Structural and Multidisciplinary Optimization, 2014
Analysis within the field of Multidisciplinary Design Optimization (MDO) generally falls under th... more Analysis within the field of Multidisciplinary Design Optimization (MDO) generally falls under the headings of architecture proofs and sensitivity information manipulation. We propose a differential geometry (DG) framework for further analyzing MDO systems, and here, we outline the theory undergirding that framework: general DG, Riemannian geometry for use in MDO, and the translation of MDO into the language of DG. Calculating the necessary quantities requires only basic sensitivity information (typically from the state equations) and the use of the implicit function theorem. The presence of extra or non-differentiable constraints may limit the use of the framework, however. Ultimately, the language and concepts of DG give us new tools for understanding, evaluating, and developing MDO methods; in Part I, we discuss the use of these tools and in Part II, we provide a specific application.
Neutron clustering is a recently identified problem with Monte Carlo eigenvalue calculations whic... more 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.
Since the use of deterministic transport code WIMS can significantly reduce the computational tim... more Since the use of deterministic transport code WIMS can significantly reduce the computational time compared to the Monte Carlo (MC) code Serpent and hybrid MC code MONK, one of the major objectives of this study is to observe whether deterministic code WIMS can provide accuracy in reactor physics calculations while comparing Serpent and MONK. Therefore, numerical benchmark calculations for a soluble-boron-free (SBF) small modular reactor (SMR) assembly have been performed using the WIMS, Serpent and MONK. Although computationally different in nature, these codes can solve the neutronic transport equations and calculate the required neutronic parameters. A comparison in neutronic parameters between the three codes has been carried out using two types of candidate fuels: 15% 235 U enriched homogeneously mixed all-UO 2 fuel and 18% 235 U enriched micro-heterogeneous ThO 2-UO 2 duplex fuel in a 2D fuel assembly model using a 13×13 arrangement. The eigenvalue/reactivity (k ∞) and 2D assembly pin power distribution at different burnup states in the assembly depletion are compared using three candidate nuclear data files: ENDF/B-VII, JEF2.2 and JEF3.1. A good agreement in k ∞ values was observed among the codes for both the candidate fuels. The differences in k ∞ between the codes are ∼200 pcm when cross-sections based on the same nuclear data file are used. A higher difference (up to ∼450 pcm) in the k ∞ values is observed among the codes using cross-sections based on different data files. Finally, it can be concluded from this study that the good agreement in the results between the codes found provides enhanced confidence that modeling of SBF, SMR propulsion core systems with micro-heterogeneous duplex fuel can be performed reliably using deterministic neutronics code WIMS, offering the advantage of less expensive computation than that of the MC Serpent and hybrid MC MONK codes.
UK plutonium (Pu) management is expected to focus on the use of uranium-plutonium (U-Pu) mixed ox... more UK plutonium (Pu) management is expected to focus on the use of uranium-plutonium (U-Pu) mixed oxide (MOX) fuel. However, research has shown that thorium-plutonium (Th-Pu) may be a viable alternative, offering favourable performance characteristics. A scoping study was carried out to determine the effect of isotopic composition and spectral hardening in standard and reduced moderation Pressurised Water Reactors (PWRs and RMPWRs). Lattice calculations were performed using WIMS to investigate safety parameters (Doppler Coefficient (DC), Moderator Temperature Coefficient (MTC), Void Coefficient (VC)-in this case Fully Voided Reactivity (FVR)-and Boron Worth (BW)), maximum theoretically achievable discharge burnup, Pu consumption and transuranic (TRU) composition of spent nuclear fuel (SNF) for the two reactor types. Standard grades of Pu were compared to a predicted UK Pu vector. MTC and FVR were found to be strongly influenced by the isotopic composition of the fuel. MTC was determined to be particularly sensitive to positive 'peak' contributions from fissile isotopes in the energy range 0.1-1 eV which diminish as the Pu content increases. The more extreme nature of the perturbation in FVR cases results in key differences in the contributions from fissile isotopes in the thermal energy range when compared with MTC, with no positive contributions from any isotope <500 eV. Where the requirement for MTC to remain negative was the limiting factor, a higher maximum fissile loading, discharge burnup and Pu consumption rate were possible in the PWR than the RMPWR, although the two reactors types typically produced similar levels of U233. However, for the majority of Pu grades the total minor actinide (MA) content in SNF was shown to be significantly lower in the RMPWR. Where FVR is the limiting factor, the maximum fissile loading and discharge burnup are similar in both reactor types, while increased Pu consumption rates were possible in the PWR. In this case, lower concentrations of U233 and MAs were found to be present in the PWR. These results are for a single pass of fuel through a reactor and, while the response of fissile isotopes at given energies to temperature perturbations will not vary significantly, the maximum achievable discharge burnup, Pu consumption rate and TRU build-up would be very different in a multi-recycle scenario.
