Multi-group SP₃ approximation for simulation of a three-dimensional PWR rod ejection accident

Lee, Deokjung,Kozlowski, Tomasz,Downar, Thomas J. Elsevier 2015 Annals of nuclear energy Vol.77 No.-

<P><B>Abstract</B></P> <P>Previous researchers have shown that the simplified P<SUB>3</SUB> (SP<SUB>3</SUB>) approximation is capable of providing sufficiently high accuracy for both static and transient simulations for reactor core analysis with considerably less computational expense than higher order transport methods such as the discrete ordinate or the full spherical harmonics methods. The objective of this paper is to provide a consistent comparison of two-group (2G) and multi-group (MG) diffusion and SP<SUB>3</SUB> transport for rod ejection accident (REA) in a practical light water reactor (LWR) problem. The analysis is performed on two numerical benchmarks, a 3×3 assembly mini-core and a full pressurized water reactor (PWR) core. The calculations were performed using pin homogenized and assembly homogenized cross sections for a series of benchmarks of increasing difficulty, in two-dimensional (2D) and three-dimensional (3D), 2G and MG, diffusion and transport, as well as with and without feedback. All results show consistency with the reference results obtained from higher-order methods. It is demonstrated that the analyzed problems show small group-homogenization effects, but relatively significant transport effects which are satisfactorily addressed by the SP<SUB>3</SUB> transport method. The sensitivity tests also show that, for the REA simulation, the MG is more conservative than 2G, P<SUB>1</SUB> is more conservative than SP<SUB>3</SUB> for a 1/3 MOX loaded full-core problem.</P> <P><B>Highlights</B></P> <P> <UL> <LI> The multi-group SP<SUB>3</SUB> method developed and implemented in PARCS for the MOX analysis. </LI> <LI> The verifications were performed in 2D and 3D, 2G and MG, diffusion and transport, with and without feedback. </LI> <LI> All results show consistency with the reference results obtained from the ANL P<SUB>N</SUB> transport code VARIANT for steady-state and transport calculations. </LI> <LI> It was found that the SP<SUB>3</SUB> angular approximation captures sufficient transport effects for both steady-state and transient, and provides essentially the same results as the VARIANT P<SUB>5</SUB> method. </LI> <LI> From the transient results of the full-core problem, it was noted that MG is more conservative than 2G, and P<SUB>1</SUB> is more conservative than SP<SUB>3</SUB>. </LI> </UL> </P>

Loss of coolant accident analysis under restriction of reverse flow

Majdi I. Radaideh,Tomasz Kozlowski,Yousef M. Farawila 한국원자력학회 2019 Nuclear Engineering and Technology Vol.51 No.6

This paper analyzes a new method for reducing boiling water reactor fuel temperature during a Loss ofCoolant Accident (LOCA). The method uses a device called Reverse Flow Restriction Device (RFRD) at theinlet of fuel bundles in the core to prevent coolant loss from the bundle inlet due to the reverse flow aftera large break in the recirculation loop. The device allows for flow in the forward direction which occursduring normal operation, while after the break, the RFRD device changes its status to prevent reverseflow. In this paper, a detailed simulation of LOCA has been carried out using the U.S. NRC's TRACE code toinvestigate the effect of RFRD on the flow rate as well as peak clad temperature of BWR fuel bundlesduring three different LOCA scenarios: small break LOCA (25% LOCA), large break LOCA (100% LOCA), anddouble-ended guillotine break (200% LOCA). The results demonstrated that the device could substantiallyblock flow reversal in fuel bundles during LOCA, allowing for coolant to remain in the core during thecoolant blowdown phase. The device can retain additional cooling water after activating the emergencysystems, which maintains the peak clad temperature at lower levels. Moreover, the RFRD achieved thereflood phase (when the saturation temperature of the clad is restored) earlier than without the RFRD.

