Theory of pump-induced pulsating coolant pressure in pressurized water reactors

The theory of pump-induced pulsating pressure distributions in a PWR coolant annulus is developed. The calculated pressure distribution can then be applied to predict the dynamic responses of the reactor internals. The mathematical analysis is formulated in accordance with the linearized Navier-Stokes' equations by assuming a compressible, inviscid liquid. These equations are combined to form a single equation in terms of the unknown pressure distribution. The boundary conditions are two concentric rigid walls in the radial direction and any combination of closed, open, and piston-spring supported end conditions in the axial direction. The pulsating pump pressure which induces the pressure fluctuation in the annulus is prescribed at a small opening of the outer cylindrical wall (pump inlet of the reactor).An approximate solution is obtained by introducing the concept of time-dependent body force in the governing differential equations. With this conceptual substitution for the actual loading, the time-dependent, mixed boundary value problem can be represented as a forced vibration problem with homogeneous boundary conditions. This problem can then be solved by the method of normal modes. Numerical examples are provided which give the pressure distribution in the axial and circumferential directions of the annulus for various configurations of one and/or several pumps.     

Neutron noise measurements on pressurized water reactors

Noise analysis contributes to increase significantly understanding of safety and monitoring of PWR. The difficulties of a correct interpretation of noise signal in a power reactor encourage a deeper insight into the theoretical model. Following, this paper is dealing with 4 topics:

• - theoretical model

• - measurements made in PWR's, and evolution of power spectral densities,

• - experimental test of models,

• - future study in this range : methodology for early detection of failure and to indicate incipient failure.

Using the expressions for linear system and for feedback loop, we obtain a simplified diagram for PWR with reactivity, temperature, velocity of fluid inputs and movement of internal structures.

Neutron noise measurements are performed periodically on the “Centrale Nucléaire des Ardennes”. An investigation is also performed, in order to detect core barrel movements.

The change of neutron noise at several power levels is shown, and used to check the model.

The development of signal analysis and models for PWR is investigated in the last chapter.     

Active measures to preclude breaks in the reactor coolant lines of pressurized water reactors

The active measures which preclude a spontaneous failure of the reactor coolant lines are exemplarily shown. With the basic safety concept a quality standard is achieved characterized by high-grade material properties, a structure that is adequate to the loads to which the components will be subjected in service and is amenable to inspection, precise load and stress evaluation, optimized manufacturing and operation monitoring. The possible failure types are described and the safety against failure is assessed.     

Neutron noise monitoring of pressurized water reactor internal vibrations

Analytical and experimental results have shown that the neutron noise signals are typically the sum of a number of different noise sources. These can have significant interactions due to structural coupling and summation effects in the sensor. Analytical techniques have been developed to identify major neutron noise sources and to separate and account for some of the noise source coupling effects.

This work has demonstrated the use of various noise source models in neutron noise monitoring applications. Methods of identifying and separating the noise sources have been used to relate changes in the measured spectra to particular noise source properties. The noise source models can then be used to relate noise source properties to physical properties of the system. These techniques are used in routine surveillance applications and have provided proper evaluation of several trends and changes that have been observed in neutron noise monitoring programs.

All neutron noise measurements have shown small vibration amplitudes that are in agreement with results from preoperational measurements and analysis. Neutron noise monitoring is being continued on an optional basis in a number of plants as a means of monitoring core clamping and general long-term performance.     

Counter-current flow limitations during hot leg injection in pressurized water reactors

A one-dimensional model is presented to predict counter-current flow limitations during hot leg injection in pressurized water reactors. Different from previous models, it may also be applied in case of high Froude numbers of the liquid flow, such as to be expected in the case of emergency coolant injection through the hot leg. The model has been verified with an extensive experimental program performed in the WENKA test facility at the Forschungszentrum Karlsruhe. Typical flow regimes were investigated for a wide range of flow conditions, simulated with air and water at ambient pressure and temperature, in a simplified Pressurized Water Reactor (PWR) hot leg geometry. Depending on the water and air flow rates, flow phenomena such as a hydraulic jump and flow reversal were experimentally observed. The theoretical model shows that not only the nondimensional superficial velocities of liquid and gas, but also the Froude number of the liquid at the injection point and the Reynolds number of the gas play an important role for the prediction of flow reversal. In case of a high liquid inlet Froude number, a flow reversal could only be observed if the liquid flow became locally subcritical, i.e. if a hydraulic jump occurred in the channel. The flow reversal is predicted by the presented model with good accuracy.     

