Koroush Shirvan

Inverse uncertainty quantification using the modular Bayesian approach based on Gaussian Process, Part 2: Application to TRACE

Abstract Inverse Uncertainty Quantification (UQ) is a process to quantify the uncertainties in random input parameters while achieving consistency between code simulations and physical observations. In this paper, we performed inverse UQ using an improved modular Bayesian approach based on Gaussian Process (GP) for TRACE physical model parameters using the BWR Full-size Fine-Mesh Bundle Tests (BFBT) benchmark steady-state void fraction data. The model discrepancy is described with a GP emulator. Numerical tests have demonstrated that such treatment of model discrepancy can avoid over-fitting. Furthermore, we constructed a fast-running and accurate GP emulator to replace TRACE full model during Markov Chain Monte Carlo (MCMC) sampling. The computational cost was demonstrated to be reduced by several orders of magnitude. A sequential approach was also developed for efficient test source allocation (TSA) for inverse UQ and validation. This sequential TSA methodology first selects experimental tests for validation that has a full coverage of the test domain to avoid extrapolation of model discrepancy term when evaluated at input setting of tests for inverse UQ. Then it selects tests that tend to reside in the unfilled zones of the test domain for inverse UQ, so that one can extract the most information for posterior probability distributions of calibration parameters using only a relatively small number of tests. This research addresses the “lack of input uncertainty information” issue for TRACE physical input parameters, which was usually ignored or described using expert opinion or user self-assessment in previous work. The resulting posterior probability distributions of TRACE parameters can be used in future uncertainty, sensitivity and validation studies of TRACE code for nuclear reactor system design and safety analysis.

Inverse uncertainty quantification using the modular Bayesian approach based on Gaussian process, Part 1: Theory

Abstract In nuclear reactor system design and safety analysis, the Best Estimate plus Uncertainty (BEPU) methodology requires that computer model output uncertainties must be quantified in order to prove that the investigated design stays within acceptance criteria. “Expert opinion” and “user self-evaluation” have been widely used to specify computer model input uncertainties in previous uncertainty, sensitivity and validation studies. Inverse Uncertainty Quantification (UQ) is the process to inversely quantify input uncertainties based on experimental data in order to more precisely quantify such ad-hoc specifications of the input uncertainty information. In this paper, we used Bayesian analysis to establish the inverse UQ formulation, with systematic and rigorously derived metamodels constructed by Gaussian Process (GP). Due to incomplete or inaccurate underlying physics, as well as numerical approximation errors, computer models always have discrepancy/bias in representing the realities, which can cause over-fitting if neglected in the inverse UQ process. The model discrepancy term is accounted for in our formulation through the “model updating equation”. We provided a detailed introduction and comparison of the full and modular Bayesian approaches for inverse UQ, as well as pointed out their limitations when extrapolated to the validation/prediction domain. Finally, we proposed an improved modular Bayesian approach that can avoid extrapolating the model discrepancy that is learnt from the inverse UQ domain to the validation/prediction domain.

Steady State and Accident Transient Analysis Burning Weapons-Grade Plutonium in Thorium and Uranium with Silicon Carbide Cladding

Abstract A comparison of burning weapons-grade plutonium in a standard pressurized water reactor (PWR) using thoria or urania as a fuel matrix has been performed. Two cladding options were considered: a silicon carbide (SiC) matrix of 0.76-mm thickness and Zircaloy of 0.57-mm thickness. As expected, in terms of percentage and total plutonium mass burned, there was a large benefit in using thoria as a matrix compared to urania. Additionally, a smaller amount of plutonium is required in a core when SiC is the cladding because of lower neutron absorption in SiC. The thorium system was also better from a plutonium-burning viewpoint. It resulted in less weapons-useable U and Pu at discharge and more burned over an assembly’s lifetime. At discharge, the fuel was shown to have lower multiples of minimum amounts needed for weapons, even when 233U breeding was taken into account. Thoria-plutonia fuel has different kinetic characteristics from urania-plutonia or enriched urania fuel, so a limited safety comparison of such fuels was made for two reactivity insertion accidents: (1) the highest worth rod ejection and (2) main-steam-line break (MSLB). The accident analyses were performed at both beginning and end of cycle. While the control rod worths are higher in the simulated thoria-plutonia and urania-plutonia cores than in conventional urania-loaded cores, the enthalpy added during the accident was lower than current safety limits for conventional cores. During the MSLB accident, all cases showed acceptable behavior, indicating that the less negative moderator temperature coefficients of thoria-plutonia and urania-plutonia fuel were not limiting.

