Papers by Tim van der Hagen
Investigating the Stability Characteristics of Natural-Circulation Boiling Water Reactors Using Root Loci of a Reduced-Order Model
Nuclear Technology, 2001
Nuclear Science and Engineering, 2008
In this paper, two-phase-flow oscillations at the natural-circulation CIRCUS test facility are in... more In this paper, two-phase-flow oscillations at the natural-circulation CIRCUS test facility are investigated in a two-riser configuration. These oscillations are driven by flashing (and to some extent by geysering). For a given range of operating conditions of the facility, the oscillations exhibit erratic behavior. This study demonstrates that this behavior can be attributed to deterministic chaos. This is proven by performing a continuous wavelet transform of the measured time series. Any hidden selfsimilarity in the measurement is seen in the corresponding scale-space plane. The novelty of the present investigation lies with the multifractal approach used for characterizing the chaos. Both nonlinear time series analysis and wavelet-based analysis methods show that the dynamics of the flow oscillations has a multifractal structure. For the former, both Higuchi's method and detrended fluctuation analysis (DFA) were used, whereas for the latter, the wavelet-transform modulus-maxima method was used. The strange attractor corresponding to the dynamics of the system can thus be described as a set of interwoven monofractal objects. The global singular properties of the measured time series is then fully characterized by a spectrum of singularities f (a), which is the Hausdorff dimension of the set of points where the multifractal object has singularities of strength (or Hölder exponents of) a. Whereas Higuchi's method and DFA allow easily determining whether the deterministic chaos has a monofractal or multifractal hierarchy, the wavelet-transform modulus-maxima has the advantage of giving a quantitative estimation of the fractal spectrum. The time-modeling of such behavior of the facility is therefore difficult since there is sensitive dependence on initial conditions. From a regulatory point of view, such behavior of naturalcirculation systems in a multiple-riser configuration has thus to be avoided.
International Journal of Multiphase Flow, 2006
For the first time, an experimental three-dimensional reconstruction and visualization of station... more For the first time, an experimental three-dimensional reconstruction and visualization of stationary and transient flashing flow in a vertical pipe (47 mm diameter) is presented. The measurements have been performed by means of wire-mesh sensors. This type of sensor delivers two-dimensional void-fraction distributions in the pipe cross-section where it is mounted with a maximum sampling rate of 10,000 frames per second. A sampling rate of 1200 frames per second has been used in this work. Steam bubbles have been identified from the wire-mesh data and their complete three-dimensional reconstruction has been performed by taking into account the steam bubble velocity. For the estimation of the bubble velocity, two wire-mesh sensors positioned at a small axial distance from each other have been used. The velocity has been determined by cross-correlation of the two wire-mesh signals, by direct identification of the traveling time of the steam bubbles between the two sensors and by means of a drift-flux model. A comparison between the three methods of bubbles velocity measurement is reported. Stationary and time-dependent bubble size distributions have been derived. The stationary radial void-fraction profiles have been decomposed according to bubble size classes and compared with the results obtained with an equilibrium model.
Burnup calculations have been performed on a standard HTR fuel pebble (R=3 cm) containing 9 grams... more Burnup calculations have been performed on a standard HTR fuel pebble (R=3 cm) containing 9 grams of 8% enriched uranium and burnable particles made of B 4 C highly enriched in B-10. The radius of the burnable particles and the number of particles per fuel pebble have been varied to find the flattest reactivity-to-time curve. It was found that for a target k∞ of 1.1, a reactivity swing as low as 2.4% can be obtained when each fuel pebble contains about 1300 burnable particles with a radius of 70 µm. For other values of the target k∞ even lower values can be obtained. For 'hollow' burnable particles that consist of a graphite kernel with a radius of 300 µm covered with a burnable poison layer of 30 µm, the reactivity swing is only 2%. In general, the modification of the geometry of burnable particles is an effective means to tailor the reactivity curve of HTRs.
The gas cooled fast reactor (GFR) is one of the generation IV designs currently being evaluated f... more The gas cooled fast reactor (GFR) is one of the generation IV designs currently being evaluated for future use. It is intended to behave as an isobreeder, producing the same amount of fuel as it consumes during operation. The actinides in the fuel will be recycled repeatedly in order to minimise the waste output to fission products only. Striking the balance of the fissioning of various actinides against transmutation and decay to achieve these goals is a complex problem. This is compounded by the time required for burn-up modelling, which can be considerable for a single cycle, and even longer for studies of fuel evolution over many cycles.
