Analysis of nonlinear fluid-structure interaction in LMFBR containment

A generalized Eulerian method has been incorporated into ICECO for analyzing the nonlinear fluid-structure interaction in the primary containment of an LMFBR, consisting of complicated structural components such as the radial shield, core barrel, core-support structure, and the primary vessel. The method employs a Poisson equation to determine the hydrodynamic pressure in the fluid region, while using a relaxation equation to compute the pressure adjacent to the structure. A generalized coupling scheme is developed for treating the sliding condition at the fluid-structure interface, modeling the perforated structure, and analyzing the fluid motion at the geometrical discontinuities. Detailed formulations are given. Sample problems concerning wave propagation in a typical reactor containment are presented. It is shown from the results that this implicit, iterative method is unconditionally stable, and is especially suitable for excursions involving large material distortions.     

Analysis and application of prestressed concrete reactor vessels for LMFBR containment

An analytical model of a prestressed concrete reactor vessel (PCRV) for LMFBR and the associated finite element computer code, involving an explicit time integration procedure, is described. The model is axisymmetric and includes simulations of the tensile cracking of concrete, the reinforcement, and a prestressing capability. The tensile cracking of concrete and the steel reinforcement are both modeled as continuously distributed within the finite element. The stresses in the reinforcement and concrete are computed separately and combined to give an overall stress state of the composite material. The reinformcement is assumed to be elastic, perfectly-plastic; the concrete is taken to be elastic, with tensile and compressive stress limits. Cracking of concrete is based on the criterion of maximum principal stress; a crack is assumed to form normal to the direction of the maximum principal stress. Attention is also given to the fact that cracks do not form instantaneously, but develop gradually. Thus, after crack initiation the normal stress is reduced to zero gradually as a function of time. Residual shear resistance of cracks due to aggregate interlock is also taken into account. An existing crack is permitted to close. Prestressing of the PCRV is modeled by special structural members which represent an averaged prestressing layer equivalent to an axisymmetric shell. The internal prestressing members are superimposed over the reinforced concrete body of the PCRV; they are permitted to stretch and slide in a predetermined path, simulating the actual tendons.The validity of the code is examined by comparison with experimental data. Both static and dynamic data are compared with code predictions, and the agreement is satisfactory. A preliminary design has been developed for both pool and loop-type PCRVs. The code was applied to the analysis of these designs. This analysis reveals that the critical locations in such a design would be the head cover and the junction between the cover and the vessel wall and indicates the pattern of crack development. The results show that the development of a design adequate for current HCDA loads is quite feasible for pool-type or loop-type PCRVs.     

Application of containment codes to LMFBRs in the united states

This paper describes the application of containment codes to predict the response of the fast reactor containment and the primary piping loops to HCDAs. Five sample problems are given to illustrate their applications. The first problem deals with the response of the primary containment to an HCDA. The second problem deals with the coolant flow in the reactor lower plenum. The third problem concerns sodium spillage and slug impact. The fourth problem deals with the response of a piping loop. The fifth problem analyzes the response of a reactor head closure. Application of codes in parametric studies and comparison of code predictions with experiments are also discussed.     

Comparison among MCNP-based depletion codes applied to burnup calculations of pebble-bed HTR lattices

The double-heterogeneity characterising pebble-bed high temperature reactors (HTRs) makes Monte Carlo based calculation tools the most suitable for detailed core analyses. These codes can be successfully used to predict the isotopic evolution during irradiation of the fuel of this kind of cores. At the moment, there are many computational systems based on MCNP that are available for performing depletion calculation. All these systems use MCNP to supply problem dependent fluxes and/or microscopic cross sections to the depletion module. This latter then calculates the isotopic evolution of the fuel resolving Bateman's equations.In this paper, a comparative analysis of three different MCNP-based depletion codes is performed: Montburns2.0, MCNPX2.6.0 and BGCore. Monteburns code can be considered as the reference code for HTR calculations, since it has been already verified during HTR-N and HTR-N1 EU project. All calculations have been performed on a reference model representing an infinite lattice of thorium-plutonium fuelled pebbles. The evolution of k-inf as a function of burnup has been compared, as well as the inventory of the important actinides.The k-inf comparison among the codes shows a good agreement during the entire burnup history with the maximum difference lower than 1%. The actinide inventory prediction agrees well. However significant discrepancy in Am and Cm concentrations calculated by MCNPX as compared to those of Monteburns and BGCore has been observed. This is mainly due to different Am-241 (n,γ) branching ratio utilized by the codes.The important advantage of BGCore is its significantly lower execution time required to perform considered depletion calculations. While providing reasonably accurate results BGCore runs depletion problem about two times faster than Monteburns and two to five times faster than MCNPX.     