Stability Analysis of BWR-HD: An Optimized Boiling Water Reactor with High Power Density

Abstract A boiling water reactor (BWR) with high power density (BWR-HD) was designed through an optimization search that was constrained to a square lattice fuel array. It has a power level of 5000 MW(thermal), equivalent to a 26% uprated Advanced BWR (ABWR), the latest version of operating BWR. This results in economic benefits, estimated to be ~20% capital and operations and maintenance costs and similar total fuel cycle cost per unit electricity. The stability of the ABWR and BWR-HD were assessed for the three modes of density wave oscillations: single-channel thermal hydraulics, coupled neutronic regional core oscillations, and coupled neutronic global core oscillations. The sensitivity to design parameters such as inlet subcooling, presence of water rods, and inlet orifice coefficient as well as to changes in reactor power, flow rate, and void coefficient were examined using the STAB frequency domain code. The BWR-HD’s stability performance and sensitivity were concluded to be similar to those of the ABWR. The results of the frequency domain analysis indicate that the shorter core and smaller void coefficient lowered the oscillation decay ratio, while the cooler inlet temperature and higher void fraction increased the decay ratio. Also the S3K code was utilized to perform three-dimensional coupled stability analysis and to formulate an operation exclusion zone region for the BWR-HD design. It was found that a reduction in the allowable operational zone of the BWR-HD design is warranted, due to its decay ratio being higher than that of the ABWR for whole-core oscillations. However, the inlet orificing (pressure loss coefficient) of the assemblies can be increased to obtain the same stability performance as the ABWR. This strategy is deemed plausible since the pumping power needed for the BWR-HD, even with the increase in pressure losses at the inlet of assemblies, will still be less than that of the ABWR and will have negligible effects on the safety performance.

BWR-HD: An Optimized Boiling Water Reactor with High Power Density

Abstract Increasing the economic competitiveness of nuclear energy is vital to its future. One way to reduce the cost of the plant is by extracting more power from the same volume. A scoping study is conducted to maximize the power density in boiling water reactors (BWRs) under the constraints of using fuel with traditional materials and cylindrical geometry, and enrichments below 5% to enable its licensability with no changes to present facilities. An optimization search over all other design parameters yields a BWR with high power density (BWR-HD) at a power level of 5000 MW(thermal), equivalent to a 26% uprated Advanced BWR (ABWR), the most recently built version of BWR. The BWR-HD utilizes about the same number of wider fuel assemblies, with 16 × 16 pin arrays and 35% shorter active fuel than the 10 × 10 assemblies of the ABWR. The fuel rod diameter and pitch are also reduced to just over 70% of the ABWR values. Thus, it is possible to increase the power density and specific power by 65% while maintaining the nominal ABWR minimum critical power ratio margin. The optimum core pressure is found to be the same as the current 7.2 MPa. The core exit quality is increased to 19% from the ABWR nominal exit quality of 15%. The pin linear heat generation rate is 20% lower, and the core pressure drop and mass of uranium are 30% lower. The BWR-HD’s fuel, modeled with FRAPCON 3.4, showed similar performance to the ABWR pin design. This results in 20% reduced operations and maintenance and capital costs per unit energy, but total fuel cycle cost similar to that of the 18-month ABWR fuel cycle.

