A Monte Carlo approach to the theoretical prediction of temperature noise in LMFBR sub-assemblies

A candidate technique for detecting incipient blockages in the fuel sub-assemblies of liquid-metal-cooled fast-breeder reactors is the measurement of coolant outlet temperature fluctuations caused by turbulence. A theoretical basis for the method is required, and one model is discussed in this paper.

The model requires the paths of individual fluid particles to be traced, allowing their motions to vary randomly, subject to certain constraints of the turbulent motion. It is a Monte Carlo method, already used successfully in predicting the transport of scalar fluctuations. Its advantage is that it allows actual time-dependent temperatures to be computed, and so various methods of analysis (power spectral density, amplitude probability distribution, for example) can be examined. The effect of heat conduction is neglected at present.

Computed results show the way in which mean temperature and rms temperature-noise profiles develop in a turbulent flow in a pipe downstream of a plane at which a steady mean profile is maintained. Power spectral densities and amplitude-probability densitiesare presented, and it is shown how an amplitude-probability density plot distinguishes between a temperature-gradient input profile and a gaussian input profile.

Comparisons are given with experimental measurements made in representative heated pin rigs in sodium, with good agreement. Some of the problems associated with extrapolation to real sub-assemblies are discussed.     

Experimental and theoretical investigation of droplet emission from tungsten melt layer

Tungsten in form of macrobrush structure is foreseen as one of candidate materials for the ITER divertor and the dome. Melting of tungsten and the following melt motion and melt splashing are expected to be the main mechanisms of damage which determine the lifetime of plasma facing components. New experimental investigations of droplet emission from the W melt layer for the Edge Localised Mode (ELM)-like heat loads have been carried out at the plasma gun facility quasistationary plasma accelerators (QSPA-T). In these experiments the threshold for droplet emission and the distributions of velocity on emission angles and amplitude of the ejected droplets were determined. In the paper the main physical mechanism (the Kelvin–Helmholtz instability) of the melt splashing under the heat loads being applied at QSPA-T and those anticipated after the ITER transients is analyzed. These numerical simulations demonstrated a reasonable agreement with the experimental data on the droplet sizes and droplet velocities and allowed the projections upon the W melt splashing at ITER conditions.     

Subassembly experiments and a computer code to analyze the dynamic core deformation during local failure propagation

Safety investigations for LMFBRs have to consider local failure situations in one fuel element which may escalate to a hypothetical CDA. Such initiating events could produce high pressure pulses in a single subassembly which may expand and rupture the wrapper as well as load adjacent elements impulsively. The associated nonlinear dynamic core deformation problem is treated in this paper. In particular the multirow structural dynamics code CØRE-1 and underlying mechanical models are described. Each subassembly is simulated by an equivalent system of point masses and nonlinear coupling springs. The motion of the coolant layer between the elements is treated by an incompressible, non-stationary frictional flow model. In order to obtain realistic code input four types of static single subassembly deformation experiments are described which provided strongly nonlinear load deformation characteristics. Furthermore the transient pressure distribution within the core is obtained from a full scale explosion test. Finally code application is demonstrated and results are given of a transient analysis of the SNR 300 core.     

Experimental and theoretical investigation of gas-liquid flow pressure drop across rupture discs

Experiments of air-water two-phase flow pressure drop through rupture discs have been carried out. The tested rupture discs of DN 25 and DN 40 are made of graphite with and without vacuum support. The experiments were performed under the following conditions of two-phase parameters; mass flux from 2000 up to 4000 kg/m² s, quality from 1 to 20% and system pressure from 3 to 7 bar. The results demonstrate that the effect of the above-mentioned parameters is very significant at high ranges of mass flow quality, due to the increasing of two-phase flow resistance, energy dissipations, friction losses and interaction of the two phases. Based on the presented experimental results and the data published in the literature, new correlation has been developed to calculate the two-phase pressure across rupture discs. The model includes the relevant primary influencing parameter, fit the data well, and is sufficiency accurate for engineering purposes. The reproductive accuracy of the proposed model and the statistical comparison, based on about 1000 measured data in the literature, demonstrated that the proposed model is the best overall agreement with the data. The standard deviation of the data is less than 10%. The results reported enable practical designs with standard products and optimization of the geometry of the rupture discs installed in nuclear reactors.     

Experimental investigation of the failure behavior of notched wall-thinned pipes

The present study performed full-scale pipe tests using 100A Schedule 80 pipe specimens with simulated notched and circular wall thinning to investigate the failure behavior of notched wall-thinned pipes. The tests were conducted under both monotonic and cyclic bending moments at a constant internal pressure of 10 MPa at room temperature. The failure pattern, load carrying capacity, deformation ability, and fatigue strength of the notched wall-thinned pipes were evaluated by comparing results to those of circular wall-thinned pipes. The investigation showed that the effect of the type of thinning on the failure behavior was more sensitive under cyclic loading conditions than under monotonic loading conditions. The load carrying capacity of pipes with notched wall thinning was approximately the same or slightly less than that of pipes with circular wall thinning when the thinning area was subjected to tensile stress. However, when the thinning area was subjected to compressive stress, the load carrying capacity of pipes with notched wall thinning was greater than that of pipes containing circular wall thinning. The deformation ability and fatigue strength increased proportionally with the axial length of the thinning defect, and thus these properties were significantly reduced in notched wall-thinned pipes.     