Computed phase equilibria for burnable neutron absorbing materials for advanced pressurized heavy water reactors

Burnable neutron absorbing materials are expected to be an integral part of the new fuel design for the Advanced CANDU^®[CANDU is as a registered trademark of Atomic Energy of Canada Limited.] Reactor. The neutron absorbing material is composed of gadolinia and dysprosia dissolved in an inert cubic-fluorite yttria-stabilized zirconia matrix. A thermodynamic model based on Gibbs energy minimization has been created to provide estimated phase equilibria as a function of composition and temperature. This work includes some supporting experimental studies involving X-ray diffraction.     

Investigation of low-frequency neutron and temperature noise signals induced by local coolant boiling in a PWR

In special experiments performed in a PWR-NPP low-frequency neutron noise effects were found to be induced by local coolant boiling. A model for describing this phenomenon is developed. It is based on the assumption that integral void fluctuations are the neutron physical perturbation source. The void fluctuations themselves depend on primary noise sources (fluctuations of inlet temperature, coolant flow rate, reactor power) which are estimated with a thermohydraulic model from the axial dependence of temperature noise signals. The theoretical results are compared with measured values. It is shown that the low-frequency neutron noise can be used for boiling monitoring in PWRs.     

MTC estimation based on neutron noise and propagating temperature perturbation in VVER-440 reactors

Moderator Temperature Coefficient (MTC) is an important parameter characterizing inherent safety in PWRs. Noise diagnostics provides a theoretically well established method to estimate its value without changing the reactor state with using fluctuation of the temperature and neutron flux measurements in frequency domain. However, several difficulties arise when determining the core average neutron and temperature fluctuation from the real measured signals, due to the specific instrumentation of each reactor type. Coolant temperature fluctuations originate from inhomogeneities traveling with the coolant flow and the treatment of this phenomenon requires an approach using the theory of propagating perturbations. Traditional MTC estimation methods do not consider these effects and they result in substantial under- and overestimations.     

Spatial instability analysis in pressurized water reactors

A simple methodology has been developed to assess the spatial dynamic behavior of large PWRs against xenon spatial instability in different modes. Method of analysis aims to analyze xenon dynamic behavior against anticipated reactivity perturbations. Reactivity perturbations in different modes have been evaluated based on reactivity device movements as well as localized thermal variations in the core. Effect of individual core design and operating parameters on xenon spatial instability has been studied. Behavior of spatial stability index (SI) with core size is investigated. Based on SI-core size curve, a threshold core size has been determined beyond which a PWR core tends to become spatially unstable. Methodology has been used to assess the spatial xenon dynamic behavior of different modes of oscillations in VVER1000 and AP1000 reactor cores.     