In recent years, a number of authors have studied entropy generation in Wells turbines. This is p... more In recent years, a number of authors have studied entropy generation in Wells turbines. This is potentially a very interesting topic, as it can provide important insights into the irreversibilities of the system, as well as a methodology for identifying, and possibly minimizing, the main sources of loss. Unfortunately, the approach used in these studies contains some crude simplifications that lead to a severe underestimation of entropy generation and, more importantly, to misleading conclusions. This paper contains a re-examination of the mechanisms for entropy generation in fluid flow, with a particular emphasis on RANS equations. An appropriate methodology for estimating entropy generation in isolated airfoils and Wells turbines is presented. Results are verified for different flow conditions, and a comparison with theoretical values is presented.
A new, alternative approach is proposed for natural convection simulation by means of stimulated ... more A new, alternative approach is proposed for natural convection simulation by means of stimulated thermocapillary currents created by virtual walls. In contrast to the well-known effective thermal conductivity model, in the proposed approach it is the mass motion due to the convective currents which is intended to be simulated and the heat flux is a consequence of such flows. As a result, no a priori knowledge of the Nusselt number is needed and thus the approach is more suitable for complex geometries. Utilizing a simplified physical model and the definition of hydraulic diameter, a generalized expression for enclosed geometries is derived which offers thermal engineers a powerful analysis tool that can use virtual walls with an associated fictitious Marangoni stress for pre-screening and estimation of Nusselt numbers.
Recently, the study of micro fluidic devices has gained much interest in various fields from biol... more Recently, the study of micro fluidic devices has gained much interest in various fields from biology to engineering. In the constant development cycle, the need to optimise the topology of the interior of these devices, where there are two or more optimality criteria, is always present. In this work, twin physical situations, whereby optimal fluid mixing in the form of vorticity maximisation is accompanied by the requirement that the casing in which the mixing takes place has the best structural performance in terms of the greatest specific stiffness, are considered. In the steady state of mixing this also means that the stresses
This paper presents an analysis of a homogeneous thorium-plutonium fuel cycle developed for the I... more This paper presents an analysis of a homogeneous thorium-plutonium fuel cycle developed for the Integral Inherently Safe LWR (I 2 S-LWR). The I 2 S-LWR is an advanced 2850 MWt integral PWR with inherent safety features. Its baseline fuel and cladding materials are U 3 Si 2 and advanced FeCrAl steel, respectively. The advanced steel cladding can withstand longer exposure periods with significantly lower degradation rates compared to traditional Zr-based alloys. However, longer fuel cycles would require higher fuel enrichment, and this is currently limited to 5 w % in the I 2 S-LWR. Therefore, an alternative thorium-plutonium mixed oxide (TOX) fuel cycle is investigated. In principle, the TOX fuel cycle has no fissile content limitation and becomes even more attractive for long irradiation periods, due to the efficient build-up of 233 U, which increases its cumulative energy share and hence decreases the initial Pu requirements per unit of energy produced by the fuel. Current Pu recycling practice in the form of U-Pu mixed oxide (MOX) fuel is not well-suited for Pu disposition due to continuous Pu production from 238 U. This study compares the TOX and MOX cores in terms of efficiency of Pu disposition. The results show that the burnt Pu fraction in the TOX cycle is much higher, and could be further enhanced for longer irradiations (100 MWd/kg or more).
Structural and Multidisciplinary Optimization, 2017
To date the design of structures using topology optimization methods has mainly focused on single... more To date the design of structures using topology optimization methods has mainly focused on single-objective problems. Since real-world design problems typically involve several different objectives, most of which counteract each other, it is desirable to present the designer with a set of Pareto optimal solutions that capture the trade-off between these objectives, known as a smart Pareto set. Thus far only the weighted sums and global criterion methods have been incorporated into topology optimization problems. Such methods are unable to produce evenly distributed smart Pareto sets. However, recently the smart normal constraint method has been shown to be capable of directly generating smart Pareto sets. Therefore, in the present work, an updated smart Normal Constraint Method is combined with a Bi-directional Evolutionary Structural Optimization (SNC-BESO) algorithm to produce smart Pareto sets for multiobjective topology optimization problems. Two examples are presented, showing that the Pareto solutions found by the SNC-BESO method make up a smart Pareto set. The first example, taken from the literature, shows the benefits of the SNC-BESO method. The second example is an industrial design problem for a micro fluidic mixer. Thus, the problem is multi-physics as well as multiobjective, highlighting the applicability of such methods to real-world problems. The results indicate that the method is capable of producing smart Pareto sets to industrial problems in an effective and efficient manner.
