Hugo van Dam

Self-stabilizing criticality waves

Abstract An analysis is presented of a recently developed concept, so-called self-stabilizing criticality waves. These waves can be ignited in originally subcritical systems under the condition that the burn up dependent properties of the system satisfy certain requirements, as is shown for an analytically solvable model. The waves have a soliton character, i.e. as a consequence of the non-linear properties of the system they have a self-stabilizing form and a phase velocity that depends on the wave amplitude. For the analytically solvable model (as far as the asymptotic waves are concerned) expressions are given for ignition conditions, wave form, amplitude (i.e. reactor power) and phase velocity. The results are corroborated by computer simulations and the latter are also used for ilustrating a non-analytically solvable case and for studying the pre-ignition phase and the evolution to an asymptotic wave.

Inhour equation and kinetic distortion in a two-point reactor kinetic model

Abstract A two-point reactor kinetic model for a strongly reflected reactor is developed and relevant parameters are assessed for the experimental zero-power reactor PROTEUS. The results are described in terms of an extended inhour equation and neutron source transfer functions for the core and the reflector. These transfer functions are applied to analyze reactor response to a pulsed neutron source which can be positioned in the core or in the reflector. The model gives a good description of the so-called kinetic distortion effect which complicates the reactivity determination by pulsed neutron source measurements. Quantitative results are in agreement with experimental data and with correction factors obtained with more detailed space dependent calculations. In order to deduce a correct reactivity value it is advised to apply a modified Simmons-King method with a two-point model version of the inhour equation.

Long-term control of excess reactivity by burnable particles

Abstract An analysis is presented of the feasibility of the use of burnable particles with spherical or cylindrical geometry in graphite moderated reators. This is in fact an application of the phenomenon of so-called burn up waves in strongly absorbing media. A simple ‘peeling model’ is used to treat the wave progression in neutronically ‘black’ particles. It is shown that this special case of heterogeneous poisoning offers some degrees of freedom in design that can be used to ‘tailor’ the excess reactivity as a function of core burn up.

Physics of a gaseous core reactor

A specific type of gaseous core reactor consists of a UF/sub 4//CF/sub 4/ fuel mixture in chemical equilibrium with a graphite reflector wall. Criticality calculations show that such a system requires a relatively small fuel investment. Temperaturedependent fuel redistribution at power is shown to give a minor positive reactivity effect, which does not jeopardize safe reactor operation. Analysis of heat transport demonstrates that very high temperatures in the core center can be realized at moderate gas pressures, which opens a way to improve the efficiency of fission energy conversion processes.

Flux distributions in stable criticality waves

Abstract An analysis is presented of so-called self-stabilizing criticality waves, as can be ignited in originally subcritical systems under the condition that the burn up dependent properties of the system satisfy certain requirements, as was shown in a previous publication for an analytically solvable model. For the solution of the analytically solvable model (as far as the asymptotic waves are concerned) a new approach was adopted, based on taking the flux-fluence space as a starting point. In this way the expressions for ignition condition, wave form, amplitude (i.e. reactor power) and phase velocity are obtained in a more systematic way than before. The analysis is extended to skew criticality waves by adopting cubic flux-fluence trajectories. From the parameters of these trajectories the parameters of the associated burn up functions and the wave properties are inferred. For a particular case the results are corroborated by a computer simulation.

Long-term control of excess reactivity by burnable poison in reflector regions

Abstract An analysis is presented of the feasibility of the use of burnable poisons in reflector regions of graphite moderated reactors. This is in fact an application of the phenomenon of so-called burn up waves in diffusive media. It is shown that this special case of heterogeneous poisoning offers some degrees of freedom in design that can be used to ‘tailor’ the excess reactivity as a function of core burn up. Two cases are used for illustrative purposes: a cylindrical core with outer reflector and an annular core with both inner and outer reflector.

