In the pebble bed reactor, large number of fuel pebbles’ movement law and moving state can affect the reactor’s design, operation and safety directly. Therefore the pebble flow, which is based on the theory of particle streaming, is one of the most important research subjects of the pebble bed reactor engineering. The in-core pebble flow is a very slow particle flow (or called quasi-static particle flow), which is very different from the usual particle motion. How to accurately describe the characteristics of in-core pebble flow is a central issue for this subject. Due to the presence of random flow, the cross-mixing phenomenon will occur inevitably. In the present paper, the mixing phenomenon of pebble flow is generalized on the basis of experiment results. The pebble flow cross-mixing probability serves as the parameter which describes both the regularity and the randomness of pebble flow. The results are provided in the form of diagrammatic presentation.

Steam generator (SG) is one of the key equipment of nuclear power units. Because of the large range of its loads changing, the water level control of SG effectively is an essential secure guarantee of nuclear power plants. SG is a complex system, besides imbalance and non-minimum phase characteristic, it also has the properties of nonlinearity, time-varying and with small stability margin. There are many difficulties in water level control of SG. Of which false water level and varying parameters are the most severe problems. In this paper, first the water level features and the water level control principle of U-tube steam generator (UTSG) are introduced. Then mathematical model mechanism and both the static and dynamic characteristic of it water level are discussed. Finally various control methods are used for comparing the control effect. Intelligent control is a type of control strategy which imitates human intelligence behavior. It is mainly aimed at the controlled plant with complicate model parameters, or which model structure hard to describe accurately by mathematical method. Cloud Model theory is proposed by Academician Li Deyi based on the idea of artificial intelligence with uncertainty. This theory focus on analyzing the uncertainty of control plant, realizes the uncertain conversion between qualitative concept and quantitative numerical by combining ambiguity and randomness. In the field of control technology, ambiguity and randomness make it difficult to establishing precise mathematical model of control plant, and become a bottleneck during the research of improving stability, accuracy and quickness of control system. In this context, Cloud Model can be a good conversion between qualitative concept and quantitative numerical due to its ability of showing the uncertainty of qualitative concept which described by natural language. Under the action of external input, system control can be realized by inferencing according to the qualitative concept and uncertainty rules of Cloud Model. In this paper, the researched Cloud Model control system is based on normal distribution, because a large number of random events in nature and society obey or approximately obey normal distribution. The rate of convergence of Cloud Model control is evidently faster than PID. Moreover, the capability of Cloud Model control in tracking, adapting, anti-interference and overcoming large time lag are apparently superior when comparing with the control effect of PID.

Japan Nuclear Safety Institute had recently reported the pioneering deterministic evaluation approach for nuclear power plant under seismic induced fault displacement. But the uncertainty of fault displacement based on probabilistic hazard analysis is described to be greater than that of other natural phenomena e.g. earthquake ground motions or seismic acceleration vibration in the report. Furthermore, for plant-wide risk assessment against fault displacement hazards beyond design basis displacement level, it is seriously necessary to promote a series of fundamental studies and develop the standard procedures regarding not only accident sequence analysis but also fragility analysis of buildings and structures as well as components and piping systems. Based on the above background, the objective of this study is focusing to obtain basic fragility data for the aleatory and epistemic uncertainties of structural responses for nuclear power plant buildings against fault displacement. A number of nonlinear soil-structure finite element analyses against relatively large fault displacement are performed with the randomness of soil and building material properties, the uncertainly of contact parameters relating to friction between soil and building, and also the uncertainty of fault hazards such as fault types and geometries. Their quantitative results for fragility data are shown in this paper.