The continuous fuel cycle model [1] was created to predict the composition of reactor fuel after ... more The continuous fuel cycle model [1] was created to predict the composition of reactor fuel after many cycles without the need for multiple lengthy burn-up calculations. Averaging the behaviour of the fuel composition over a cycle and modelling unloading and reloading as continuous processes results in significant simplification of the equations governing fuel composition, and the information gained remains useful in studies of the long term issues of the nuclear fuel cycle. Given that the questions of sustainability and waste minimization are major issues for nuclear power, it is appropriate to return to the continuous model and examine how it may be usefully applied to contemporary problems. We have experimented with adding nuclides to the continuous model in order to make it more applicable to modern fast reactor designs. The composition and system growth values obtained from this extended model are compared to those from more traditional fuel cycle modelling. The effects of replacing the constraint on the reactivity of each core with a power constraint are also investigated.
Constrained Quantities in Uncertainty Quantification: Ambiguity and Tips to Follow
The nuclear community relies heavily on computer codes and numerical tools. The results of such c... more The nuclear community relies heavily on computer codes and numerical tools. The results of such computations can only be trusted if they are augmented by proper sensitivity and uncertainty (S&U) studies. This paper presents some aspects of S&U analysis when constrained quantities are involved, such as the fission spectrum or the isotopic distribution of elements. A consistent theory is given for the derivation and interpretation of constrained sensitivities as well as the corresponding covariance matrix normalization procedures. It is shown that if the covariance matrix violates the “generic zero column and row sum” condition, normalizing it is equivalent to constraining the sensitivities, but since both can be done in many ways different sensitivity coefficients and uncertainties can be derived. This makes results ambiguous, underlining the need for proper covariance data. It is also highlighted that the use of constrained sensitivity coefficients derived with a constraining proced...
On the Use of PN and SN Methods for Radiative Heat Transfer in a Fluidized Bed Nuclear Reactor (A Case Study for Passive Removal of Decay Heat)
Numerical simulations have been performed to investigate the possibility of passive decay heat re... more Numerical simulations have been performed to investigate the possibility of passive decay heat removal in a fluidized bed nuclear reactor. The conduction, convection and radiative heat transfer were included and the high Reynolds number k-ε turbulence model was applied for the flow calculations. The P 1 and S N approximation methods for participating media were used for the radiation model. The reactor was modeled as a 2D axisymmetric cylinder. Calculations were performed for an initial operating power of 60 MW. The results show that P 1 method is quite good to be applied in the particle bed but it fails in the freeboard. The high order S N method can be applied extremely good both in the particle bed and the freeboard. The drawback of the S N method is its long computational time. The invalidity of P 1 method leads to a high fuel particle temperature, exceeding its allowable maximum value. Such situation, however, does not occur in the S N method.
Annals of Nuclear Energy, 2014
Nuclear Science and Engineering, 2013
Sensitivity analysis is a technique that is widely used in reactor physics calculations to effici... more Sensitivity analysis is a technique that is widely used in reactor physics calculations to efficiently obtain first-order changes in responses of interest due to variations of input parameters. This paper presents an extension of the well-known perturbation procedures for the critical eigenvalue and flux functionals. The extended method makes it possible to determine sensitivities in coupled criticality problems with mutual feedback between neutronics and one or more augmenting systems (e.g., thermal hydraulics or fission product poisoning). The technique uses appropriate neutronic and augmenting adjoint functions, which can be obtained by solving a system of coupled adjoint equations. Three different approaches are presented for considering the effects of perturbations in coupled criticality problems with feedback: The steady-state power level is allowed to adjust to maintain criticality with the perturbed parameters (power perturbation), a change is allowed in the critical eigenvalue while the flux is constrained (eigenvalue perturbation), or simultaneous perturbations are made to ensure criticality at the unperturbed power level (control parameter perturbation). In the case of power and eigenvalue perturbations, sensitivities can be obtained with or without power-and k-reset procedures, respectively, yielding identical results to control parameter perturbation. The paper presents the theoretical background, an application to a one-dimensional slab problem with thermal and fission product feedback, and a numerical procedure to obtain the necessary adjoint functions. The proposed technique relies on using the neutronics and augmenting codes separately as a preconditioner for Krylov methods employed to the coupled adjoint problem. This makes the development of new codes unnecessary and provides means of large-scale implementation.
Annals of Nuclear Energy, 2014
The evaluation of experimental techniques for the determination of the subcriticality level of an... more The evaluation of experimental techniques for the determination of the subcriticality level of an ADS core relies on reactor point kinetics. The measured parameters depend on the detector position, and the reactivity values are subject to spatial correction factors (SCFs). In this paper the contribution of different eigenmodes to the SCF for the pulsed neutron source (PNS) technique is assessed. Moreover by pulse simulations, precise values of the correction factor are obtained. As case study, the VENUS-F SC1 subcritical core is investigated, with a pulsed neutron source in the center of the core, generated by the GENEPI-3C deuteron accelerator. Much more than 100 modes need to be taken into account to precisely obtain the spatial correction factor for the area method evaluation of this core. Especially the modes with a maximum in the center of the core contribute significantly to the SCF. No spatial correction needs to be applied close to the zeros of the first mode with a maximum in the center of the core (different from the fundamental one). In the reflector zone, the absolute reactivity level is overestimated.