Computer Methods in Applied Mechanics and Engineering, 2016
A monotonic, non-kernel density variant of the density-matching technique for optimization under ... more A monotonic, non-kernel density variant of the density-matching technique for optimization under uncertainty is developed. The approach is suited for turbomachinery problems which, by and large, tend to exhibit monotonic variations in the circumferentially and radially mass-averaged quantities-such as pressure ratio, efficiency and capacity-with common aleatory turbomachinery uncertainties. The method is successfully applied to de-sensitize the effect of an uncertainty in rear-seal leakage flows on the fan stage of a modern jet engine.
This study compares homogeneous and heterogeneous thorium-plutonium (Th-Pu) fuel assemblies (with... more This study compares homogeneous and heterogeneous thorium-plutonium (Th-Pu) fuel assemblies (with high Pu content-20 wt%), and examines whether there is an increase in Pu incineration in the latter. A seed-blanket configuration based on the Radkowsky thorium reactor concept is used for the heterogeneous assembly. This separates the thorium blanket from the uranium seed, or in this case a plutonium seed. The seed supplies neutrons to the subcritical thorium blanket which encourages the in-situ breeding and burning of 233 U, allowing the fuel to stay critical for longer, extending burnup of the fuel. While past work on Th-Pu seed-blanket units shows superior Pu incineration compared to conventional U-Pu mixed oxide fuel, there is no literature to date that directly compares the performance of homogeneous and heterogeneous Th-Pu assembly configurations. Use of exactly the same fuel loading for both configurations allows the effects of spatial separation to be fully understood. It was found that the homogeneous fuel with and without burnable poisons were able to achieve much higher Pu incinerations than the heterogeneous fuel configurations, while still attaining a reasonably high discharge burnup. This is because in the heterogeneous cases, 233 U breeding is faster, thereby contributing to a much larger fraction of total power produced by the assembly. In contrast, 233 U build-up is slower in the homogeneous case and therefore Pu burning is greater. This 233 U begins to contribute a significant fraction of power produced only towards the end of life, thus extending criticality, allowing more Pu to burn.
An approach to support the computational aerodynamic design process is presented and demonstrated... more An approach to support the computational aerodynamic design process is presented and demonstrated through the application of a novel multi-objective variant of the Tabu Search optimization algorithm for continuous problems to the aerodynamic design optimization of turbomachinery blades. The aim is to improve the performance of a specific stage and ultimately of the whole engine. The integrated system developed for this purpose is described. This combines the optimizer with an existing geometry parameterization scheme and a well-established CFD package. The system's performance is illustrated through case studiesone two-dimensional, one three-dimensional-in which flow characteristics important to the overall performance of turbomachinery blades are optimized. By showing the designer the trade-off surfaces between the competing objectives, this approach provides considerable insight into the design space under consideration and presents the designer with a range of different Pareto-optimal designs for further consideration. Special emphasis is given to the dimensionality in objective function space of the optimization problem, which seeks designs that perform well for a range of flow performance metrics. The resulting compressor blades achieve their high performance by exploiting complicated physical mechanisms successfully identified through the design process. The system can readily be run on parallel computers, substantially reducing wall-clock run times-a significant benefit when tackling computationally demanding design problems. Overall optimal performance is offered by compromise designs on the Pareto trade-off surface revealed through a true multi-objective design optimization test case. Bearing in mind the continuing rapid advances in computing
High-dimensional design optimisation continues to present many challenges for engineers. Traditio... more High-dimensional design optimisation continues to present many challenges for engineers. Traditional model-based optimisation strategies can be difficult to implement for high-dimensional problems, as surrogate models often require sample sizes which are exponential in the number in number of variables. In this paper, we present an algorithm which combines ideas from ridge function approximations and trust-region methods to perform optimisation on high-dimensional functions with underlying low-dimensional structure. This approach allows us to efficiently explore the design space by focusing on the few directions in which the objective varies the most. By slowly increasing the problem dimension, this algorithm also can further explore regions of interest in detail. This allows for more accurate solutions than previous approaches which have used ridge functions during optimisation. We test this algorithm against a number of common model-based optimisation methods, and it is shown to be effective for a class of high-dimensional problems. In particular, we apply the method to a NACA 0012 aerofoil to obtain an optimal design with respect to drag. During this study, we demonstrate how ridge functions can be vital tools for design space exploration, and, with our algorithm, how they can be used for optimisation refinement.