In recent years, the nuclear industry and the Nuclear Regulatory Commission (NRC) have made a tremendous effort to assess the safety of nuclear power plants as advances in seismology have led to the perception that the potential earthquake hazard in the United States may be higher than originally assumed. The Seismic Probabilistic Risk Assessment (S-PRA) is a systematic approach used in the nuclear power plants in the U.S. to realistically quantify the seismic risk as by performing an S-PRA, the dominant contributors to seismic risk and core damage can be identified. The assessment of component fragility is a crucial task in the S-PRA and because of the conservatism in the design process imposed by stringent codes and regulations for safety related structures, structures and safety related items are capable of withstanding earthquakes larger than the Safe Shutdown Earthquake (SSE). One major aspect of conservatism in the design is neglecting the effect of Soil-Structure-Interaction (SSI), from which conservative estimates of In-Structure Response Spectra (ISRS) are calculated resulting in conservative seismic demands for plant equipment. In this paper, a typical Reactor Building is chosen for a case study by discretizing the building into a lumped mass stick model (LMSM) taking into account model eccentricities and concrete cracking for higher demand. The model is first analyzed for a fixed base condition using the free field ground motion imposed at the foundation level from which ISRS are calculated at different elevations. Computations taking into account the SSI effects are then performed using the subtraction method accounting for inertial interactions by using frequency dependent foundation impedance functions depicting the flexibility of the foundation as well as the damping associated with foundation-soil interaction. Kinematic interactions are also taken into account in the SSI analysis by using frequency dependent transfer functions relating the free-field motion to the motion that would occur at the foundation level as the presence of foundation elements in soil causes foundation motions to deviate from free-field motions as a result of ground motion incoherence and foundation embedment. Comparing the results of the seismic response analyses, the effects of the SSI is quantified on the overall seismic risk and the SSI margin is calculated. A family of realistic seismic fragility curves of the structure are then developed using common industry safety factors (capacity, ductility, response, and strength factors), and also variability estimates for randomness and uncertainty. Realistic fragility estimates for structures directly enhances the component fragilities from which enhanced values of Core Damage Frequency (CDF) and Large Energy Release Frequency (LERF) are quantified as a final S-PRA deliverable.

The volumetrically heated packed bed has been widely utilized in modern industry, however, due to the variability and randomness of packed bed channels, flow boiling heat transfer characteristics is complex. To study subcooled flow boiling heat transfer characteristics of volumetrically heated packed bed, here electromagnetic induction heating method was used to heat the oxidized carbon steel balls adopted to stack packed bed, while water was utilized as refrigerant in the experiment. The mass flux and heat flux effects on the subcooled flow boiling heat transfer were analyzed. A new correlation was developed to predict the subcooled flow boiling heat transfer coefficient in volumetrically heated packed bed.

The identification of chaos in the two-phase natural circulation system under rolling motion can provide theoretical guidance for forecasting and control of natural circulation flow instability. The surrogate-data technique is one of effective methods to identify the chaos in the time series exactly. It can avoid the limitation of the positively identifying chaos. In this paper, correlation dimension and principal component analysis (PCA) was used as the identification evidence; the surrogate-data technique was used for the identification of chaos in time series of the irregular complex flow oscillations. The results indicate that there is chaos in the natural circulation system under rolling motion and the surrogate-data technique can identify chaos exactly.

Our goal is to evaluate validity of numerical simulation results in the nuclear field in order to estimate real behavior of nuclear plants and thus to contribute their security and safety. Recently, it becomes possible to execute a full-scale numerical simulation under a real condition, such as a seismic behavior of entire nuclear plant. To estimate real behavior accurately by such simulations, it is indispensable to evaluate validity of simulation results because numerical simulations include various uncertainties such as “uncertainty due to randomness” and “uncertainty due to lack of knowledge”. As one of approaches to evaluate validity of simulation results, we introduce “the degree of certainty” of simulations to real behavior. Here, to get a more accurate degree of certainty, we try to confirm the degree of influence about unevenness of uncertainty and to reduce uncertainty due to lack of knowledge. For this, we research and develop a validity evaluation system composed of three tools. One is a tool able to introduce the degree of certainty from various uncertainties to put together various uncertainties. Another is a tool able to analyze the sensitivity of each uncertainty to whole uncertainty. Moreover, we research a tool able to analyze factors of various uncertainties. We have applied them to our seismic simulation system which enables to execute the assembly structure analysis of an entire nuclear plant and confirmed that their functions are applicable to the simulation.

