V. Venkat Raj

Uncertainty in fault tree analysis: a fuzzy approach

Abstract In fault tree analysis, the uncertainties in the failure probability and/or failure rate of system components or basic events can be propagated to find the uncertainty in the overall system failure probability. The conventional approach is Monte-Carlo simulation by assuming a probability distribution for the failure probability. In addition, a new methodology based on fuzzy set theory is also being used in the fault tree analysis for quantifying the basic event uncertainty and for propagating it. However, identification of the components which contribute maximum to the system failure probability is also important in fault tree analysis. Similarly, ranking the components based on their contribution of uncertainty to the uncertainty of the system failure probability is also very important. This paper presents a comparative study of probabilistic and fuzzy methodologies for top event uncertainty evaluation. Further, it explains a new approach to rank the system components or basic events depending on (1) their contribution to the top event failure probability and (2) their uncertainty contribution to the uncertainty of the top event based on fuzzy set theory.

Profiles of doses to the population living in the high background radiation areas in Kerala, India

A sample study of the profiles of radiation exposures to the populations living in the high background radiation areas (HBRAs) of the monazite-bearing region in Kerala, India, has been conducted by monitoring 200 dwellings selected from two villages in this region. Each of these dwellings was monitored for 1 year and the study lasted for a period of 2 years. The indoor gamma ray dose measurements were carried out using thermo luminescent dosimeters (TLDs) and the inhalation doses due to radon, thoron and their progenies were monitored using solid-state nuclear track detector (SSNTD) based twin-cup dosimeters. Outdoor gamma ray dose measurements were carried out using Geiger Muller (GM) tube based survey meters. Annual effective doses were computed, using occupancy factors of 0.8 and 0.2, respectively, for indoor and outdoor, by adding the three components. Occupants of 41.6% of the houses surveyed were observed to receive the annual effective doses ranging between 0.5 and 5 mSv/a, 41.6% between 5 and 10 mSv/a, 10.2% between 10 and 15 mSv/a and 6.6% greater than 15 mSv/a. The inhalation component was generally smaller than the external gamma ray component and on an average it was found to constitute about 30% of the total dose. The paper presents the details of the methodology adopted and the analysis of the results.

Analytical study of nuclear-coupled density-wave instability in a natural circulation pressure tube type boiling water reactor

Abstract An analytical model has been developed to study the nuclear-coupled density-wave instability in the Indian advanced heavy water reactor (AHWR) which is a natural circulation pressure tube type boiling water reactor. The model considers a point kinetics model for the neutron dynamics and a lumped parameter model for the fuel thermal dynamics along with the conservation equations of mass, momentum and energy and equation of state for the coolant. In addition, to study the effect of neutron interactions between different parts of the core, the model considers a coupled multipoint kinetics equation in place of simple point kinetics equation. Linear stability theory was applied to reveal the instability of in-phase and out-of-phase modes in the boiling channels of the AHWR. The results indicate that the stability behavior of the reactor is greatly influenced by the void reactivity coefficient, fuel time constant, radial power distribution and channel inlet orificing. The delayed neutrons were found to have a strong influence on the Type I and Type II instabilities observed at low and high channel powers, respectively. Also, it was found that the coupled multipoint kinetics model and the modal point kinetics model predict the same threshold power for out-of-phase instability if the coupling coefficient in the former model is half the eigen value separation between the fundamental and the first harmonic mode in the latter model. Decay ratio maps were predicted considering various operating parameters of the reactor, which are useful for its design.

Experimental studies on rewetting of hot vertical annular channel

Abstract Studies on the rewetting behaviour of hot vertical annular channels are of interest in the context of emergency core cooling in nuclear reactors following LOCA. Experimental studies were carried out to study the rewetting behaviour of a hot vertical annular channel, with hot inner tube, for bottom flooding and top flow rewetting conditions. The length of the inner tube of the test section was 3030 mm for bottom flooding rewetting experiments and 2630 mm for top flow rewetting experiments. The tube was made of stainless steel. Experiments were conducted for water flow rates in the annulus upto 7 lpm (11.7×10 −5 m 3 s −1 ). The initial surface temperature of the inner tube was varied from 200 to 500°C. The experimental studies show that for a given initial surface temperature of the tube, the rewetting velocity increases with an increase in flow rate of water and it decreases with an increase in the initial surface temperature for a given water flow rate. For a given water flow rate and initial surface temperature, the rewetting velocity is higher in the case of rewetting under bottom flooding conditions as compared to that in the case of rewetting under top flow conditions. These conclusions agree with the conclusions reported in the earlier literature. Using the experimental data of the present work, correlations for bottom flooding and top flow rewetting velocities are developed.

Mathematical modelling of the stability characteristics of a natural circulation loop

The natural circulation phenomenon in a rectangular loop has been mathematically simulated and its stability characteristics have been investigated. The conservation equations of mass, momentum and energy in the transient form were solved numerically using the finite difference method. The stable, unstable and neutrally stable points were identified by examining the amplitude of flow and temperature oscillations with time for a given set of operating conditions. The stability behaviour of the loop has also been investigated using the linear stability theory. The results show that the stability maps obtained by the two methods are in close agreement.