This paper discusses work done to find an estimate of the maximum achievable discharge burnup in ... more This paper discusses work done to find an estimate of the maximum achievable discharge burnup in an open cycle molten salt reactor (MSR). An in-development deterministic code (WIMS11) is used to create a model of a simple generic MSR, and the methodology employed is discussed. Some experimentation is done with regards to the internal set-up of the ‘unit cells’ within the core, which shows there is a strong link between this geometry and the achievable burnup. Work is done to quantify the effects of removing volatile fission products and implementing a two-batch refuelling scheme. Finally, an optimization process is carried out whereby the optimal proportion of graphite moderator within the core is found which balances power across the regions while maximising discharge burnup. Two fuels are tested, one which carries only 235U and 238U, and another which also carries 232Th. It is found that the maximum achievable discharge burnup is approximately 155 MWd/kg, which is considerably hig...
Design of a deep learning surrogate model for the prediction of FHR design parameters
All rights reserved. Following previous work by Xing and Shwageraus, a large corpus of data has b... more All rights reserved. Following previous work by Xing and Shwageraus, a large corpus of data has been collected for simulated AGR-style fuel assembly design in FHRs. The results exhibit a nonlinear system response, so a 'deep' multi-layer perceptron surrogate model is designed and tested for prediction of design parameters. This neuro-surrogate regression model could be useful for the fast optimization of the design parameters, for example in multiobjective optimization problems, due to the extremely fast evaluation time. Source code is made available for the audit and authentication of the scientific method.
Multi-objective optimization of nuclear engineering fuel assembly design problems is particularly... more Multi-objective optimization of nuclear engineering fuel assembly design problems is particularly difficult due to the highly non-linear interactions of a large number of possible variables. In addition, effective optimization algorithms are often highly problem-dependent and require extensive tuning, which reduces their applicability to the real world. To address this issue, Differential Evolution (DE) algorithms have been proposed as a new and effective method for heterogeneous fuel assembly optimization design problems. This paper presents the first complete study to investigate their applicability and performance. Firstly, two multi- objective DE algorithms have their performance compared against an Evolutionary Algorithm (EA) from the literature in optimizing a CORAIL mixed-oxide (MOX) fuel assembly for maximum plutonium content and minimum power peaking factor. Statistical analysis of the results shows the DE algorithms exhibit superior performance to the EA. The DE algorithms...
Reactor Physics Analysis of Thorium-Based Fuel for Long-Life SMR Cores Using Seed-Blanket Fuel Concept
This study examines the feasibility of thorium-based seedblanket (SB) fuel for small modular reac... more This study examines the feasibility of thorium-based seedblanket (SB) fuel for small modular reactor (SMR) core derived from a previous study [1]. The study aims to develop a reactor physics core design for SMR where net breeding of fuel can be achieved with higher end-of-life (EOL) fissile content than the initial loading. SB fuel assembly and core design studies were performed to design a core that can operate over a 20 effective full-power-years life at 333 MWth, utilizing the improved cumulative energy share of U-233. A heterogeneous fuel assembly with a uniform distribution of fissile nuclides was modified to create a heterogeneous two fuel zone configuration: the “seed" region containing 19% U-235 enriched UO2 and a fertile “blanket" region of 100% ThO2. The UO2 rich seed is the supplier of neutrons, and the ThO2 blanket generates new fuel (U-233) from Th-232 through neutron capture. We use WIMS to develop subassembly designs and PANTHER to examine whole-core arrange...
This paper discusses work done to benchmark the deterministic code WIMS [1] against the Monte Car... more This paper discusses work done to benchmark the deterministic code WIMS [1] against the Monte Carlo code Serpent [2] and experiment. Comparison is made against the Molten Salt Reactor Experiment at Oak Ridge National Laboratory as well as a Serpent model produced at the University of California, Berkeley. Producing a model for an MSR is possible thanks to the development of the next version of WIMS, WIMS11. The structure of the WIMS model built is discussed, and the final predicted criticality value for the MSR is given. This compares favourably with the Serpent model; however, both codes predict values considerably different to those expected. Potential reasons for this are suggested. However, it is concluded that WIMS has successfully been benchmarked against the current state of the art. This provides confirmation that this is a valid approach for molten salt reactor research analysis.
Pressurised Water Reactor (PWR) fuel management is an operational problem for nuclear operators, ... more Pressurised Water Reactor (PWR) fuel management is an operational problem for nuclear operators, requiring solutions on a regular basis throughout the life of the plant. A variety of conflicting factors and changing goals mean that fuel loading pattern design problems are multiobjective and, by design, have many input variables. This causes a combinatorial explosion, known as the ‘curse of dimensionality’, which makes these complex problems difficult to investigate. In this thesis, the method of surrogate model optimisation is adapted to PWR loading pattern generation. Surrogate models are developed based around three approaches: deep learning methods (convolutional neural networks and multi-layer perceptrons), the fission matrix and simulated quantum annealing. The models are used to predict core parameters of reactors in simplified optimisation scenarios for a microcore, a small modular reactor, and a ‘standard’ PWR. The experiments with deep learning models show that competitive ...