The paper studies the fragility of high-pressure emergency cooling water tanks in Loviisa Nuclear Power Plant located on the elevation +25.40 in the reactor building. The seismic fragility is defined as the conditional probability of its failure given a value of the response parameter, such as peak ground acceleration. Using the lognormal-distribution assumption, the fragility (i.e., the probability of failure, f ′ ) at any non-exceedance probability level Q can be derived as Equation 1 f ′ = Φ [ ( ln ( a / A ¯ ) + β U Φ − 1 ( Q ) ) / β R ] where Q = P(f<f ′ |a) is the probability that the conditional probability f is less than f ′ for a peak ground acceleration a. A is the median ground acceleration capacity, β R is the logarithmic standard deviation representing the randomness about A, and β U is the logarithmic standard deviation representing the uncertainty. The quantity Φ(.) is the standard Gaussian cumulative distribution function. In order to assess the fragility of the tanks the strain time histories for tank supports and piping nozzles were calculated using the joint structural-equipment model. The ground motion response spectra shape used in the structural response analysis has been taken from the YVL 2.6 – guide [1]. This shape represents the envelope spectrum for Southern Finland corresponding to the median annual frequency of 10 −5 . The sampling of the model properties was carried out with the aid of the Latin hypercube sampling method. In order to find the failure modes the strain time histories were calculated for the piping nozzles and for support structures of the tanks. Since strain is the best measure of energy absorption, energy limited events need to be based on the strain acceptance criteria. The adopted failure limit is the cumulated plastic strain of 8% in the tank sheet metal or in the supporting structures. This failure limit has taken from the reference [2]. The end result of the study is the presentation of the median fragility curve for the tanks as well as 95% and 5% fractile curves.

Two-phase flow instability and dynamics of a parallel multichannel system has been theoretically studied under periodic excitation induced by rolling motion in the present research. Based on the homogeneous flow model considering the rolling motion, the parallel multichannel model and system control equations are established by using the control volume integrating method. Gear method is used to solve the system control equations. The influences of the inlet, upward sections, and heating power on the flow instability under rolling motion have been analyzed. The marginal stability boundary (MSB) under rolling motion condition is obtained. The unstable regions occur in both low and high equilibrium quality and inlet subcooling regions. The multiplied period phenomenon occurs in the high equilibrium quality region and the chaos phenomenon appears on the right of MSB. The concept of stability space is presented.

To perform fracture mechanics analysis of reactor vessel, fracture toughness ( K Ic ) at various temperatures would be necessary. In a best estimate approach, K Ic uncertainties resulting from both lack of sufficient knowledge and randomness in some of the variables of K Ic must be characterized. Although it may be argued that there is only one type of uncertainty, which is lack of perfect knowledge about the subject under study, as a matter of practice K Ic uncertainties can be divided into two types: aleatory and epistemic. Aleatory uncertainty is related to uncertainty that is very difficult to reduce, if not impossible; epistemic uncertainty, on the other hand, can be practically reduced. Distinction between aleatory and epistemic uncertainties facilitates decision-making under uncertainty and allows for proper propagation of uncertainties in the computation process. Typically, epistemic uncertainties representing, for example, parameters of a model are sampled (to generate a “snapshot,” single-value of the parameters), but the totality of aleatory uncertainties is carried through the calculation as available. In this paper a description of an approach to account for these two types of uncertainties associated with K Ic has been provided.

The present paper is concerned with the seismic response and fragility evaluation of a water storage structure. Seismic analysis has been carried out considering the hydrodynamic effects of the contained water. The various parameters that could affect the seismic structural response include material strength of concrete, structural damping available within the structure and the normalized ground motion response spectral shape. Based on this limited case study; the seismic fragility of the structure is developed as families of conditional probability curves plotted against peak ground acceleration (PGA) at the location of interest. The procedure adopted incorporates the various randomness and uncertainty associated with the parameters under consideration.

The various uncertainties and randomness associated with the occurrence of earthquakes and the consequences of their effects on the NPP components and structures call for a probabilistic seismic risk assessment (PSRA). However, traditionally, the seismic design basis ground motion has been specified by normalised response spectral shapes and peak ground acceleration (PGA). The mean recurrence interval (MRI) used to be computed for PGA only. The present work develops uniform hazard response spectra i.e. spectra having the same MRI at all frequencies for Kakrapar Atomic Power Station site. Sensitivity of the results to the changes in various parameters has also been presented. These results determine the seismic hazard at the given site and the associated uncertainties. The paper also presents some results of the seismic fragility for an existing containment structure. The various parameters that could affect the seismic structural response include material strength of concrete, structural damping available within the structure and the normalized ground motion response spectral shape. Based on this limited case study the seismic fragility of the structure is developed. The results are presented as families of conditional probability curves plotted against the peak ground acceleration (PGA). The procedure adopted incorporates the various randomness and uncertainty associated with the parameters under consideration.