Analysis of LMFBR containment response using a multifield implicit continuous-fluid eulerian code (MICE)

An Eulerian computer code, MICE, for analyzing multifield-fluid flow problems in LMFBR containments is presented. The hydrodynamics of the MICE code is based upon the implicit multifield (IMF) method which includes the treatment of multifield fluids, the interpenetration of materials, the heat transfer, and the material phase changes. The finite-difference equations and the numerical techniques used in obtaining the equilibrium pressures and in calculating the fluid-structure interactions are described in detail. Sample problems are given to illustrate the capabilities of the code.     

A benchmark exercise on the use of CFD codes for containment issues using best practice guidelines: A computational challenge

In the framework of the 5th EU-FWP project ECORA the capabilities of CFD software packages for simulating flows in the containment of nuclear reactors was evaluated. Four codes were assessed using two basic tests in the PANDA facility addressing the transport of gases in a multi-compartment geometry. The assessment included a first attempt to use Best Practice Guidelines (BPGs) for the analysis of long, large-scale, transient problems. Due to the large computational overhead of the analysis, the BPGs could not fully be applied. It was thus concluded that the application of the BPGs to full containment analysis is out of reach with the currently available computer power. On the other hand, CFD codes used with a sufficiently detailed mesh seem to be capable to give reliable answers on issues relevant for containment simulation using standard two-equation turbulence models. Development on turbulence models is constantly ongoing. If it turns out that advanced (and more computationally intensive) turbulence models may not be needed, the use of the BPGs for ‘certified’ simulations could become feasible within a relatively short time.     

Intercomparison of unfolding codes for benchmark gamma spectrometry

The unfolding codes FERDOR and RADAK were selected to compare gamma photon spectra from experimental measurements. The input data were obtained from penetration measurements of 6 MeV gamma photons from a 0.86 m diameter uniform isotropic disc source through 10 cm of steel and 5 cm and 10 cm of lead. Both codes produced similar spectra but RADAK allows adjustment to the response matrix elements within real constraints and has a realistic approach to error analysis. RADAK is recommended as a standard unfolding code to provide experimental benchmark data.     

Sprays in containment: Final results of the SARNET spray benchmark

The influence of containment sprays on atmosphere behaviour, a sub-task of the Work Package WP12-2 CAM (Containment Atmosphere Mixing), has been investigated through benchmark exercises based on TOSQAN (IRSN) and MISTRA (CEA) experiments. These tests are being simulated with lumped-parameter (LP) and Computational Fluid Dynamics (CFD) codes. Both atmosphere depressurization and mixing are being studied in two phases: a ‘thermalhydraulic part’, which deals with depressurization by sprays (TOSQAN 101 and MISTRA MASPn), and a ‘dynamic part’, dealing with light gas stratification break-up by spray (TOSQAN 113 and MISTRA MARC2b).In the thermalhydraulic part of the benchmark, participants have found the appropriate modelling to obtain good global results in terms of experimental pressure and mean gas temperature, for both TOSQAN and MISTRA tests. It can thus be considered that code users have a good knowledge of their spray modelling parameters. On a local level, for the TOSQAN test, single droplet behaviour is found to be well estimated by some calculations, but the global modelling of multiple droplets, i.e. of the spray, specifically for the spray dilution, is questionable in some CFD calculations. It can lead to some discrepancies localized in the spray region and can thus have a high impact on the global results, since most of the heat and mass transfers occur inside this region. In the MISTRA tests, wall condensation mass flow rates and local temperatures were used for code-experiment comparison and show that improvement of the local modelling, including initial conditions determination, is needed.In this dynamic part, a general result, in both tests, is that calculations do not recover the same kinetics of the mixing. Furthermore, concerning global mixing, LP contributions seem not suitable here. For the TOSQAN benchmark, the one-phase CFD calculations recover partially the phenomena involved during the mixing, whereas the two-phase flow CFD contributions generally recover the phenomena. Moreover, one important result is also that none of the contributions finds the exact amount of helium remaining in the dome above the spray nozzle in the TOSQAN 113. Discrepancies are rather high (above 5%vol of helium). Results are thus encouraging, but the level of validation should be improved. The same kind of conclusions can be drawn for the MISTRA MARC2B tests.As a conclusion of this SARNET spray benchmark, the level of validation obtained here is encouraging for the use of spray modelling for risk analysis. However, some more detailed investigations are needed to improve model parameters and decrease the uncertainty for containment applications as well as to increase the predictability of the phenomena within the containment analyses. Further activities are well encouraged on this topic, such as numerical benchmarks on analytical separate-effect experiments.     