Structural and Multidisciplinary Optimization, 2014
Analysis within the field of Multidisciplinary Design Optimization (MDO) generally falls under th... more Analysis within the field of Multidisciplinary Design Optimization (MDO) generally falls under the headings of architecture proofs and sensitivity information manipulation. We propose a differential geometry (DG) framework for further analyzing MDO systems, and here, we outline the theory undergirding that framework: general DG, Riemannian geometry for use in MDO, and the translation of MDO into the language of DG. Calculating the necessary quantities requires only basic sensitivity information (typically from the state equations) and the use of the implicit function theorem. The presence of extra or non-differentiable constraints may limit the use of the framework, however. Ultimately, the language and concepts of DG give us new tools for understanding, evaluating, and developing MDO methods; in Part I, we discuss the use of these tools and in Part II, we provide a specific application.
Neutron clustering is a recently identified problem with Monte Carlo eigenvalue calculations whic... more 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.
Since the use of deterministic transport code WIMS can significantly reduce the computational tim... more Since the use of deterministic transport code WIMS can significantly reduce the computational time compared to the Monte Carlo (MC) code Serpent and hybrid MC code MONK, one of the major objectives of this study is to observe whether deterministic code WIMS can provide accuracy in reactor physics calculations while comparing Serpent and MONK. Therefore, numerical benchmark calculations for a soluble-boron-free (SBF) small modular reactor (SMR) assembly have been performed using the WIMS, Serpent and MONK. Although computationally different in nature, these codes can solve the neutronic transport equations and calculate the required neutronic parameters. A comparison in neutronic parameters between the three codes has been carried out using two types of candidate fuels: 15% 235 U enriched homogeneously mixed all-UO 2 fuel and 18% 235 U enriched micro-heterogeneous ThO 2-UO 2 duplex fuel in a 2D fuel assembly model using a 13×13 arrangement. The eigenvalue/reactivity (k ∞) and 2D assembly pin power distribution at different burnup states in the assembly depletion are compared using three candidate nuclear data files: ENDF/B-VII, JEF2.2 and JEF3.1. A good agreement in k ∞ values was observed among the codes for both the candidate fuels. The differences in k ∞ between the codes are ∼200 pcm when cross-sections based on the same nuclear data file are used. A higher difference (up to ∼450 pcm) in the k ∞ values is observed among the codes using cross-sections based on different data files. Finally, it can be concluded from this study that the good agreement in the results between the codes found provides enhanced confidence that modeling of SBF, SMR propulsion core systems with micro-heterogeneous duplex fuel can be performed reliably using deterministic neutronics code WIMS, offering the advantage of less expensive computation than that of the MC Serpent and hybrid MC MONK codes.
UK plutonium (Pu) management is expected to focus on the use of uranium-plutonium (U-Pu) mixed ox... more UK plutonium (Pu) management is expected to focus on the use of uranium-plutonium (U-Pu) mixed oxide (MOX) fuel. However, research has shown that thorium-plutonium (Th-Pu) may be a viable alternative, offering favourable performance characteristics. A scoping study was carried out to determine the effect of isotopic composition and spectral hardening in standard and reduced moderation Pressurised Water Reactors (PWRs and RMPWRs). Lattice calculations were performed using WIMS to investigate safety parameters (Doppler Coefficient (DC), Moderator Temperature Coefficient (MTC), Void Coefficient (VC)-in this case Fully Voided Reactivity (FVR)-and Boron Worth (BW)), maximum theoretically achievable discharge burnup, Pu consumption and transuranic (TRU) composition of spent nuclear fuel (SNF) for the two reactor types. Standard grades of Pu were compared to a predicted UK Pu vector. MTC and FVR were found to be strongly influenced by the isotopic composition of the fuel. MTC was determined to be particularly sensitive to positive 'peak' contributions from fissile isotopes in the energy range 0.1-1 eV which diminish as the Pu content increases. The more extreme nature of the perturbation in FVR cases results in key differences in the contributions from fissile isotopes in the thermal energy range when compared with MTC, with no positive contributions from any isotope <500 eV. Where the requirement for MTC to remain negative was the limiting factor, a higher maximum fissile loading, discharge burnup and Pu consumption rate were possible in the PWR than the RMPWR, although the two reactors types typically produced similar levels of U233. However, for the majority of Pu grades the total minor actinide (MA) content in SNF was shown to be significantly lower in the RMPWR. Where FVR is the limiting factor, the maximum fissile loading and discharge burnup are similar in both reactor types, while increased Pu consumption rates were possible in the PWR. In this case, lower concentrations of U233 and MAs were found to be present in the PWR. These results are for a single pass of fuel through a reactor and, while the response of fissile isotopes at given energies to temperature perturbations will not vary significantly, the maximum achievable discharge burnup, Pu consumption rate and TRU build-up would be very different in a multi-recycle scenario.
