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Civilian marine reactors face a unique set of design challenges in addition to the usual irradiation and thermal-hydraulic limits affecting all reactors. These include requirements for a small core size, long core lifetime, a 20% cap on fissile loading, and limitations on the use of soluble boron. One way to achieve higher burnup/longer core life is to alter the neutron spectrum by changing the hydrogen-to-heavy-metal ratio, thus increasing the conversion of fertile isotopes in the fuel. In this reactor physics study, we optimize the two-dimensional lattice geometry of a 333 MWth soluble-boron-free marine PWR for 18% 235U enriched micro-heterogeneous ThO2-UO2 duplex fuel and 15% 235U enriched homogeneously mixed all-UO2 fuel. We consider two types of coolant: H2O and mixed 80% D2O + 20% H2O. We aim to observe in which spectrum discharge burnup is maximized in order to improve uranium utilization, while satisfying the constraint on moderator temperature coefficient. It is observed that higher discharge burnup for the candidate fuels is achievable by using either a wetter lattice or a much drier lattice than normal, while epithermal lattices are distinctly inferior performers. The thorium-rich duplex fuel exhibits higher discharge burnup potential than the all-UO2 fuel for all moderation regimes for both coolants. The candidate fuels exhibit higher initial reactivity and discharge burnup with the mixed D2O-H2O coolant than with the H2O coolant in the under-moderated regime, whereas these values are lower for the D2O-H2O coolant in the over-moderated regime.

Uncertainty-based design optimization (UBDO) is becoming increasingly important with great attention to critical system reliability and robustness. However, most traditional UBDO methods only consider low-order response moments and a limited number of aleatory uncertainties, which desiderates to be resolved. In this study, an efficient UBDO approach based on cumulative distribution matching is presented to address all response moments under mixed aleatory and epistemic uncertainties. The mathematical formulation of cumulative distribution function (CDF) matching is systematically derived including the distance metric definition and numerical computation process. Uncertainty analysis within the CDF matching optimization loop is also investigated, including the identification of active subspaces and the propagation of constructed surrogate model in reduced dimensions. Extended active subspaces are furthered discussed for mixed uncertainty analysis to obtain the bounds of CDF efficiently, instead of the time-consuming full-dimensional simulation. The proposed approach is illustrated by three typical optimization examples, i.e., response function matching, standard NASA test problem, and satellite system design in aerospace engineering. The UBDO results based on the CDF matching are discussed and compared with the probability density function matching, which exhibits higher efficiency and better convergence in tackling constrained optimization design problems subject to mixed uncertainties.

Civil marine reactors face a unique set of design challenges. These include requirements for a small core size and long core lifetime, a 20% cap on fissile loading, and limitations on using soluble neutron absorbers. In this reactor physics study, we seek to design a core that meets these requirements over a 15 effective full-power-years (EFPY) life at 333 MWth using homogeneously mixed all-UO2 and micro-heterogeneous ThO2-UO2 duplex fuels. In a companion (Part I) paper, we found assembly designs using 15% and 18% 235 U for UO2 and duplex fuels, respectively, loaded into 13 × 13 pin arrays. High thickness (150 μm) ZrB2 integral fuel burnable absorber (IFBA) pins and boron carbide (B4C) control rods are used for reactivity control. Taking advantage of self-shielding effects, these designs maintain low and stable assembly reactivity with little burnup penalty. In this paper (Part II), whole-core design analyses are performed for small modular reactor (SMR) to determine whether the core remains critical for at least 15 EFPY with a reactivity swing of less than 4000 pcm, subject to appropriate constraints. The main challenge is to keep the radial form factor below its limit (1.50). Burnable poison radial-zoning is examined in the quest for a suitable arrangement to control power peaking. Optimized assemblies are loaded into a 3D reactor model in PANTHER. The PANTHER results confirm that the fissile loadings of both fuels are well-designed for the target lifetime: at the end of the ∼ 15-year cycle, the cores are on the border of criticality. The duplex fuel core can achieve ∼ 4% longer core life, has a ∼ 3% lower initial reactivity and ∼ 30% lower reactivity swing over life than the final UO2 core design. The duplex core is therefore the more successful design, giving a core life of ∼ 16 years and a reactivity swing of less than 2500 pcm, while satisfying all the neutronic safety parameters. In particular, one of the major objectives of this study is to offer/explore a thorium-based candidate alternative fuel platform for the proposed marine core. It is proven by literature reviews that the ability of the duplex fuel was never explored in the context of a single-batch, LEU, SBF, long-life SMR core. In this regard, the motivation of this paper is to understand the underlying physics of the duplex fuel and ‘open the option’ of designing the functional cores with both the duplex and UO2 fuel cores.