The role of reliability and risk assessment in LMFBR design: Implementation of reliability in LMFBR design

This paper concerns future developments in LMFBR licensing technology.Federal Regulations (10 CFR 50.34) require that the preliminary safety analysis provide analysis and evaluation “with the objective of assessing the risk to public health and safety” to determine margins of safety and the adequacy of the plant. Hitherto the assessment of risk has been qualitative but it has become increasingly apparent that quantitative assessments would provide a better basis for judgement. Potential future roles of reliability and risk assessment are discussed in the context of providing additional confirmation of the safety of LMFBR designs. Potential acceptability criteria for risk evaluations are outlined.The reliability implications of designing components to the ASME Code Section III requirements are discussed. General judgements are provided as well as the preliminary results of probabilistic studies of selected specific limits. There is a different reliability significance for the mandatory rules for normal, upset, and emergency conditions versus the non-mandatory rules for normal, upset, and emergency conditions versus the non-mandatory guidance for faulted conditions.     

Core-wide statistical evaluation of the effect of uncertainties in clad temperature, material property data, and burnup on the probability of LMFBR fuel rod failure due to creep rupture

Rigorous treatment of the uncertainties inherent in LMFBR core component design requires the development of probabilistic design tools to analyze life-limiting loading mechanisms. One of these tools is a Monte Carlo simulation technique that has been developed to analyze sealed plenum fuel rods subject to fission gas-induced creep rupture. This Monte Carlo technique avoids the need for simplifying the forms of probability distributions and is able to correctly simulate the interaction of many random variables by including all such variables in the analysis. With the use of a biased sampling technique, sufficiently accurate predictions of the number of fission gas pressure-induced failures in the core are obtained in typical calculations for less than $50 ($500 without biasing) on the Honeywell 6000 computer. The application of the biasing technique to core-wide analysis provides a major new capability at a cost that allows routine design use. The PECS (probabilistic evaluation of clad stress) computer code, which employs these techniques, has been applied to study the significance of uncertainties in material properties, temperature, dimensions and burnup. The effect of thermal-hydraulic design optimization is investigated probabilistically to illustrate potential applications of the method.     

Numerical simulation of local non-linearities due to tube-support interaction

Flow-induced vibrations are liable for the majority of failures due to tube wear in process equipment such as steam generator and command gaps that often have weak support conditions. Local impact and sliding may occur. In order to evaluate the wear of the components, we need to compute adequately the localized contact forces and other parameters. In this paper a technique for solving friction-gap problems in tube support structures is described. The technique can be applied to various problems and allows a quite reasonable computation time.     

Transient failure analysis of liquid-filled shells Part I: Theory

In this paper, the governing equations which consider dynamic fluid-structure interaction, modal coupling in both axial and circumferential directions, and dynamic buckling are derived. The various pressure components acting on the shell wall due to a seismic event are also analyzed. The matrix equation of motion for liquid-filled shells is obtained through a Galerkin/Finite Element discretization procedure. The modal coupling among the various combinations of axial and circumferential modes are identified with a particular reference to the fluid-structure system under seismic excitation. Finally, the equations for the dynamic stability analysis of liquid-filled shells are presented.     

A three-dimensional theoretical investigation of the local and global component of neutron noise in bare homogeneous water moderated reactors and applications

Starting from the time-dependent three-dimensional two-group diffusion equations for a bare homogeneous critical reactor, it is shown that the fluctuations of the neutron population can be uniquely separated into a local and a global component with each component satisfying a second-order differential equation. It is shown that under certain limitations, the two-group treatment of the neutron noise and the subsequent derivation of the two components, is equivalent to the one-group theory in which the slowing down of the fast neutrons is taken into account through an appropriately chosen slowing down kernel.The theory so developed, is applied in order to investigate the local component of the neutron noise induced by a randomly vibrating infinitely thin absorber in a two-dimensional cylindrical reactor and the neutron noise due to axially propagating perturbations of the moderator density, in a multi-channel model of a three-dimensional slab reactor.     

Experimental investigation of local two-phase flow parameters of a subcooled boiling flow in an annulus

As a series of subcooling boiling flow tests, local two-phase flow parameters were obtained at SUBO (subcooled boiling) test facility under steam–water flow conditions. The test section is a vertical annulus of which the axial length is 4.165 m with a heater rod at the center of a channel. The inner and outer diameters of the test section and the heater rod are 35.5 mm and 9.98 mm, respectively. The test was performed by a two-stage approach. Stage-I for the measurement of local bubble parameters has been already done (Yun et al., 2009). The present work focused on the stage-II test for the measurement of local liquid parameters such as a local liquid velocity and a liquid temperature for a given flow condition of stage-I. A total of six test cases were chosen by following the test matrix of stage-I. The flow conditions are in the range of the heat flux of 370–563 kW/m², mass flux of 1110–2100 kg/(m² s) and inlet subcooling of 19–31 °C at pressure condition of 0.15–0.2 MPa. From the test, local liquid parameters were measured at 6 elevations along the test section and 11 radial locations of each elevation in addition to the previously obtained local void fraction, interfacial area concentration, Sauter mean diameter and bubble velocity. The present subcooled boiling (SUBO) data completes a data set for use as a benchmark, validation and model development of the Computational Fluid Dynamics (CFD) codes or existing safety analysis codes.     

