A. John Arul

Adjoint operator approach to functional reliability analysis of passive fluid dynamical systems

Reliability analysis of passive systems mainly involves quantification of the margin to safety limits in probabilistic terms. For systems represented by complex models, propagating input uncertainty to get the response uncertainty and hence probability information requires intensive computational effort. Here a computationally efficient method for the functional reliability analysis of passive fluid dynamical systems is presented. The approach is based on continuous adjoint operator technique to generate a response surface approximating the given system model from the sensitivity coefficients. A numerical application of this method to the reliability analysis of heat transport in an asymmetrical natural convection loop is demonstrated. Computational efficiency and accuracy compared with the direct Monte-Carlo and forward response surface methods.

Determination of neutron energy spectrum at KAMINI shielding experiment location

The neutron spectrum at KAMINI reactor south beam tube end has been determined using multifoil activation method. This beam tube is being used for characterizing neutron attenuation of novel shield materials. Starting from a computed guess spectrum, the spectrum adjustment/unfolding procedure makes use of minimization of a modified constraint function representing (a) least squared deviations between the measured and calculated reaction rates, (b) a measure of sharp fluctuations in the adjusted spectrum and (c) the square of the deviation of adjusted spectrum from the guess spectrum. The adjusted/unfolded spectrum predicts the reaction rates accurately. The results of this new procedure are compared with those of widely used SAND-II code.

Comparison of neutron attenuation properties of ferro boron slabs containing 5% natural boron with other high density materials

Modeling and designing cost-effective neutron attenuation along with shield volume reduction is a challenging task in fast reactors. It involves reducing the neutron energy and absorbing them with suitable materials. A series of experiments were conducted in the South beam end of Kalpakkam Mini reactor with powders of ferro boron (FeB), ferrotungsten (FeW), boron carbide, slabs of FeB, and mild steel plates to study their neutron attenuation characteristics. In one of the experiments, FeB slab cast with 5% natural boron was used, and neutron attenuation measurements were carried out. The attenuation factors were found over a thickness of 28 cm for the measured reaction rates of 195 Pt (n, n′) 195m Pt, 111 Cd (n, n′) 111m Cd, 103 Rh (n, n′) 103m Rh, 115 In (n, n′) 115m In, 180 Hf (n, n′) 180m Hf, 63 Cu (n,g) 64 Cu, 23 Na (n,g) 24 Na, 55 Mn (n,g) 56 Mn, and 197 Au (n,g) 198 Au reactions representative of fast, epithermal, and thermal neutron fluxes. A comparative analysis of the neutron attenuation behavior measured with various materials is presented. In case of attenuation of both thermal and fast fluxes, FeB is better than other high density materials such as mild steel and FeW. The outcome of the experimental study is that FeB slab cast with 5% natural boron can be utilized as cost-effective neutron shield in streaming paths in nuclear reactors.

Level-1 Probabilistic Safety Analysis of Prototype Fast Breeder Reactor

This paper summarizes the results from the level-l Probabilistic Safety Analysis of Prototype Fast Breeder Reactor (PFBR) which is under construction at Kalpakkam. The scope of this study is limited to internal events at full power. The regulatory requirement in India is risk informed and the required target value for overall core damage frequency (CDF) < 1e−6 1 / ry. The salient feature of this study is the inclusion of functional failure of natural convection based system in event tree development. For this study three categories of end states namely, pin failures, sub-assembly failures and whole core accident were identified. With conservative assumptions the estimated core damage frequency is about 0.9−1.3E−6 / ry. This includes the contribution from sub-assembly failures and whole core accident. Loss of Steam Water System (Heat Sink) is the dominant contributor. Modeling Sub-Assembly flow blockage event tree is found to have large uncertainties.

Reliability comparison of computer based core temperature monitoring system with two and three thermocouples per sub-assembly for Fast Breeder Reactors