In recent years, a number of authors have studied entropy generation in Wells turbines. This is p... more In recent years, a number of authors have studied entropy generation in Wells turbines. This is potentially a very interesting topic, as it can provide important insights into the irreversibilities of the system, as well as a methodology for identifying, and possibly minimizing, the main sources of loss. Unfortunately, the approach used in these studies contains some crude simplifications that lead to a severe underestimation of entropy generation and, more importantly, to misleading conclusions. This paper contains a re-examination of the mechanisms for entropy generation in fluid flow, with a particular emphasis on RANS equations. An appropriate methodology for estimating entropy generation in isolated airfoils and Wells turbines is presented. Results are verified for different flow conditions, and a comparison with theoretical values is presented.
A new, alternative approach is proposed for natural convection simulation by means of stimulated ... more A new, alternative approach is proposed for natural convection simulation by means of stimulated thermocapillary currents created by virtual walls. In contrast to the well-known effective thermal conductivity model, in the proposed approach it is the mass motion due to the convective currents which is intended to be simulated and the heat flux is a consequence of such flows. As a result, no a priori knowledge of the Nusselt number is needed and thus the approach is more suitable for complex geometries. Utilizing a simplified physical model and the definition of hydraulic diameter, a generalized expression for enclosed geometries is derived which offers thermal engineers a powerful analysis tool that can use virtual walls with an associated fictitious Marangoni stress for pre-screening and estimation of Nusselt numbers.
Recently, the study of micro fluidic devices has gained much interest in various fields from biol... more Recently, the study of micro fluidic devices has gained much interest in various fields from biology to engineering. In the constant development cycle, the need to optimise the topology of the interior of these devices, where there are two or more optimality criteria, is always present. In this work, twin physical situations, whereby optimal fluid mixing in the form of vorticity maximisation is accompanied by the requirement that the casing in which the mixing takes place has the best structural performance in terms of the greatest specific stiffness, are considered. In the steady state of mixing this also means that the stresses
This paper presents an analysis of a homogeneous thorium-plutonium fuel cycle developed for the I... more This paper presents an analysis of a homogeneous thorium-plutonium fuel cycle developed for the Integral Inherently Safe LWR (I 2 S-LWR). The I 2 S-LWR is an advanced 2850 MWt integral PWR with inherent safety features. Its baseline fuel and cladding materials are U 3 Si 2 and advanced FeCrAl steel, respectively. The advanced steel cladding can withstand longer exposure periods with significantly lower degradation rates compared to traditional Zr-based alloys. However, longer fuel cycles would require higher fuel enrichment, and this is currently limited to 5 w % in the I 2 S-LWR. Therefore, an alternative thorium-plutonium mixed oxide (TOX) fuel cycle is investigated. In principle, the TOX fuel cycle has no fissile content limitation and becomes even more attractive for long irradiation periods, due to the efficient build-up of 233 U, which increases its cumulative energy share and hence decreases the initial Pu requirements per unit of energy produced by the fuel. Current Pu recycling practice in the form of U-Pu mixed oxide (MOX) fuel is not well-suited for Pu disposition due to continuous Pu production from 238 U. This study compares the TOX and MOX cores in terms of efficiency of Pu disposition. The results show that the burnt Pu fraction in the TOX cycle is much higher, and could be further enhanced for longer irradiations (100 MWd/kg or more).
Structural and Multidisciplinary Optimization, 2017
To date the design of structures using topology optimization methods has mainly focused on single... more To date the design of structures using topology optimization methods has mainly focused on single-objective problems. Since real-world design problems typically involve several different objectives, most of which counteract each other, it is desirable to present the designer with a set of Pareto optimal solutions that capture the trade-off between these objectives, known as a smart Pareto set. Thus far only the weighted sums and global criterion methods have been incorporated into topology optimization problems. Such methods are unable to produce evenly distributed smart Pareto sets. However, recently the smart normal constraint method has been shown to be capable of directly generating smart Pareto sets. Therefore, in the present work, an updated smart Normal Constraint Method is combined with a Bi-directional Evolutionary Structural Optimization (SNC-BESO) algorithm to produce smart Pareto sets for multiobjective topology optimization problems. Two examples are presented, showing that the Pareto solutions found by the SNC-BESO method make up a smart Pareto set. The first example, taken from the literature, shows the benefits of the SNC-BESO method. The second example is an industrial design problem for a micro fluidic mixer. Thus, the problem is multi-physics as well as multiobjective, highlighting the applicability of such methods to real-world problems. The results indicate that the method is capable of producing smart Pareto sets to industrial problems in an effective and efficient manner.