Neutron clustering is a recently identified problem with Monte Carlo eigenvalue calculations which can produce significantly erroneous results. Previous work by Sutton & Mittal (2017) considered neutron clustering as a problem of maintaining ‘genetic diversity’ within the neutron population. This paper proposes reducing the extent of neutron clustering by replacing fission neutrons in the source bank with uncorrelated neutrons, sampled from a uniform source distribution – effectively adding new neutron genealogies to the population. The efficacy of the method is demonstrated on a number of simple problems, showing improved behaviour of the Shannon entropy and neutron centre-of-mass. Although currently limited in scope, this paper intends to provide a route to reducing clustering effects in more general problems.

Best estimate plus uncertainty is the leading methodology to validate existing safety margins. It remains a challenge to develop and license these approaches, in part due to the high dimensionality of system codes. Uncertainty quantification is an active area of research to develop appropriate methods for propagating uncertainties, offering greater scientific reason, dimensionality reduction and minimising reliance on expert judgement. Inverse uncertainty quantification is required to infer a best estimate back on the input parameters and reduce the uncertainties, but it is challenging to capture the full covariance and sensitivity matrices. Bayesian inverse strategies remain attractive due to their predictive modelling and reduced uncertainty capabilities, leading to dramatic model improvements and validation of experiments. This paper uses state-of-the-art data assimilation techniques to obtain a best estimate of parameters critical to plant safety. Data assimilation can combine computational, benchmark and experimental measurements, propagate sparse covariance and sensitivity matrices, treat non-linear applications and accommodate discrepancies. The methodology is further demonstrated through application to hot zero power tests in a pressurised water reactor (PWR) performed using the BEAVRS benchmark with Latin hypercube sampling of reactor parameters to determine responses. WIMS 11 (dv23) and PANTHER (V.5:6:4) are used as the coupled neutronics and thermal-hydraulics codes; both are used extensively to model PWRs. Results demonstrate updated best estimate parameters and reduced uncertainties, with comparisons between posterior distributions generated using maximum entropy principle and cost functional minimisation techniques illustrated in recent conferences. Future work will improve the Bayesian inverse framework with the introduction of higher-order sensitivities.

Optimization problems in the research literature are typically simplified and/or heavily constrained and focus on a single set of physical processes. Real-world nuclear engineering problems feature competing multi-physics phenomena and require equally complex analysis. To prove its usefulness in this area, optimization must demonstrate an ability to handle many competing objectives whilst accurately simulating the reactor environment. This paper applies the MOJADE optimization algorithm to two design problems, a 3D PWR Supercell and a 3D BWR fuel assembly, evaluating performance objectives related to neutronics and thermal hydraulics simultaneously, using the concept of Pareto dominance. In both cases, MOJADE was able to find competitive or non-dominated designs compared to baseline solutions generated from the literature and required no control parameter tuning or training time. Analysis revealed that MOJADE can identify key variables which impact objective performance, demonstrating the algorithm’s ability to provide new insight to complex 3D problems featuring multi-physics analysis.

This paper presents a critical appraisal of the paper “Performance analysis of Wells turbine blades using the entropy generation minimization method” by Shehata, A. S., Saqr, K. M., Xiao, Q., Shahadeh, M. F. and Day, A., published in Renewable Energy, volume 86, pp. 1123–1133. The discussion focuses in particular on five aspects of the work being critiqued: the set-up of the numerical experiment, the similarity of the problem studied with the large existing literature on oscillating airfoils, the estimation of entropy generation through the numerical solution of the Navier-Stokes equations, the equivalence between entropy and drag, and finally a comparison of the results presented with existing literature. From this appraisal, it is concluded that the problem studied is not representative of a Wells turbine and that the article contains a number of fundamental errors that lead to incorrect results. These mistakes would have been evident had the results been analyzed critically and compared to the existing literature on the subject. If the results had been presented in non-dimensional form, as best practice recommends, they would have been more readily comparable to those in existing literature and important discrepancies might not have been obscured.