Construction management of Indian pressurized heavy water reactors

Pandit Jawaharlal Nehru and Dr. Homi J. Bhabha, the visionary architects of Science and Technology of modern India foresaw the imperative need to establish a firm base for indigenous research and development in the field of nuclear electricity generation. The initial phase has primarily focused on the technology development in a systematic and structured manner, which has resulted in establishment of strong engineering, manufacturing and construction base.The nuclear power program started with the setting up of two units of boiling light water type reactors in 1969 for speedy establishment of nuclear technology, safety culture, and development of operation and maintenance manpower. The main aim at that stage was to demonstrate (to ourselves, and indeed to the rest of the world) that India, inspite of being a developing country, with limited industrial infrastructure and low capacity power grids, could successfully assimilate the high technology involved in the safe and economical operation of nuclear power reactors. The selection of a BWR was in contrast to the pressurized heavy water reactors (PHWR), which was identified as the flagship for the first stage of India's nuclear power program. The long-term program in three stages utilizes large reserves of thorium in the monazite sands of Kerala beaches in the third stage with first stage comprising of series of PHWR type plants with a base of 10,000 MW. India has at present 14 reactors in operation 12 of these being of PHWR type.The performance of operating units of 2720 MW has improved significantly with an overall capacity factor of about 90% in recent times.The construction work on eight reactor units with installed capacity of 3960 MW (two PHWRs of 540 MW each, four PHWRs of 220 MW each and two VVERs of 1000 MW each) is proceeding on a rapid pace with project schedules of less than 5 years from first pour of concrete. This is being achieved through advanced construction technology and management. Present efforts are focused on further reduction of gestation period. This is in contrast to construction period of 7–14 years in the earlier projects with labour intensive construction methods, learning period and indigenisation. The schedule and cost are interrelated and ultimately determine the viability and competitive edge of a project. With rich experience of over 30 years of operation and construction management it is well established that setting up of nuclear power projects in India in 4–5 years is quite feasible because of tremendous developments in construction technology; mechanization, parallel civil works and equipment erection, computerized project monitoring and accounting systems. By considering the best achieved times for the critical path activities of previous and ongoing projects, even a 4-year schedule is achievable. For nuclear power to be competitive it is essential that the gestation period is reduced and the capacity utilization enhanced. Both of these are the goals of the Indian nuclear power program. Presently the overnight cost per kW installed capacity is in the range of US$ 1100–1300 with levellised tariff of 5 c/kWh.     

Applicability of neutron noise technique for diagnostics of in-core components for heavy water reactors

Neutron flux signal is composed of a steady or mean component resulting from the flux produced by power operation of the reactor and a very small fluctuating component called ‘noise’ component. Analysis of neutron noise from suitably located sensors is a proven technique to monitor the in-core components of light water reactors (LWRs). However, the use of neutron noise has been rare, if any, for heavy water reactors (HWRs) as it was generally felt that the unfavourable transfer function characteristics of the reactors would limit its applicability. To assess the applicability of technique in pressurised heavy water reactors (PHWRs), experiments were carried out using in-core and out-of-core neutron sensors in a research reactor. This paper discusses the measurement details and results of the experiment. This paper concludes that the neutron noise technique can be effectively utilised for diagnostics/characterisation of the in-core components of heavy water reactors.     

Measurement of the coolant flow rate using correlation of temperature fluctuations

The transit time of the coolant, and thus its velocity, has been measured using the temperature fluctuation at the outlet of a reactor core. An impulse response function estimation is introduced, which substitutes the widely used cross-correlation measurement technique. It is shown in theory and practice that the time delay estimation is improved when using the impulse response function instead of the cross-correlation function in parameter estimation. Extremely low velocities (down to 2 cm/sec) have been measured in a natural circulation regime in a research reactor.     

In-core fuel management optimization of pebble-bed reactors

A reduction of the power peak in the core of High Temperature pebble-bed reactors is attractive to decrease the maximum fuel temperature and to increase fuel performance. A calculation procedure was developed, which combines fuel depletion, neutronics and thermal–hydraulics to investigate the impact of a certain (re)loading scheme for the pebble-bed type HTR. The procedure has been applied to a model of the Pebble Bed Modular Reactor (400 MW) design.This paper shows that an important reduction in axial power peaking can be achieved by adopting a multi-pass recycling scheme for the pebbles. By dividing the core into several radial fuel zones in combination with multi-pass recycling the power profile can be flattened in the radial direction. For a core with two fuel zones the impact on the k_eff and maximum power density as a function of the zone size has been investigated. A heuristic method has been used to find the optimal pebble loading pattern for several (re)loading schemes. Using this method a reduction of the maximum power density from 10.0 to 8.2 MW/m³ has been achieved for a core with three radial fuel zones.The effects of the improved power profiles on the fuel temperature during normal operation and a Depressurized Loss Of Coolant (DLOFC) accident have been analyzed. It was found that the optimized power profile results in a reduction of the maximum fuel temperature of 80 °C and 300 °C for normal operation and DLOFC conditions, respectively.     