Experimental evaluation of the effect of local wall thinning on the failure pressure of elbows

This study performed a series of burst tests using real-scale elbow specimens containing simulated local wall thinning to evaluate the effects of wall-thinning defects on the failure pressure of pipe bends and elbows. The tests were conducted under simple internal pressure at ambient temperature. The experiments included various wall-thinning geometries with different thinning depths, lengths, and circumferential angles, as well as various thinning locations such as extrados, intrados, and full-circumference. The failure pressure decreased exponentially with increasing axial thinning length and decreased almost linearly with increasing thinning depth. These tendencies are similar to those observed for wall-thinned straight pipe. The failure pressure also decreased and gradually saturated with increasing circumferential thinning angle, unlike the results of wall-thinned straight pipe. All specimens failed by bulging, followed by cracking. The axial crack always occurred at the center of the wall-thinned area in the extrados and intrados wall-thinning cases. For the full-circumference wall-thinning case, however, the crack location and pattern were dependent on the axial thinning length. A comparison of the failure pressure with the results of existing models showed that the existing models were excessively conservative in all cases and could not properly predict the dependence of failure pressure on the wall-thinning geometry.     

Finite element analysis for creep failure of coolant pipe in light water reactor due to local heating under severe accident condition

During severe accident of a light water reactor (LWR), the piping of the reactor cooling system would be damaged when the piping is subjected to high internal pressure and very high temperature, resulted from high temperature gas generated in a reactor core and decay heat released from the deposit of fission products. It is considered that, under such a condition, short-term creep at high temperatures would cause the piping failure. For the evaluation of piping integrity under a severe accident, a method to predict such high temperature short-term creep deformation should be developed, using a creep constitutive equation considering tertiary creep. In this paper, the creep constitutive equation including tertiary creep was applied to nuclear-grade cold-drawn pipe of 316 stainless steel (SUS316), based on the isotropic damage mechanics proposed by Kachanov and Ravotnov. Tensile creep test data for the material of a SUS316 cold-drawn pipe were used to determine the coefficients of the creep constitutive equation. Using the constitutive equation taking account of creep damage, finite element analyses were performed for the local creep deformation of the coolant piping under two types of conditions; uniform temperature (isothermal condition) and temperature gradient of circumferential direction (non-isothermal condition). The analytical results show that the damage variable integrated into the creep constitutive equation can predict the pipe failure in the test performed by Japan Atomic Energy Research Institute, in which failure occurred from the outside of the pipe wall.     

Imaging of voids due to deformation in alloy steel using micro-focus X-ray beam

A micro-focus X-ray beam source along with computed tomography technique has been used to image the voids developed during tensile deformation in alloy steel used as structural material for nuclear power plant components. The technique was successful to characterize the internal void structure in the necked region of CrMoV type steel in terms of the size, distribution and volume fraction. The void volume fraction was found to be about 0.03% in a volume of 1.4 mm³ of the necked region reduced in diameter by 32% as a result of tensile deformation.     

Fracture and deformation behaviors of tee pipe with local wall thinning

Monotonic four-point bending tests were conducted using tee pipe specimens having local wall thinning. The effects of local wall thinning on the fracture behaviors of tee pipes were investigated. Local wall thinning was machined on the inside of pipes in order to simulate metal loss due to erosion corrosion. The configurations of the eroded area were l = 100 mm in eroded axial length, d/t = 0.5 and 0.8 in eroded ratio, and 2θ = 90° in eroded angle. The area undergoing local wall thinning was subjected to either tensile or compressive stress. It was found that the type of fracture could be classified into ovalization, local buckling, and crack initiation, depending on pipe shape, eroded ratio, and stress at the eroded area. Fracture behaviors of the tee pipes were compared with those of straight pipes. Three-dimensional elasto-plastic analyses were also carried out using the finite element method, which was able to accurately simulate fracture behaviors.     

The application of the simple fuel pin transient and melting model to thermal-hydraulics in LMFBR subassembly

A simple conduction model with phase change has been developed for the transient analysis of a reactor fuel pin based on lumped parameter techniques. The purpose of this analysis is to provide a simple useful tool to obtain the general information about fuel and clad leaning into the cooling transients and melting. Such a simple fuel and clad thermal transient model is particularly useful to multichannel analysis where conventional conduction computer codes require considerable computing time and storage space. At the present, this formulation is being employed for the analysis of sodium thermohydraulics, sodium voiding, and melting of cladding and fuel in a subassembly of a fast reactor core. A detailed analysis of the predicted coolant, fuel and cladding thermal transients leading into sodium voiding and fuel pin melting has been made in comparison with the results of various in-pile experiments and with the predictions from the existing more complicated codes.