Gelina neutron target optimisation
Radiation Protection Dosimetry, 2005
A study is being performed on the properties of the Geel Electron Linear Accelerator (GELINA), a ... more A study is being performed on the properties of the Geel Electron Linear Accelerator (GELINA), a powerful white neutron source, designed for the high-energy resolution time-of-flight measurements. The main aim of this study is to reduce the time spread of neutrons of the given energy without compromising the neutron yield. Both time spread and neutron intensity influence the experimental accuracy of high-resolution neutron cross section measurements, which are particularly important in the resonance region. The quantities of interest have been simulated with coupled electron-photon-neutron steady state and transient MCNP4C3 calculations. Following benchmarking of the code to the properties of the existing target, neutron yield, energy spectra, resolution functions, and neutron and heat spatial distributions have been determined for various alternative geometries and materials. At a fixed accelerator power, actinides deliver the highest neutron yield and a small target provides the best time resolution. The resulting high-power density requires a joint optimisation of the thermal hydraulics and neutronics properties.
Fuel Particle Design for a Fluidized Bed Reactor
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2004
Coupled electron-photon-neutron transport calculations were performed with the Monte Carlo code M... more Coupled electron-photon-neutron transport calculations were performed with the Monte Carlo code MCNP4C3 to model the GELINA neutron target. Our calculations were compared with measurements of the direct and moderated flux distributions and agreement was achieved within 20%. Further, the present simulations were compared with the resolution functions established earlier with a dedicated program and with measured data for 56 Fe. Here too, the agreement is excellent. New IAEA photonuclear libraries were implemented to perform these calculations. The simulations crucially rely on the new MCNP4C3 photonuclear capabilities and are made efficient by using the variance reduction and TALLYX features.
Nuclear Engineering and Design, 1994
The Dodewaard BWR is cooled via natural circulation. To be able to study the thermohydraulic beha... more The Dodewaard BWR is cooled via natural circulation. To be able to study the thermohydraulic behaviour of such a nuclear reactor, a freon-cooled scaled version of one fuel assembly of this reactor is designed. The scaling criteria for the design are obtained from a one-dimensional drift flux model. The emphasis in the derivation is on correct development of the flow quality and the different flow regimes that are present inside the assembly. Two distinct regimes have been taken in consideration, the lower part of the assembly in which subcooled boiling is present and the upper part of the assembly which is in thermal equilibrium. The outcome of the analysis is that, by using freon-12 as a modelling fluid, all system setup parameters are fixed while scaling on all possible flow regimes at the same time: the linear dimensions have to be reduced by a factor of 0.46, the working pressure and the temperature are lowered substantially to 11.6 bar and 48°C respectively and the power consumption of the scaled assembly is only 2% of that of a Dodewaard assembly.
Planned experimental studies on natural-circulation and stability performance of boiling water reactors in four experimental facilities and first results (NACUSP)
Nuclear Engineering and Design, 2003
Within the 5th Euratom framework programme the NACUSP project focuses on natural-circulation and ... more Within the 5th Euratom framework programme the NACUSP project focuses on natural-circulation and stability characteristics of Boiling Water Reactors (BWRs). This paper gives an overview of the research to be performed. Moreover, it shows the first results obtained by one of the four experimental facilities involved. Stability boundaries are given for the low-power low-pressure operating range, measured in the CIRCUS
Nuclear Engineering and Design, 2005
Nuclear Engineering and Design, 2010
By altering the coolant flow direction in a pebble bed reactor from axial to radial, the pressure... more By altering the coolant flow direction in a pebble bed reactor from axial to radial, the pressure drop can be reduced tremendously. In this case the coolant flows from the outer reflector through the pebble bed and finally to flow paths in the inner re
Flashing-induced density wave oscillations in a natural circulation BWR—mechanism of instability and stability map
Nuclear Engineering and Design, 2005
Experiments were conducted to investigate two-phase flow instabilities due to flashing in a boili... more Experiments were conducted to investigate two-phase flow instabilities due to flashing in a boiling natural circulation loop with a chimney at low pressure. The SIRIUS-N facility was designed to have non-dimensional values nearly equal to those of typical natural circulation boiling water reactor (BWR).The observed instability is suggested to be flashing-induced density wave oscillations, since the oscillation period correlated well
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Papers by Tim van der Hagen