Analysis of different containment models for IRIS small break LOCA, using GOTHIC and RELAP5 codes

Advanced nuclear water reactors rely on containment behaviour in realization of some of their passive safety functions. Steam condensation on containment walls, where non-condensable gas effects are significant, is an important feature of the new passive containment concepts, like the AP600/1000 ones.In this work the international reactor innovative and secure (IRIS) was taken as reference, and the relevant condensation phenomena involved within its containment were investigated with different computational tools. In particular, IRIS containment response to a small break LOCA (SBLOCA) was calculated with GOTHIC and RELAP5 codes. A simplified model of IRIS containment drywell was implemented with RELAP5 according to a sliced approach, based on the two-pipe-with-junction concept, while it was addressed with GOTHIC using several modelling options, regarding both heat transfer correlations and volume and thermal structure nodalization. The influence on containment behaviour prediction was investigated in terms of drywell temperature and pressure response, heat transfer coefficient (HTC) and steam volume fraction distribution, and internal recirculating mass flow rate. The objective of the paper is to preliminarily compare the capability of the two codes in modelling of the same postulated accident, thus to check the results obtained with RELAP5, when applied in a situation not covered by its validation matrix (comprising SBLOCA and to some extent LBLOCA transients, but not explicitly the modelling of large dry containment volumes).The option to include or not droplets in fluid mass flow discharged to the containment was the most influencing parameter for GOTHIC simulations. Despite some drawbacks, due, e.g. to a marked overestimation of internal natural recirculation, RELAP5 confirmed its capability to satisfactorily model the basic processes in IRIS containment following SBLOCA.     

Analysis of the primary containment response using a hydrodynamic-elastic-plastic computer code

The dynamic response of the primary reactor containment system to a hypothetical core disruptive accident (HCDA) is determined from the basic equations of mass, momentum, and energy, and the equations of state of the medium. These equations are first expressed in material coordinates and then set into finite difference form solved numerically on the computer using a hydrodynamic-elastic-plastic computer code, REXCO-HEP developed at ANL. Propagation of pressure waves, loads imposed on different parts of the reactor components, and the resulting deformations are determined at every time step throughout the sequence of the calculation. As a sample calculation, the code was applied to analyze the response of the FFTF reactor to a 150 MWsec HCDA. The mathematical model is described in detail, particularly in the areas of modeling reactor internals and extending the time range to cover the entire excursion phenomenon. Finally, the results obtained from the computer analysis are discussed in detail.     

Thermal hydraulic investigations of primary coolant pipe rupture in an LMFBR

High quality for primary coolant pipes in fast reactors is ensured through utmost care taken in the design and manufacture. Demonstration of high structural reliability of them by extensive experimental and theoretical studies renders the double-ended guillotine rupture (DEGR) of a primary pipe a highly improbable event. However, as a defense in depth approach instantaneous DEGR of one of the pipes has been considered in design. Thermal hydraulic analyses of this event in a typical liquid metal cooled fast breeder have been carried out to study its consequences and to establish the availability of safety margins. Various uncertainties relevant to the event have been analysed to evaluate the sensitivity of each parameter. For this purpose, one-dimensional plant dynamics studies using thermal and hydraulic models of core subassemblies and primary sodium circuit have been performed. Validity of the assumptions made in the one-dimensional model like, uniform flow through all subassemblies in core under pipe ruptured condition and non possibility of sodium boiling by flashing have also been investigated through detailed three-dimensional and pressure transient studies. Analyses indicate the availability of good margins against the design safety limits in all the parametric cases analysed.     