Prototype Fast Breeder Reactor (PFBR) is a mixed oxide fuelled, sodium cooled, 500 MWe, pool type fast breeder reactor under construction at Kalpakkam, India. The reactor core consists of fuel pins assembled in a number of hexagonal shaped, vertically stacked SubAssemblies (SA). Sodium flows from the bottom of the SAs, takes heat from the fission reaction, comes out through the top. Reactor protection systems are provided to trip the reactor in case of design basis events which may cause the safety parameters (like clad, fuel and coolant temperature) to cross their limits. Computer based Core temperature monitoring system (CTMS) is one of the protection systems. CTMS for PFBR has two thermocouples (TC) at the outlet of each SA(other than central SA) to measure coolant outlet temperature, three TC at central SA outlet and six thermocouples to measure coolant inlet temperature. Each thermocouple at SA outlet is electronically triplicated and fed to three computer systems for further processing and generate reactor trip signal whenever necessary. Since the system has two sensors per SA and three processing units the redundancy provided is not independent. A study is done to analyze the reliability implications of providing three thermocouples at the outlet of each SA and thereby feed independent thermocouple signals to three computer systems. Failure data derived from fast reactor experiences and from reliability prediction methods provided by handbooks are used. Fault trees are built for the existing CTMS system with two TC per SA and for the proposed system with three TC per SA. Failure probability upon demand and spurious trip rates are estimated as reliability indicators. Since the computer systems have software intelligence to sense invalid field inputs, not all sensor failures would directly affect the system probability to fail upon a demand. For instance, the coolant outlet temperature cannot be lower than the coolant inlet temperature. This intelligence is taken into account by assuming different “fault coverage percentage” and comparing the results. A 100% fault coverage means the software algorithm could detect all of the possible thermocouple faults. It was found that the system probability to fail upon demand is reduced in the new independent system but the spurious trip rate is slightly worse. The diagnostic capability is marginally affected due to complete independence. The paper highlights how an intelligent computer based safety system poses difficulties in modeling and the checks and balances between an interlinked and independent redundancy.

The power law character of off-site power failures

Abstract A study on the behavior of off-site AC power failure recovery times at three nuclear plant sites is presented. It is shown, that power law is appropriate for the representation of failure frequency–duration correlation function of off-site power failure events, based on simple assumptions about component failure and repair rates. It is also found that the annual maxima of power failure duration follow Frechet distribution, which is a type II asymptotic distribution, strengthening our assumption of power law for the parent distribution. The extreme value distributions obtained are used for extrapolation beyond the region of observation.

Reliability Model of a Safety System with an Imperfect Tester

High reliability digital systems designed for safety applications employ external or built in test and surveillance systems. The overall reliability is determined by the combined reliability of the safety system and that of the testing system. In this study we derive an expression for the overall system unavailability using Markov model and from that derive an approximate formula that could be used in fault tree analysis of larger systems. The approximate expression is validated by numerical case studies as applied to solid state voting logic with online fine impulse testing system (SLFIT) used in the shutdown system of a nuclear reactor.

Generalized hybrid approach to adjoint code derivation for efficient uncertainty and reliability studies

We investigate a generalized hybrid adjoint procedure for deriving the adjoint code for efficient sensitivity analysis and uncertainty propagation. The hybrid approach is a combination of generalized adjoint equations at higher level and automatic differentiation at subroutine level. The procedure developed is studied for implementation issues for the problem of uncertainty propagation in natural convection heat transport system temperature evolution. The results obtained by this method is validated by finite difference computation. The results demonstrate that for this application reasonably accurate results can be obtained efficiently by the proposed methodology compared to direct Monte-Carlo with response surface methodology.

Accident Sequence Modeling Methodology for External Flood Probabilistic Safety Analysis of Prototype Fast Breeder Reactor

This paper compares two different accident sequence methodologies for external flood probabilistic safety analysis (EFPSA). It is shown that the two methodologies lead to identical expression for CDF with an example. Using accident sequences developed for internal events PSA is recommended for detailed external flood probabilistic safety analysis of prototype fast breeder reactor.

Variance quantification of functional reliability estimates using re-sampling techniques

Passive systems, which completely depend on natural phenomena such as gravity, conduction and convection to accomplish the safety functions, are increasingly being used in new generation nuclear reactor designs. However, since the driving forces of passive systems are weak, they are more vulnerable to associated uncertainties and there may be a non-zero probability for the system to deviate from the intended behavior and leads to functional failure. Methods for quantification of the functional failure include Monte-Carlo simulation of the system uncertainties using a validated mechanistic code. Generally, the mechanistic codes used for complex system modeling are computationally expensive and Monte- Carlo simulation for estimating small failure probabilities requires more time and often become prohibitive. In this respect, recently, functional reliability methodologies including advanced simulation techniques such as subset simulation, Markov chain Monte-Carlo, importance sampling, and response conditioning method are reported in open literature. Unlike in the case of direct Monte Carlo simulation, for the probability estimates obtained using these advanced simulations, analytical formulas are not available to estimate standard error and confidence interval. In this paper, the estimation of standard error and confidence interval of functional reliability estimates using computationally efficient re-sampling methods based on bootstrap technique are described. Numerical application of these methods, to quantify the variability of functional reliability estimates, is also explained.