Assessment of the Subchannel Code CTF for Single- and Two-Phase Flows

Abstract As part of the Consortium for Advanced Simulation of Light Water Reactors, the subchannel code CTF is being used for single-phase and two-phase flow analysis under light water reactor operating conditions. Accurate determination of flow distribution, pressure drop, and void content is crucial for predicting margins to thermal crisis and ensuring more efficient plant performance. In preparation for the intended applications, CTF has been validated against data from experimental facilities comprising the General Electric (GE) 3 × 3 bundle, the boiling water reactor full-size fine-mesh bundle tests (BFBTs), the Risø tube, and the pressurized water reactor subchannel and bundle tests (PSBTs). Meanwhile, the licensed, well-recognized subchannel code VIPRE-01 was used to generate a baseline set of simulations for the targeted tests and solution parameters were compared to the CTF results. The flow split verification problem and single-phase GE 3 × 3 results are essentially in perfect agreement between the two codes. For the two-phase GE 3 × 3 cases, flow and quality discrepancies arise in the annular-mist flow regime, yet significant improvement is observed in CTF when void drift and two-phase turbulent mixing enhancement are considered. The BFBT pressure drop benchmark shows close agreement between predicted and measured results in general, although considerable overprediction by CTF is observed at relatively high void locations of the facility. This overestimation tendency is confirmed by the Risø cases. While overall statistics are satisfactory, both BFBT and PSBT bubbly-to-churn flow void contents are markedly overpredicted by CTF. The issues with two-phase closures such as turbulent mixing, interfacial and wall friction, and subcooled boiling heat transfer need to be addressed. Preliminary sensitivity studies are presented herein, but more advanced models and code stability analysis require further investigation.

Modeling physical vapor deposition of energetic materials

Morphology and microstructure of organic explosive films formed using physical vapor deposition (PVD) processes strongly depends on local surface temperature during deposition. Currently, there is no accurate means of quantifying the local surface temperature during PVD processes in the deposition chambers. This work focuses on using a multiphysics computational fluid dynamics tool, STARCCM+, to simulate pentaerythritol tetranitrate (PETN) deposition. The PETN vapor and solid phase were simulated using the volume of fluid method and its deposition in the vacuum chamber on spinning silicon wafers was modeled. The model also included the spinning copper cooling block where the wafers are placed along with the chiller operating with forced convection refrigerant. Implicit time-dependent simulations in two- and three-dimensional were performed to derive insights in the governing physics for PETN thin film formation. PETN is deposited at the rate of 14 nm/s at 142.9 °C on a wafer with an initial temperature of...

Critical Power and Void Fraction Prediction of Tight Bundle Designs

Abstract With the objective of providing long-term energy supply via actinide breeding and burning, the next-generation boiling water reactor (BWR) design, the Hitachi’s resource-renewable BWR (RBWR), has been proposed. Unlike a traditional square lattice BWR fuel bundle, the RBWR bundles are shorter with hexagonal tight lattice arrangement and heterogeneous axial fuel zoning. The RBWR’s different core geometry combined with the higher power-to-flow ratio and void fraction necessitates the reexamination of the standard BWR thermal-hydraulic models. For the prediction of dryout, the previously derived best-estimate empirical correlation showed significant scatter when compared to experimental data within its calibration database. In this work, the correlation is further calibrated and improved by supplementing tight bundle data with relevant critical power data for tubes and annuli to better quantify the effects of various parameters and by incorporating subchannel-level results to account for intra-assembly flow mixing. Another approach using the mechanistic three-field model is also investigated, and the minimum critical power ratio of the RBWR design is evaluated. For the prediction of void fraction, measurements and the three-field model in annular flow regime reveal that the common drift flux approaches tend to overestimate the void fraction at small hydraulic diameters. The void fraction dependence on hydraulic diameter below 10 mm requires further experimentation and high-fidelity mechanistic simulations.