Computer Methods in Applied Mechanics and Engineering, 2016
A monotonic, non-kernel density variant of the density-matching technique for optimization under ... more A monotonic, non-kernel density variant of the density-matching technique for optimization under uncertainty is developed. The approach is suited for turbomachinery problems which, by and large, tend to exhibit monotonic variations in the circumferentially and radially mass-averaged quantities-such as pressure ratio, efficiency and capacity-with common aleatory turbomachinery uncertainties. The method is successfully applied to de-sensitize the effect of an uncertainty in rear-seal leakage flows on the fan stage of a modern jet engine.
This study compares homogeneous and heterogeneous thorium-plutonium (Th-Pu) fuel assemblies (with... more This study compares homogeneous and heterogeneous thorium-plutonium (Th-Pu) fuel assemblies (with high Pu content-20 wt%), and examines whether there is an increase in Pu incineration in the latter. A seed-blanket configuration based on the Radkowsky thorium reactor concept is used for the heterogeneous assembly. This separates the thorium blanket from the uranium seed, or in this case a plutonium seed. The seed supplies neutrons to the subcritical thorium blanket which encourages the in-situ breeding and burning of 233 U, allowing the fuel to stay critical for longer, extending burnup of the fuel. While past work on Th-Pu seed-blanket units shows superior Pu incineration compared to conventional U-Pu mixed oxide fuel, there is no literature to date that directly compares the performance of homogeneous and heterogeneous Th-Pu assembly configurations. Use of exactly the same fuel loading for both configurations allows the effects of spatial separation to be fully understood. It was found that the homogeneous fuel with and without burnable poisons were able to achieve much higher Pu incinerations than the heterogeneous fuel configurations, while still attaining a reasonably high discharge burnup. This is because in the heterogeneous cases, 233 U breeding is faster, thereby contributing to a much larger fraction of total power produced by the assembly. In contrast, 233 U build-up is slower in the homogeneous case and therefore Pu burning is greater. This 233 U begins to contribute a significant fraction of power produced only towards the end of life, thus extending criticality, allowing more Pu to burn.
An approach to support the computational aerodynamic design process is presented and demonstrated... more An approach to support the computational aerodynamic design process is presented and demonstrated through the application of a novel multi-objective variant of the Tabu Search optimization algorithm for continuous problems to the aerodynamic design optimization of turbomachinery blades. The aim is to improve the performance of a specific stage and ultimately of the whole engine. The integrated system developed for this purpose is described. This combines the optimizer with an existing geometry parameterization scheme and a well-established CFD package. The system's performance is illustrated through case studiesone two-dimensional, one three-dimensional-in which flow characteristics important to the overall performance of turbomachinery blades are optimized. By showing the designer the trade-off surfaces between the competing objectives, this approach provides considerable insight into the design space under consideration and presents the designer with a range of different Pareto-optimal designs for further consideration. Special emphasis is given to the dimensionality in objective function space of the optimization problem, which seeks designs that perform well for a range of flow performance metrics. The resulting compressor blades achieve their high performance by exploiting complicated physical mechanisms successfully identified through the design process. The system can readily be run on parallel computers, substantially reducing wall-clock run times-a significant benefit when tackling computationally demanding design problems. Overall optimal performance is offered by compromise designs on the Pareto trade-off surface revealed through a true multi-objective design optimization test case. Bearing in mind the continuing rapid advances in computing
High-dimensional design optimisation continues to present many challenges for engineers. Traditio... more High-dimensional design optimisation continues to present many challenges for engineers. Traditional model-based optimisation strategies can be difficult to implement for high-dimensional problems, as surrogate models often require sample sizes which are exponential in the number in number of variables. In this paper, we present an algorithm which combines ideas from ridge function approximations and trust-region methods to perform optimisation on high-dimensional functions with underlying low-dimensional structure. This approach allows us to efficiently explore the design space by focusing on the few directions in which the objective varies the most. By slowly increasing the problem dimension, this algorithm also can further explore regions of interest in detail. This allows for more accurate solutions than previous approaches which have used ridge functions during optimisation. We test this algorithm against a number of common model-based optimisation methods, and it is shown to be effective for a class of high-dimensional problems. In particular, we apply the method to a NACA 0012 aerofoil to obtain an optimal design with respect to drag. During this study, we demonstrate how ridge functions can be vital tools for design space exploration, and, with our algorithm, how they can be used for optimisation refinement.