Investigating the stability characteristics of natural-circulation boiling water reactors using root loci of a reduced-order model

Abstract Linear stability analysis of a natural-circulation boiling water reactor (BWR) and the underlying thermal-hydraulic subsystem is performed using a reduced-order BWR dynamic model. The root-locus method is used to examine the stability of the system. The relation between the poles of the system and the physical processes causing the instabilities is investigated. For a natural-circulation thermal-hydraulic system, the two types of instabilities (type-I and type-II oscillations) can clearly be attributed to the dynamics of different types of pressure drops. However, it is not possible to associate these instability types with certain poles of the system. The root loci of a reactor with weak void reactivity feedback and those of the thermal-hydraulic system behave similarly: The same pole pair remains the least stable one as the operating conditions move from the type-I instability region to the type-II region. In the case of a reactor with strong void reactivity feedback, an exchange in the stability of two pole pairs is found: The least stable pole pair in the type-II region is not the same as in the type-I region.

On an improved design of a fluidized bed nuclear reactor-I: Design modifications and steady-state features

Abstract This paper describes several modifications to the design of a fluidized bed nuclear reactor in order to improve its performance. The goal of these modifications is to achieve a higher power output, requiring an excess reactivity of 4% at maximum expansion of the bed. The modifications are also intended to obtain a larger safety margin when the reactor does not operate; a shutdown margin of 4% is required when the bed is in a packed state. The modifications include installing an embedded side absorber, changing the reactor cross-section area, and modifying the moderator-to-fuel ratio. The new design based on the modifications related to the aforementioned parameters achieves the desired shutdown margin and the excess reactivity. A model describing the coupling of neutronics and thermal/fluid dynamics is developed, and it is used to study the behavior of the reactor at steady conditions. The results show that the reactor can achieve a high output temperature of 1163 K and produce a thermal power of ~120 MW. Further, the results indicate that the power level of the reactor can be controlled easily by adjusting the flow of helium into the core without any further use of control rods or other active control mechanisms.

Delayed neutron effectiveness in a fluidized bed fission reactor

Abstract In a fluidized bed of fuel particles suspended by gas a considerable spatial redistribution of delayed neutron precursors occurs due to mixing processes. On the basis of a simple reactor model the reactivity effect of precursor redistribution is analyzed. This analysis is performed for both the limit case of ideal mixing and the general case of finite precursor diffusion length. It is shown that k-infinity and the ratio between precursor diffusion length and neutron diffusion length are the relevant parameters determining the reactivity effect and the effectiveness of the delayed neutrons.

On an Improved Design of a Fluidized Bed Nuclear Reactor—II: Linear Stability and Transient Analysis

Abstract A new design of a fluidized bed has been proposed and it has been shown that under steady condition the reactor is able to produce power up to 120 MW. To study the behavior of the reactor under transient conditions as well as its stability, a model describing the coupling of neutronics, thermal hydraulics, and fluidization is applied. The objective of this study is to comprehend whether the reactor is stable under its operational range. Further, knowledge of the extent of operational parameters under large perturbations is necessary for a safe operation. The stability of the system is investigated by numerical means and is performed by linearizing and perturbing the system around its equilibrium points to form Jacobian matrices. The resulting matrices are further used to obtain the eigenvalues of the system. The system is investigated under variation of mass flow rate, and it is found that within the operational range the eigenvalues are located in the negative part of the phase plane, implying linear stability. Further, the calculated decay ratios indicate a strongly damped system. Simulations of transient conditions are performed, namely, a step change in coolant flow rate and inlet temperature, representing situations that might occur in real operations of the reactor. The coolant flow rate is varied by ±1 kg/s and the inlet gas temperature is varied by ±10 K from their steady state of 33 kg/s and 543 K, respectively. Another transient is also simulated, i.e., a transient related to noise resulting from stochastic movements of the fuel particles. For this purpose, an additional term is included in the reactivity feedback and modeled as a time-dependent external reactivity. Magnitude of the variance for this simulation is obtained from the preceding static calculations. These simulations show that the total power of the reactor may fluctuate and reach high values. However, the fuel temperature, thanks to passive reactivity feedback, is well below safety limits at all times.