J.E. Hoogenboom

Neutron source strength determination for on-line reactivity measurements

Abstract A method is described to determine the effective neutron source strength in a nuclear reactor, which must be known when calculating the time-varying reactivity from inverse reactor kinetics for a reactor at low power. When for an initially subcritical reactor the reactivity is changed and kept constant after the change, the effective source strength can be determined from a linear regression of reactor power to a function proportional to the emission rate of delayed neutrons, which can be calculated from the reactor power history. In view of the relatively strong noise present in the reactor power signal at low power, a grouping method for the regression is preferred over the least-squares method. Experiments with a reactor simulator with known source strength showed good agreement. Application to actual reactor signals gave consistent and satisfactory results.

The forgotten effect of the finite measurement time on various noise analysis techniques

Abstract The conventional noise analysis expressions for functions like the auto- and cross-correlation function, the variance to mean ratio, and the Rossi-α formula, diverge when the reactor is critical. This problem arises because one pole of the zero-power reactor transfer function is zero. However, in a finite measurement time, a zero frequency cannot be measured and the divergence will not be found experimentally. New expressions for the expectation values of the experimental quantities of various pulse counting techniques are derived which also take into account the dead time of the detector. These expressions do not suffer from divergence at critical. A Feynman-α experiment is simulated in two, neutronically different systems. The use of the conventional equations for the analysis of the experiments is seen to lead to a bias in the inferred reactivity value.

Application of nonlinear optimization to reactor core fuel reloading

Abstract We use mixed-integer nonlinear programming (MINLP) as the optimization method for determining optimal loading schemes in nuclear reactor fuel management. Contrary to most current methods, which treat the physical core description as a black box, the MINLP approach uses the algebraic equations describing the physical core behavior directly in the optimization program. For a simple but still quite realistic model, we compare the obtained solution quality, the speed and the flexibility of this method with the solutions obtained by currently used optimization methods. It is shown that MINLP is competitive with current methods, and that MINLP combined with local search heuristics is a promising approach to fuel management optimization.

Development of parallellized higher-order generalized depletion perturbation theory for application in equilibrium cycle optimization

Abstract As nuclear fuel economy is basically a multi-cycle issue, a fair way of evaluating reload patterns is to consider their performance in the case of an equilibrium cycle . The equilibrium cycle associated with a reload pattern is defined as the limit fuel cycle that eventually emerges after multiple successive periodic refueling, each time implementing the same reload scheme. Since the equilibrium cycle is the solution of a reload operation invariance equation, it can in principle be found with sufficient accuracy only by applying an iterative procedure, simulating the emergence of the limit cycle. For a design purpose such as the optimization of reload patterns, in which many different equilibrium cycle perturbations (resulting from many different limited changes in the reload operator) must be evaluated, this requires far too much computational effort. However, for very fast calculation of these many different equilibrium cycle perturbations it is also possible to set up a generalized variational approach. This approach results in an iterative scheme that yields the exact perturbation in the equilibrium cycle solution as well, in an accelerated way. Furthermore, both the solution of the adjoint equations occurring in the perturbation theory formalism and the implementation of the optimization algorithm have been parallellized and executed on a massively parallel machine. The combination of parallellism and generalized perturbation theory offers the opportunity to perform very exhaustive, fast and accurate sampling of the solution space for the equilibrium cycle reload pattern optimization problem.

Identification of flow patterns by neutron noise analysis during actual coolant boiling in thin rectangular channels

The primary objective of this paper is to introduce results of coolant boiling experiments in a simulated materials test reactor-type fuel assembly with plate fuel in an actual reactor environment. The experiments have been performed in the Hoger Onderwijs Reactor (HOR) research reactor at the Interfaculty Reactor Institute, Delft, The Netherlands. In the analysis, noise signals of self-powered neutron detectors located in the neighborhood of the boiling region and thermocouple in the channel wall and in the coolant are used. Flow patterns in the boiling coolant have been identified by means of analysis of probability density functions and power spectral densities of neutron noise. It is shown that boiling has an oscillating character due to partial channel blockage caused by steam slugs generated periodically between the plates. The observed phenomenon can serve as a basis for a boiling detection method in reactors with plate-type fuels.

