of International Atomic Energy Agency (IAEA) safety related benchmark. The simulation model is based on point reactor kinetics coupled with one-dimensional (1D), two-channel model for thermal hydraulics. The point kinetics equations (PKEs) have been solved using an implicit Runge–Kutta (RK) method and the coolant transport equations have been solved using implicit finite difference formulation. Accuracy of the implemented models and methods has been demonstrated. Important safety parameters like peak power, peak fuel, and coolant temperatures have been predicted for a series of transients. Intercode comparison shows that the predictions of the present simulations are in good agreement with other codes. This approach provides a time efficient solution for safety analysis of reactors with tightly coupled core where point kinetics can be applied. To address the sensitivity of predictions with respect to important input parameters, simulations have been carried out with different sets of inputs reported in the literature. They indicate that predictions for fast transients are spread over a wider range compared to slow transients. For a given transient, predictions of peak power have a wider spread, while peak temperatures are relatively less sensitive to neutronic inputs. Also, for fast transients, prompt neutron generation time and delayed neutron fraction have dominant influence on the evolution of power. For slow transients, the reactivity feedback effects are equally important.

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Generalization of the Analytical Exponential Model for Homogeneous Reactor Kinetics Equations

Journal of Applied Mathematics ◽

10.1155/2012/282367 ◽

2012 ◽

Vol 2012 ◽

pp. 1-12 ◽

Cited By ~ 5

Author(s):

Abdallah A. Nahla ◽

Mohammed F. Al-Ghamdi

Keyword(s):

Three Dimensional ◽

Coefficient Matrix ◽

Exponential Model ◽

Mathematical Form ◽

Traditional Methods ◽

Reactor Kinetics ◽

Fortran Code ◽

The Matrix ◽

Homogeneous Reactor ◽

Point Kinetics

Mathematical form for two energy groups of three-dimensional homogeneous reactor kinetics equations and average one group of the precursor concentration of delayed neutrons is presented. This mathematical form is called “two energy groups of the point kinetics equations.” We rewrite two energy groups of the point kinetics equations in the matrix form. Generalization of the analytical exponential model (GAEM) is developed for solving two energy groups of the point kinetics equations. The GAEM is based on the eigenvalues and the corresponding eigenvectors of the coefficient matrix. The eigenvalues of the coefficient matrix are calculated numerically using visual FORTRAN code, based on Laguerre’s method, to calculate the roots of an algebraic equation with real coefficients. The eigenvectors of the coefficient matrix are calculated analytically. The results of the GAEM are compared with the traditional methods. These comparisons substantiate the accuracy of the results of the GAEM. In addition, the GAEM is faster than the traditional methods.

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