Analyzing nuclear reactor simulation data and uncertainty with the group method of data handling

Radaideh, Majdi I.,Kozlowski, Tomasz Korean Nuclear Society 2020 Nuclear Engineering and Technology Vol.52 No.2

Group method of data handling (GMDH) is considered one of the earliest deep learning methods. Deep learning gained additional interest in today's applications due to its capability to handle complex and high dimensional problems. In this study, multi-layer GMDH networks are used to perform uncertainty quantification (UQ) and sensitivity analysis (SA) of nuclear reactor simulations. GMDH is utilized as a surrogate/metamodel to replace high fidelity computer models with cheap-to-evaluate surrogate models, which facilitate UQ and SA tasks (e.g. variance decomposition, uncertainty propagation, etc.). GMDH performance is validated through two UQ applications in reactor simulations: (1) low dimensional input space (two-phase flow in a reactor channel), and (2) high dimensional space (8-group homogenized cross-sections). In both applications, GMDH networks show very good performance with small mean absolute and squared errors as well as high accuracy in capturing the target variance. GMDH is utilized afterward to perform UQ tasks such as variance decomposition through Sobol indices, and GMDH-based uncertainty propagation with large number of samples. GMDH performance is also compared to other surrogates including Gaussian processes and polynomial chaos expansions. The comparison shows that GMDH has competitive performance with the other methods for the low dimensional problem, and reliable performance for the high dimensional problem.

On using computational versus data-driven methods for uncertainty propagation of isotopic uncertainties

Radaideh, Majdi I.,Price, Dean,Kozlowski, Tomasz Korean Nuclear Society 2020 Nuclear Engineering and Technology Vol.52 No.6

This work presents two different methods for quantifying and propagating the uncertainty associated with fuel composition at end of life for cask criticality calculations. The first approach, the computational approach uses parametric uncertainty including those associated with nuclear data, fuel geometry, material composition, and plant operation to perform forward depletion on Monte-Carlo sampled inputs. These uncertainties are based on experimental and prior experience in criticality safety. The second approach, the data-driven approach relies on using radiochemcial assay data to derive code bias information. The code bias data is used to perturb the isotopic inventory in the data-driven approach. For both approaches, the uncertainty in k_eff for the cask is propagated by performing forward criticality calculations on sampled inputs using the distributions obtained from each approach. It is found that the data driven approach yielded a higher uncertainty than the computational approach by about 500 pcm. An exploration is also done to see if considering correlation between isotopes at end of life affects k_eff uncertainty, and the results demonstrate an effect of about 100 pcm.

Application of deep neural networks for high-dimensional large BWR core neutronics

Abu Saleem, Rabie,Radaideh, Majdi I.,Kozlowski, Tomasz Korean Nuclear Society 2020 Nuclear Engineering and Technology Vol.52 No.12

Compositions of large nuclear cores (e.g. boiling water reactors) are highly heterogeneous in terms of fuel composition, control rod insertions and flow regimes. For this reason, they usually lack high order of symmetry (e.g. 1/4, 1/8) making it difficult to estimate their neutronic parameters for large spaces of possible loading patterns. A detailed hyperparameter optimization technique (a combination of manual and Gaussian process search) is used to train and optimize deep neural networks for the prediction of three neutronic parameters for the Ringhals-1 BWR unit: power peaking factors (PPF), control rod bank level, and cycle length. Simulation data is generated based on half-symmetry using PARCS core simulator by shuffling a total of 196 assemblies. The results demonstrate a promising performance by the deep networks as acceptable mean absolute error values are found for the global maximum PPF (~0.2) and for the radially and axially averaged PPF (~0.05). The mean difference between targets and predictions for the control rod level is about 5% insertion depth. Lastly, cycle length labels are predicted with 82% accuracy. The results also demonstrate that 10,000 samples are adequate to capture about 80% of the high-dimensional space, with minor improvements found for larger number of samples. The promising findings of this work prove the ability of deep neural networks to resolve high dimensionality issues of large cores in the nuclear area.