A method for solving a stochastic eigenvalue problem applied to criticality

We present a novel approach to calculate stochastic eigenvalues of differential and integral equations using polynomial chaos theory. The method is applied to a criticality problem using the diffusion equation. This technique has the advantage of avoiding the non-linear terms in the conventional method of stochastic eigenvalue calculation but it does require an additional, ‘pseudo-time’, independent variable t.     

Comparison of RELAP5 calculations of VVER-1000 coolant transient benchmark phase 1 at different power

This paper provides comparisons between experimental data of “MCP switching on when the other three MCPs are in operation” and RELAP5 calculations with different initial levels of the reactor power 29.45% and 27.47% from the nominal.

The reference power plant for this analysis is Unit 6 at the Kozloduy nuclear power plant (NPP) site. RELAP5/MOD3.2 computer code has been used to simulate the investigated transient. Operational data from Kozloduy NPP have been used for the purpose of assessing how the RELAP5 model compares against plant data. During the plant-commissioning phase at Kozloduy NPP Unit 6 a number of experiments have been performed. One of them is switching on MCP when the other three MCPs are in operation.

This investigation was possible through the participation of leading specialists from Kozloduy NPP and with the support of Argonne National Laboratory, under the International Nuclear Safety Program (INSP) of the United States Department of Energy.     

Application of liquid-metal MHD generators to the LMFBR

The feasibility of coupling two-phase liquid-metal magnetohydrodynamic generators (LMMHD) to liquid-metal fast breeder reactors (LMFBR) is examined. Important constraints on the LMFBR-LMMHD system that were not accounted for in earlier studies have been included.A LMMHD cycle coupled to a gas turbine cycle yielded an overall cycle efficiency of 35.2% which is less than the efficiency of 36.2% when the gas turbine cycle is utilized by itself. However, a LMMHD cycle coupled to a steam cycle shows a slight advantage (38.9–39.8% overall cycle efficiencies for generator efficiencies varying from 80 to 90%) over the conventional steam cycle (38.5% efficiency).     

Assessment of CDFR primary containment capability under HCDA loading

The paper reviews UK studies of fast reactor containment response under hypothetical core disruptive accident (HCDA) loading, describing the evolution of complementary programmes of model experiments, numerical methods development and code validation. Results are presented from studies of the CDFR primary vessel, roof and core support structure, with particular emphasis on recent experimental work: these examples illustrate the level of detail required in the assessment of containment structures. The status of the work is critically reviewed, drawing attention to problems associated with the extrapolation of data from model experiments to the reactor situation. The likely direction of future work is indicated, focussing on more detailed assessment of particular structural features, the performance of seals and the study of leakage.     

Analysis of primary containment response with upper internal structure

In the fast reactor containment the upper internal structure is a massive structural component located in the region above the core. The main body of this structure consists of four support columns, an upper plate and a lower plate holding numerous coolant passageways for directing the core sodium to the outlet plenum. The aim of this paper is to provide hydrodynamic analysis of the fluid motion in the above core region and to study the effect of the upper internal structure on the slug impact as well as the primary system response.At ANL, two excursion containment codes, ICECO and ALICE, are chosen for such an analysis. These two codes, based on the ICE technique and ICED-ALE method, respectively, are ideal for analyzing flow through coolant passageways and flow blockage near the bottom plate. They also have other advantages, such as: (1) treating fluid motion around internal structure with geometrical discontinuities; (2) investigating excursions with large distortions; (3) handling two-dimensional sliding conditions; and (4) providing a stable solution throughout the entire excursion.In both ICECO and ALICE the upper internal structure can be modelled by rigid obstacles similar to the scheme used in the MAC method. The coolant passageways can be approximated by means of narrow cells. Another option is provided in the ICECO code in which the upper internal is considered as a perforated structure. In this model large cells can be used over the entire computational region. The analysis utilizes a control-volume technique to solve the conservation equations of mass, momentum, and energy. The basic idea is to use the actual fluid volume and the actual flow area in the mathematical formulation. Three modified Poisson equations are derived which govern the hydrodynamic pressures inside, above, and below the perforated structure. These three equations, in conjunction with the Poisson equation of the ICE technique as well as the relaxation equation at the moving boundary, are solved iteratively.Two sample problems are given. The first one deals with the ICECO analysis of primary containment response to an HCDA. The effect of the upper internal structure on the wave propagation and slug impact are investigated. The second example presents a simulation of SRI complex vessel experiments using the Alice code. The results are discussed in detail.     