Symptom based diagnostic system for nuclear power plant operations using artificial neural networks

Abstract Nuclear power plant experiences a number of transients during its operations. These transients may be due to equipment failure, malfunctioning of process systems and unavailability of safety systems. In such a situation, the plant may result into an abnormal state which is undesired. In case of an undesired plant condition generally known as an initiating event (IE), the operator has to carry out diagnostic and corrective actions. The operators response may be too late to mitigate or minimize the negative consequences in such scenarios. The objective of this work is to develop an operator support system based on artificial neural networks that will assist the operator to identify the IEs at the earliest stages of their developments. These abnormal plant conditions must be diagnosed and identified through the process instrument readings. A symptom based diagnostic system has been developed to investigate the IEs. The event identification is carried out by using resilient back propagation neural network algorithm. Whenever an event is detected, the system will display the necessary operator actions in addition to the type of IE. The system will also show the graphical trend of relevant parameters. The developed system is able to identify the eight IEs of Narora Atomic Power Station. This paper describes the features of the diagnostic system taking one of the IEs as a case study.

Study on the stability behaviour of a natural circulation pressure tube type boiling water reactor

The stability behaviour of a natural circulation pressure tube type boiling water reactor (BWR) has been investigated analytically. The analytical model considers homogeneous two-phase flow, a point kinetics model for the neutron dynamics and a lumped heat transfer model for the fuel dynamics. The results indicate that both Type I and Type II density-wave instabilities can occur in the reactor in both in-phase and out-of-phase mode of oscillations in the boiling channels of the reactor. The delayed neutrons were found to have strong influence on the stability of Type I and Type II density-wave instabilities. Also, the stability of the reactor is found to increase with increase in negative void reactivity coefficient unlike that observed previously in vessel type BWRs. Decay ratio map was predicted considering the effects of channel power, channel inlet subcooling, feed water temperature and channel exit quality, which are useful for the design of the reactor.

Predictions of ultimate load capacity for pre-stressed concrete containment vessel model with BARC finite element code ULCA

Abstract Ultimate load capacity assessment of nuclear containments has been a thrust research area for Indian Pressurized Heavy Water Reactor (PHWR) power programme. For containment safety assessment of Indian PHWRs a finite element code ULCA was earlier developed at BARC, Trombay. This code has been extensively benchmarked with experimental results. The present paper highlights the analysis results obtained from code ULCA for Prestressed Concrete Containment Vessel (PCCV) that was tested at Sandia National Labs, USA in a Round Robin analysis. This test programme was co-sponsored by Nuclear Power Engineering Corporation (NUPEC), Japan and the US Nuclear Regulatory Commission (NRC). Three values of failure pressure predictions namely the upper bound, the most probable and the lower bound (all with 90% confidence) were made as per the requirements of the round robin analysis activity. The most likely failure pressure is predicted to be in the range of 2.95–3.15 Pd (Pd=design pressure of 0.39 MPa for the PCCV model) depending on the type of liners used in the construction of the PCCV model. The lower bound value of the ultimate pressure of 2.80 Pd and the upper bound of the ultimate pressure of 3.45 Pd are also predicted from the analysis. These limiting values depend on the assumptions of the analysis for simulating the concrete-tendon interaction and the strain hardening characteristics of the steel members. The experimental test has been recently concluded at Sandia Laboratory and the peak pressure reached during the test is 3.3 Pd that is enveloped by our upper bound prediction of 3.45 Pd and is close to the predicted most likely pressure of 3.15 Pd. This paper highlights the features of BARC code ULCA and addresses a few issues related to constitutive modeling of pre-stressed concrete structure that is relevant for ultimate load capacity prediction of nuclear containments. These would be useful for evaluation of the present numerical results with the test data obtained by Sandia National Laboratory.

Leak rates through cracks and slits in PHT pipes for LBB

Abstract The Leak Before Break (LBB) concept is widely used in the nuclear industry to eliminate the consideration of postulated double ended guillotine ruptures. This is based on the premise that a detectable leak will develop before a catastrophic break occurs. A ‘throughwall flaw’ is postulated at critical sections so that any leakage from the postulated flaw is sure to be detected. The main purpose of the present study is to develop computer codes to estimate the leakage critical flow through a postulated crack. Flow through a crack may not always attain thermodynamic equilibrium; therefore Henrys Homogeneous Non-equilibrium Model (HHNM) and a Homogeneous Frozen Model (HFM) have been adopted for the present study. Here HFM has been modified taking into account the contribution of change in liquid phase kinetic energy. According to these models, critical mass flow is expressed in terms of inlet quality and exit pressure and quality. The exit pressure is related to the inlet pressure through the cumulative effect of various pressure losses, e.g. entrance loss, friction loss and loss due to flashing. A hybrid correlation for frictional pressure drop due to surface roughness has been incorporated in the present method. Computer codes have been developed based on these models. The results obtained have been verified against published data and are found to be in good agreement. Parametric studies have been carried out to examine the effects of different physical and thermal–hydraulic parameters and to assess the extent of leakage.

Experimental studies on the pressure drop across the various components of a PHWR fuel channel

Experiments were carried out to measure the pressure drop across various components of a pressurised heavy water reactor (PHWR) fuel channel under single-phase flow conditions. Empirical correlations developed to predict the pressure drop for the various components of the fuel channel like rod bundles, end fittings, fuel locator and refuelling tools are presented. In addition, the effects of bundle alignment at the junction and creep of fuel channels (both radial and axial) on pressure drop have been studied.