Chance-constrained optimization has recently been receiving much attention from the engineering community. Uncertainties are being incorporated in increasingly large numbers to ensure reliability and robustness. However, the efficiency and accuracy of chance-constrained optimization under multiple uncertainties remains challenging. In this study, a constrained density-matching optimization methodology is established to address these pressing issues in chance-constrained optimization. The methodology employs an alternative objective metric between a designer-given target and system response, enables more uncertainties in design variables and random parameters to be handled, and accommodates multiple chance constraints with an adaptive penalty function. An active subspace identification strategy and a dynamic response surface are given to overcome the curse of uncertainty dimensionality and to guarantee sufficient samples for kernel density estimation in an uncertainty analysis. The efficacy is demonstrated...

Uncertainty quantification (UQ) within topology optimization (TO) is a growing trend, with designers recognizing that deterministic analysis does not reflect the natural variabilities found in real-world structural performance. Thus far the majority of works have dealt with uncertain loading and material properties; however, minimal research has considered uncertain boundary conditions (BCs), which play a vital role for static and dynamic analysis involving compliance and natural frequency objectives and/or constraints. BCs uncertainty is studied in this paper by assuming a random percentage of a cantilever can be freed to rotate and/or translate in space. This is firstly demonstrated through a case study on a flat plate wing where the frequency gap between two modes is maximized, and secondly through optimizing the wing of a sensorcraft where compliance is minimized. A robust objective is formulated via a weighted sum of the mean and standard deviation, which is approximated efficiently using a Non-Intrusive Polynomial Chaos Expansion (NIPC). Both studies demonstrate the pitfalls of a deterministic optimum in dealing with uncertain BCs, and how using Robust TO (RTO) can effectively reduce the variance and worst-case performance of the objective. Experimental validation for the flat plate wing is also undertaken to ensure practical feasibility of the RTO topologies and to provide motivation to study BCs uncertainty further.

In this second part of our two-part paper, we provide a detailed, frequentist framework for propagating uncertainties within our multivariate linear least squares model. This permits us to quantify the impact of uncertainties in thermodynamic measurements—arising from calibrations and the data acquisition system—and the correlations therein, along with uncertainties in probe positions. We show how the former has a much larger effect (relatively) than uncertainties in probe placement. We use this non-deterministic framework to demonstrate why the well-worn metric for assessing spatial sampling uncertainty falls short of providing an accurate characterization of the effect of a few spatial measurements. In other words, it does not accurately describe the uncertainty associated with sampling a non-uniform pattern with a few circumferentially scattered rakes. To this end, we argue that our data-centric framework can offer a more rigorous characterization of this uncertainty. Our paper proposes two new uncertainty metrics: one for characterizing spatial sampling uncertainty and another for capturing the impact of measurement imprecision in individual probes. These metrics are rigorously derived in our paper and their ease in computation permits them to be widely adopted by the turbomachinery community for carrying out uncertainty assessments.