This paper discusses work done to find an estimate of the maximum achievable discharge burnup in ... more This paper discusses work done to find an estimate of the maximum achievable discharge burnup in an open cycle molten salt reactor (MSR). An in-development deterministic code (WIMS11) is used to create a model of a simple generic MSR, and the methodology employed is discussed. Some experimentation is done with regards to the internal set-up of the ‘unit cells’ within the core, which shows there is a strong link between this geometry and the achievable burnup. Work is done to quantify the effects of removing volatile fission products and implementing a two-batch refuelling scheme. Finally, an optimization process is carried out whereby the optimal proportion of graphite moderator within the core is found which balances power across the regions while maximising discharge burnup. Two fuels are tested, one which carries only 235U and 238U, and another which also carries 232Th. It is found that the maximum achievable discharge burnup is approximately 155 MWd/kg, which is considerably hig...
Design of a deep learning surrogate model for the prediction of FHR design parameters
All rights reserved. Following previous work by Xing and Shwageraus, a large corpus of data has b... more All rights reserved. Following previous work by Xing and Shwageraus, a large corpus of data has been collected for simulated AGR-style fuel assembly design in FHRs. The results exhibit a nonlinear system response, so a 'deep' multi-layer perceptron surrogate model is designed and tested for prediction of design parameters. This neuro-surrogate regression model could be useful for the fast optimization of the design parameters, for example in multiobjective optimization problems, due to the extremely fast evaluation time. Source code is made available for the audit and authentication of the scientific method.
Multi-objective optimization of nuclear engineering fuel assembly design problems is particularly... more Multi-objective optimization of nuclear engineering fuel assembly design problems is particularly difficult due to the highly non-linear interactions of a large number of possible variables. In addition, effective optimization algorithms are often highly problem-dependent and require extensive tuning, which reduces their applicability to the real world. To address this issue, Differential Evolution (DE) algorithms have been proposed as a new and effective method for heterogeneous fuel assembly optimization design problems. This paper presents the first complete study to investigate their applicability and performance. Firstly, two multi- objective DE algorithms have their performance compared against an Evolutionary Algorithm (EA) from the literature in optimizing a CORAIL mixed-oxide (MOX) fuel assembly for maximum plutonium content and minimum power peaking factor. Statistical analysis of the results shows the DE algorithms exhibit superior performance to the EA. The DE algorithms...
Reactor Physics Analysis of Thorium-Based Fuel for Long-Life SMR Cores Using Seed-Blanket Fuel Concept
This study examines the feasibility of thorium-based seedblanket (SB) fuel for small modular reac... more This study examines the feasibility of thorium-based seedblanket (SB) fuel for small modular reactor (SMR) core derived from a previous study [1]. The study aims to develop a reactor physics core design for SMR where net breeding of fuel can be achieved with higher end-of-life (EOL) fissile content than the initial loading. SB fuel assembly and core design studies were performed to design a core that can operate over a 20 effective full-power-years life at 333 MWth, utilizing the improved cumulative energy share of U-233. A heterogeneous fuel assembly with a uniform distribution of fissile nuclides was modified to create a heterogeneous two fuel zone configuration: the “seed" region containing 19% U-235 enriched UO2 and a fertile “blanket" region of 100% ThO2. The UO2 rich seed is the supplier of neutrons, and the ThO2 blanket generates new fuel (U-233) from Th-232 through neutron capture. We use WIMS to develop subassembly designs and PANTHER to examine whole-core arrange...
This paper discusses work done to benchmark the deterministic code WIMS [1] against the Monte Car... more This paper discusses work done to benchmark the deterministic code WIMS [1] against the Monte Carlo code Serpent [2] and experiment. Comparison is made against the Molten Salt Reactor Experiment at Oak Ridge National Laboratory as well as a Serpent model produced at the University of California, Berkeley. Producing a model for an MSR is possible thanks to the development of the next version of WIMS, WIMS11. The structure of the WIMS model built is discussed, and the final predicted criticality value for the MSR is given. This compares favourably with the Serpent model; however, both codes predict values considerably different to those expected. Potential reasons for this are suggested. However, it is concluded that WIMS has successfully been benchmarked against the current state of the art. This provides confirmation that this is a valid approach for molten salt reactor research analysis.
Pressurised Water Reactor (PWR) fuel management is an operational problem for nuclear operators, ... more Pressurised Water Reactor (PWR) fuel management is an operational problem for nuclear operators, requiring solutions on a regular basis throughout the life of the plant. A variety of conflicting factors and changing goals mean that fuel loading pattern design problems are multiobjective and, by design, have many input variables. This causes a combinatorial explosion, known as the ‘curse of dimensionality’, which makes these complex problems difficult to investigate. In this thesis, the method of surrogate model optimisation is adapted to PWR loading pattern generation. Surrogate models are developed based around three approaches: deep learning methods (convolutional neural networks and multi-layer perceptrons), the fission matrix and simulated quantum annealing. The models are used to predict core parameters of reactors in simplified optimisation scenarios for a microcore, a small modular reactor, and a ‘standard’ PWR. The experiments with deep learning models show that competitive ...
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Papers by Geoff Parks