RANS modeling for flow in nuclear fuel bundle in pressurized water reactors (PWR)

This paper presents use of Reynolds-averaged Navier-Stokes (RANS) based turbulence model for single-phase CFD analysis of flow in pressurized water reactor (PWR) assemblies. An open source code called OpenFoam was used for computational fluid dynamics (CFD) study using computational meshes generated using Shari Harpoon. The PWR assembly design used in this analysis represents a 5 × 5 pin design including structural grid equipped with mixing vanes. The design specifications used in this study were obtained from the experimental setup at Texas A&M University and the results obtained are used to validate the CFD software, algorithm, and the turbulence model used in this analysis.     

Noise and DC balanced outlet temperature signals for monitoring coolant flow in LMFBR fuel elements

Local cooling disturbances in LMFBR fuel elements may have serious safety implications for the whole reactor core. They have to be detected reliably in an early stage of their formation therefore. This can be accomplished in principle by individual monitoring of the coolant flow rate or the coolant outlet temperature of the subassemblies with high precision.

In this paper a method is proposed to increase the sensitivity of outlet temperature signals to cooling disturbances. Using balanced temperature signals provides a means for eliminating the normal variations from the original signals which limit the sensitivity and speed of response to cooling disturbances. It is shown that a balanced signal can be derived easily from the original temperature signal by subtracting an inlet temperature and a neutron detector signal with appropriate time shift.

The method was tested with tape-recorded noise signals of the KNK I reactor at Karlsruhe. The experimental results confirm the theoretical predictions. A significant reduction of the uncertainty of measured outlet temperatures was achieved. This enables very sensitive and fast response monitoring of coolant flow.

Furthermore, it was found that minimizing the variance of the balanced signal offers the possibility for a rough determination of the heat transfer coefficient of the fuel rods during normal reactor operation at power.     

The inherent boron dilution mechanism in pressurized water reactors

The purpose of this paper is to describe a mechanism that inherently causes boron dilution in pressurized water reactors (PWRs). The phenomenon is due to the fact that boric acid does not markedly dissolve into steam. This is relevant for transient and accident situations in PWRs where decay heat removal is accomplished by coolant vapourization and condensation, which inherently leads to formation of dilute plugs in the primary. In particular, it is found that inherent dilution will be inevitable for a range of small break loss of coolant accidents (SB LOCAs), with maximum amount of total diluted coolant mass exceeding 20 tonnes for a modern 1300 MWe PWR equipped with U-tube steam generators. A simple analysis of dilute plug motion during the late phases of a SB LOCA and core response to boron dilution shows that the damaging potential might extend to widespread fuel failures. Other transients and accidents are also discussed from the point of view of inherent dilution. Some possible remedies to the problem, as well as suggestions for further research, are presented.     

Detection of steam generator tube leaks in pressurized water reactors

This report addresses the early detection of small steam generator tube leaks in pressurized water reactors. It discusses the third, and final, year's work on an NRC-funded project examining diagnostic instrumentation in water reactors. The first two years were broad in coverage, concentrating on anticipatory measurements for detection of potential problems in both pressurized- and boiling-water reactors, with recommendations for areas of further study. One of these areas, the early detection of small steam tube leaks in pressurized water reactors (PWRs), formed the basis of study for the last year of the project.Four tasks are addressed in this study of the detection of steam tube leaks.

1. (1) Determination of which physical parameters indicate the onset of steam generator tube leaks.

2. (2) Establishing performance goals for diagnostic instruments which could be used for early detection of steam generator tube leaks.

3. (3) Defining the diagnostic instrumentation and their location which satisfy Items 1 and 2 above.

4. (4) Assessing the need for diagnostic data processing and display.

Parameters are identified, performance goals established, and sensor types and locations are specified in the report, with emphasis on the use of existing instrumentation with a minimum of retrofitting. A simple algorithm is developed which yields the leak rate as a function of known or measurable quantities. The conclusion is that leak rates of less than one-tenth gram per second should be detectable with existing instrumentation.