Theoretical and numerical investigations into the SPRT method for anomaly detection

Abstract The sequential probability ratio test developed by Wald is a powerful method of testing an alternative hypothesis against a null hypothesis. This makes the method applicable for anomaly detection. In this paper the method is used to detect a change of the standard deviation of a Gaussian distributed white noise signal. The false alarm probability, the alarm failure probability and the average time to alarm of the method, which are important parameters for anomaly detection, are determined by simulation and compared with theoretical results. Each of the three parameters is presented in dependence of the other two and the ratio of the standard deviation of the anomalous signal and that of the normal signal. Results show that the method is very well suited for anomaly detection. It can detect for example a 50 % change in standard deviation within 1 second with a false alarm and alarm failure rate of less than once per month.

The temperature distribution in a gas core fission reactor

Abstract A model is proposed for the heat transport in a nuclear reactor with gaseous fuel at high temperatures taking into account radiative and kinetic heat transfer. A derivation is given of the equation determining the temperature distribution in a gas core reactor and different numerical solution methods are discussed in detail. Results are presented of the temperature distribution. The influence of the kinetic heat transport and of dissociation of the gas molecules is shown. Also discussed is the importance of the temperature gradient at the reactor wall and its dependence on system parameters.

Research reactor in-core fuel management optimization by application of multiple cyclic interchange algorithms

Abstract Fuel shuffling optimization procedures are proposed for the Hoger Onderwijs Reactor (HOR) in Delft, The Netherlands, a 2MWth swimming-pool type research reactor. These procedures are based on the multiple cyclic interchange approach, according to which the search for the reload pattern associated with the highest objective function value can be thought of as divided in multiple stages. The transition from the initial to the final stage is characterized by an increase in the degree of locality of the search procedure. The general idea is that, during the first stages, the ‘elite’ cluster containing the group of best patterns must be located, after which the solution space is sampled in a more and more local sense to find the local optimum in this cluster. The transition(s) from global search behaviour to local search behaviour can be either prompt, by defining strictly separate search regimes, or gradual by introducing stochastic acceptance tests. The possible objectives and the safety and operation constraints, as well as the optimization procedure, are discussed, followed by some optimization results for the HOR.

Fast measurements of the in-core coolant velocity in a BWR by neutron noise analysis

Abstract A method to determine in-core coolant velocities from neutron noise within short time intervals has been developed. The accuracy of the method was determined by using a simulation set-up and by using signals of a twin self-powered neutron detector installed in the core of the Dodewaard BWR in the Netherlands. In-core coolant velocities can be estimated within 2.5 s with a standard deviation (due to statistics) less than 2.1%. The method is suitable for velocity monitoring as is shown by the application to a stepwise velocity change of the coolant in a model of a coolant channel of a BWR. The presented technique was applied to determine the variations of the coolant velocity in the Dodewaard core during normal operation and during pressure steps. Only minor variations of the coolant velocity were detected during normal reactor conditions. An increase of those variations with pressure lowering—indicating a lower thermal hydraulic stability—could be detected. A clear velocity response to pressure steps could be determined which was also reflected in the cross-spectrum of the velocity with the vessel pressure and with the in-core neutron flux.

Experimental investigation of the count-loss effect due to the time interval between counting-gates in the Feynman-α method

Abstract Yamane and Hayashi derived a new formula for the variance-to-mean ratio that takes the channel advance time of a multi-channel scaler into account. If the channel advance time is much smaller than the channel width (as in practice), then its effect can be numerically shown to be negligible. It might be for this reason that experimental results that validate the new formula have never been published. However, by introducing an artificial long channel advance time equal to the width of one channel, the effect becomes significant and can be demonstrated experimentally. With these experimental results, the new formula could be validated.