Ultimate capacity of a mark II primary containment using new probabilistic failure criteria

In the past few years, new failure criteria to determine the ultimate capacity of nuclear primary containments associated with exceeding probability have been developed. In this paper, a study concerning the Laguna Verde Mark II reinforced concrete containment is reported. This study was accomplished using an advanced non-linear constitutive and finite element model. Analyses were performed for beyond-original-design pressure and temperature assumptions. The paper describes the non-linear analysis methodology, the various failure criteria, and the application of the results in a probabilistic framework. The probabilistic approach addresses criteria for predicting liner tear, penetration failure, and through-wall shear failure. It attempts to assign reasonable estimates of leak area to different failure mechanisms and it allows the evaluation of conditional probabilities for the postulated severe accidents selected.     

Comparison between HELIOS calculations and a PWR cell benchmark for actinides transmutation

This paper shows a comparison between the results obtained with the HELIOS code and other similar codes used in the international community, with respect to the transmutation of actinides. To do this, the international benchmark: “Calculations of Different Transmutation Concepts” of the Nuclear Energy Agency is analyzed. In this benchmark, two types of cells are analyzed: a small cell corresponding to a standard pressurized water reactor (PWR), and a wide cell corresponding to a highly moderated PWR. Two types of discharge burnup are considered: 33 GWd/tHM and 50 GWd/tHM. The following results are analyzed: the neutron multiplication factor as a function of burnup, the atomic density of the principal actinide isotopes, the radioactivity of selected actinides at reactor shutdown and cooling times from 7 until 50,000 years, the void reactivity and the Doppler reactivity. The results are compared with the following codes: KAPROS/KARBUS (FZK, Germany), SRAC95 (JAERI, Japan), TRIFON (ITTEP, Russian Federation) and WIMS (IPPE, Russian Federation). For the neutron multiplication factor, the results obtained with HELIOS show a difference of around 1% δk/k. For the isotopic concentrations: ²⁴¹Pu, ²⁴²Pu, and ^242mAm, the results of all the institutions present a difference that increases at higher burnup; for the case of ²³⁷Np, the results of FZK diverges from the other results as the burnup increases. Regarding the activity, the difference of the results is acceptable, except for the case of ²⁴¹Pu. For the Doppler coefficient, the results are acceptable, except for the cells with high moderation. In the case of the void coefficient, the difference of the results increases at higher void fractions, being the highest at 95%. In summary, for the PWR benchmark, the results obtained with HELIOS agree reasonably well within the limits of the multiple plutonium recycling established by the NEA working party on plutonium fuels and innovative fuel cycles (WPPR).     

Seismic behavior of a free-standing core in a large LMFBR

This paper describes a study on the seismic analysis and qualification of an LMFBR core. A non-linear response analysis method with FINAS is validated by comparing its results to a set of existing experimental data. The method is then applied to assess the seismic response and safety capacity of some typical configurations of a large free-standing core, under various seismic inputs including a case of base isolation. Some discussions are made on the possibility of the free-standing core.     

Parameterless evolutionary algorithm applied to the nuclear reload problem

In this work, an evolutionary algorithm with no parameters called FPBIL (parameter free PBIL) is developed based on PBIL (population-based incremental learning). Moreover, the analysis reveals how the parameters from PBIL can be replaced by self-adaptable mechanisms which appear from the radically different form by which the evolution is processed. Despite the advantages, the FPBIL reveals itself compact and relatively modest in the use of computational resources. The FPBIL is then applied to the nuclear reload problem. The experimental results observed are compared to those of other works and corroborate to affirm the superiority of the new algorithm.