Tim H. J. J. van der Hagen

Stability of natural circulation boiling water reactors : Part I. Description stability model and theoretical analysis in terms of dimensionless groups

A theoretical model describing coupled neutroni-thermohydraulic power oscillations in natural circulation boiling water reactors (BWRs) is developed. The governing equations for the thermohydraulic subsystem are transformed to a dimensionless basis, to eliminate all explicit pressure dependence in the model. It is proved that all necessary information about the operating conditions is incorporated in onlu ttwo dimensionless numbers: the Zuber and the subcooling number. The density ratio number cancels in the dimensionless equations because a homogeneous flow model is applied. The Froude number is also shown to be redundant in a natural circulation system, as it can be expressed in the other dimensionless groups. The stability boundary of the complete coupled neutronic-thermohydraulic reacotr system in the dimensionless Zuber-subcooling plane is estimated to be rather insensititve to the system pressure as well. Therefore the usage of dimensionless stability maps, instead of the traditional power-flow maps, is strongly recommended as an efficient method to determine the dynamic characteristics of natural circulation BWRs.

Stability of natural circulation boiling water reactors : Part II. Parametric study of coupled neutronic-thermohydraulic stability

A parametric study of coupled neutronic-thermohydraulic stability of natural circulation boiling water reactors (BWRs) is performed. As an example, the stability characteristics of the Dutch Dodewaard reactor, which was cooled by natural circulation, arr determined. The Dodewaard reactor can be considered as the prototype of next generation natural circulation BWRs. The stability, issues that are identified for this prototype reactor are therefore important in the design of new natural circulation BWRs. Without a riser section installed, only one region of thermohydraulic instability exists in the stability plane. The significant gravitational pressure drop in a rise section, installed to enhance the natural circulation flow, gives rise to the emergence of an additional region of instability The oscillations in this zone become especially important during low-pover/low-pressure (reactor startup) conditions. Significant, damping of these oscillations occurs in a reactor due to the nuclear void reactivity feedback. A comparison between natural circulation in-phase and out-of-phase reactor stability is made, in particular important for large reactor cores but also yielding unexpected results for small reactors. The impact of downcomer inertia on the stability of the in-phase mode is investigated in detail. Typical trajectories in the dimensionless stability plane are calculated as a function of changing operating conditions, to investigate their influence on reactor dynamics.

Stability of Natural-Circulation-Cooled Boiling Water Reactors During Startup: Experimental Results

Abstract The characteristics of flashing-induced instabilities, which are of importance during the startup phase of natural-circulation boiling water reactors, are studied. Experiments at typical startup conditions (low power and low pressure) are carried out on a steam/water natural-circulation loop. The flashing and the mechanism of flashing-induced instability are analyzed. The effect of system pressure and steam volume in the steam dome is investigated as well. The instability region is found as soon as the operational boundary between single-phase and two-phase operation is crossed. Increasing pressure has a stabilizing effect, reducing the operational region in which instabilities occur. Nonequilibrium between phases and enthalpy transport are found to play an important role in the instability process. In contrast with results reported in the literature, instabilities can occur independently of the position of the flashing boundary in the adiabatic section of the loop. The period of the oscillation is found to be about twice the fluid transit time in the system.

Investigating the Nonlinear Dynamics of Natural-Circulation, Boiling Two-Phase Flows

Abstract The nonlinear dynamics of natural-circulation, boiling two-phase flows are investigated using a two-phase flow loop. Experiments have been carried out in the unstable operating region of the facility for various system pressures and for different frictions at the exit of the riser section. It appears that the boiling two-phase flow undergoes the well-known Feigenbaum scenario, the period-doubling route toward chaotic behavior. Evaluation of the recorded signals using nonlinear time series analysis methods indicates the occurrence of chaotic density-wave oscillations.