Funder: Kuwait Institute for Scientific Research (KISR); doi: https://doi.org/10.13039/501100005074, Concerns about the effects of global warming provide a strong case to consider how best nuclear power could be applied to marine propulsion. Currently, there are persistent efforts worldwide to combat global warming, and that also includes the commercial freight shipping sector. In an effort to decarbonize the marine sector, there are growing interests in replacing the contemporary, traditional propulsion systems with nuclear propulsion systems. The latter system allows freight ships to have longer intervals before refueling; subsequently, lower fuel costs, and minimal carbon emissions. Nonetheless, nuclear propulsion systems have remained largely confined to military vessels. It is highly desirable that a civil marine core not use soluble boron for reactivity control, but it is then a challenge to achieve an adequate shutdown margin throughout the core life while maintaining reactivity control and acceptable power distributions in the core. High-thickness ZrB2 150 μm Integral Fuel Burnable Absorber (IFBA) is an excellent burnable poison (BP) candidate for long life soluble-boron-free core. However, in this study, we want to minimize the use of 150 μm IFBA since B-10 undergoes an (n, α) capture reaction, and the resulting helium raises the pressure within the plenum and in the cladding. Therefore, we have considered several alternative and novel burnable BP design strategies to minimize the use of IFBA for reactivity control in this study: (Case 1) a composite BP: gadolinia (Gd2O3) or erbia (Er2O3) with 150 μm thickness ZrB2 IFBA; (Case 2) Pu-240 or Am-241 mixed homogeneously with the fuel; and (Case 3) another composite BP: Pu-240 or Am-241 with 150 μm thickness ZrB2 IFBA. The results are compared against those for a high-thickness 150 μm 25 IFBA pins design from a previous study. The high-thickness 150 μm 25 IFBA pins design is termed the “IFBA-only” BP design throughout this study. We arrive at a design using 15% U-235 fuel loaded into 13 × 13 assemblies with Case 3 BPs (IFBA+Pu-240 or IFBA+Am-241) for reactivity control while reducing 20% IFBA use. This design exhibits lower assembly reactivity swing and minimal burnup penalty due to the self-shielding effect. Case 3 provides ~10% more initial (beginning-of-life) reactivity suppression with ~70% less reactivity swing compared to the IFBA-only design for UO2 fuel while achieving almost the same core lifetime. Finally, optimized Case 3 assemblies were loaded in 3D nodal diffusion and reactor model code. The results obtained from the 3D reactor model confirmed that the designed core with the proposed Case 3 BPs can achieve the target lifetime of 15 years while contributing to ~10% higher BOL reactivity suppression, ~70% lower reactivity swings, ~30% lower radial form factor and ~28% lower total peaking factor compared to the IFBA-only core.

Core average power density of standard small modular reactors (SMR) are generally limited to 60–65 MW/m3, which is 40% lower than for a standard civil PWR in order to accommodate better thermal margins. While designing a SMR core for civil marine propulsion systems, it is required to increase its power density to make more attractive for future deployment. However, there are obvious thermal-hydraulic (TH) concerns regarding a high power density (HPD) core, which needs to be satisfied in order to ensure safe operation through accurate prediction of the TH parameters. This paper presents a coupled neutronic/thermal-hydraulic (TH) hot channel analysis of a HPD 375 MWth soluble-boron-free PWR core using 19.25% 235U enriched micro–heterogeneous ThO2-UO2 duplex fuel and 16% 235U enriched homogeneously mixed all-UO2 fuel with a 15 effective full-power-years (EFPY) core life. To perform this analysis the hybrid Monte Carlo reactor physics code MONK is coupled with sub-channel analysis TH code COBRA-EN. This approach is used to investigate the feasibility of different HPD marine PWR concepts and to identify the main TH challenges characterising these designs. To design HPD cores of between 82 and 111 MW/m3, three cases were chosen by optimizing the fuel pin diameter, pin pitch and pitch-to-diameter ratio. These cases have been studied to determine whether TH safety limits are satisfied by evaluating key parameters, such as minimum departure from nucleate boiling ratio, surface heat flux, critical heat flux, cladding inner surface and fuel centreline temperatures, and pressure drop. The results show that it is possible to achieve a core power density of 100 MW/m3 for both the candidate fuels, a ∼50% improvement on the reference design (63 MW/m3), while meeting the target core lifetime of 15 EFPY and remaining within TH limits. The size of the pressure vessel can therefore be reduced substantially and the economic competitiveness of the proposed civil marine PWR reactor core significantly improved.

This paper presents an optimization of a thorium-plutonium (Th-Pu) fuel cycle by screening various design options for the Integral Inherently Safe Light Water Reactor (I2S-LWR). The I2S-LWR is an advanced 2850 MWt integral pressurized water reactor with enhanced safety beyond that of Gen-III+ reactors. The features of this reactor, such as material choice, make it attractive for alternative fuel cycles including the use of thorium. Recently, the feasibility of the Th-Pu cycle was studied and the benefits associated with it were demonstrated. More specifically, the Pu incineration performance was enhanced by adopting multi-batch (i.e. more than 3-batch) schemes and extended burnup (above 100 MWd/kg). The optimized design with the most favorable loading pattern was obtained by applying the Simulated Annealing optimization technique. This paper demonstrates further plausible modifications to the Th-Pu cycle design that may enhance its performance considerably. The paper seeks to identify the contributory factors, such as cladding types, plutonium vectors and initial plutonium loadings, with major impact on the incineration performance. The post-irradiation characteristics are also analyzed and suggest that such a cycle may simplify the design and operation of the waste repository.