Core Design and Fuel Management Studies of a Thorium-Breeder Pebble Bed High-Temperature Reactor

Abstract An inherently safe thorium-breeder pebble bed reactor has great potential to improve the safety and sustainability of nuclear energy. The aim of this work is to determine the conditions under which breeding is possible in a thorium-breeder pebble bed reactor (PBR) and to present possible core designs for such a reactor. A method is developed to calculate the equilibrium core configuration of a thorium-breeder PBR, consisting of a driver channel and a breed channel. The SCALE system is used for cross-section generation and fuel depletion, and a two-dimensional (r,z)-flux profile is obtained using the DALTON neutron diffusion code. With the code scheme, the influence of several geometrical, operational, and fuel management parameters on breeding capability can be studied. Four fuel reprocessing schemes are investigated. The first scheme recycles breeder pebbles into the driver channel after some delay for additional 233Pa decay. The second scheme reprocesses the discharged breeder pebbles to make driver pebbles with higher 233U content. The third scheme also reprocesses the uranium isotopes from the discharged driver pebbles. Criticality, and thus breeding, can only be achieved in practice for this case. The fourth scheme, which adjusts the driver pebble residence time to find a critical core, is used to design a thorium-breeder PBR under practical operating conditions. A breeder reactor can even be achieved for a 150-cm core diameter, the same as for the uranium-fueled HTR-PM, but the design presented operates at a significantly lower reactor power, 71 MW(thermal) compared with 250 MW(thermal).

Characteristics of Type-I Density Wave Oscillations in a Natural Circulation BWR at Relatively High Pressure

Experiments were conducted to investigate two-phase flow instabilities in a boiling natural circulation loop with a chimney at high pressure. The SIRIUS-N facility was designed to have non-dimensional values which are nearly equal to those of a typical natural circulation BWR. The observed oscillations are found to be density wave oscillations, since the void fractions in the chimney inlet and exit are out of phase. They belong to the Type-I category, since they occur at low flow qualities, according to the Fukuda—Koboris classification. Moreover, the oscillation period correlates well with the passing time of bubbles in the chimney section regardless of the system pressure, the heat flux, and the inlet subcooling. Two distinct phenomena are found in relation between the oscillation period and liquid passing time in the chimney, indicating that the driving mechanisms of the instabilities are different between low and high pressures. Stability maps were obtained in reference to the inlet subcooling and the heat flux at the system pressures of 1, 2, 4, and 7.2 MPa. The flow became stable below a certain heat flux regardless of the channel inlet subcooling. The stable region enlarges with increasing system pressure. Thus, the stability margin becomes larger in a startup process of a reactor by pressurizing the reactor sufficiently before withdrawing the control rods. The obtained stability map demonstrates that the nominal operating condition of the ESBWR has a significant stability margin to the unstable region.

Multifractal Analysis of Chaotic Flashing-Induced Instabilities in Boiling Channels in the Natural-Circulation CIRCUS Facility

Abstract 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 self-similarity 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(α), which is the Hausdorff dimension of the set of points where the multifractal object has singularities of strength (or Hölder exponents of) α. 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 natural-circulation systems in a multiple-riser configuration has thus to be avoided.

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.

Suitability of drift-flux models, void-fraction evolution, and 3-D flow pattern visualization during stationary and transient flashing flow in a vertical pipe

Abstract An assessment of void-fraction correlations and drift-flux models applied to stationary and transient flashing flows in a vertical pipe has been performed. Experiments have been carried out on a steam/water loop that can be operated both in forced- and natural-circulation conditions to provide data for the assessment. The GE-Ramp and Dix models are found to give very good predictions both for forced- and natural-circulation flow conditions, in the whole range of measured void fractions. Advanced instrumentation, namely, wire-mesh sensors, has been used to obtain a detailed picture of the void-fraction development in the system. On the basis of experimental data, a three-dimensional visualization of the transient flow pattern during flashing was achieved. A transition of the flow pattern between bubbly and slug/churn regimes was found.