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Proceedings Papers

*Proc. ASME*. ICONE26, Volume 3: Nuclear Fuel and Material, Reactor Physics, and Transport Theory, V003T02A014, July 22–26, 2018

Paper No: ICONE26-81316

Abstract

The efficient solution of the neutron diffusion equation for large scale whole core calculations is of paramount importance; especially if the detailed pin-level power distribution and reaction rates are required. For heterogeneous whole core calculations finite element based techniques have been one approach to modelling the detailed pin geometry in whole core calculations. A new approach, pioneered in the last few years, is isogeometric analysis (IGA) methods which enable the exact geometry of fuel pins to be modelled. In order to efficiently solve elliptic partial differential equations (PDEs), such as the neutron diffusion equation, typically multi-grid or multi-level iterative solution techniques are used such as the algebraic multi-grid method. However, using IGA methods it is possible to develop true geometric multi-grid techniques which are potentially much more efficient than the standard algebraic multi-grid methods. In this paper we explore the use of IGA methods to develop a scalable, multi-level, iterative algorithm which is then used to solve the neutron diffusion equation over several geometries. This multilevel solution algorithm utilises a single patch multi-grid framework suggested by Hofreither and Takacs that takes advantage of the tensor product construction to provide scalability with respect to spatial, and polynomial refinement. Furthermore, a two-level balancing Neumann-Neumann solver is used to extend the solver to multiple patches in a scalable way. It is seen that the number of iterations required depends on the mapping between the unit square and the physical geometry, as well as the material coefficients.

Proceedings Papers

*Proc. ASME*. ICONE25, Volume 3: Nuclear Fuel and Material, Reactor Physics and Transport Theory; Innovative Nuclear Power Plant Design and New Technology Application, V003T02A061, July 2–6, 2017

Paper No: ICONE25-67597

Abstract

Solving the SP3 equation is the key technology of the Next Generation Reactor Physics Calculation, and has been widely concerned. The semi-analytical nodal method (SANM) based on transverse-integrated neutron diffusion equation has the advantages of high accuracy and convenience for multi-group calculation. The 0 th -order flux and the 2 nd -order flux being Expanded with the existing 4 th -order SANM polynomials and being solved respectively, the 4 th -order algebraic accuracy flux distribution is also obtained, however, this solving process is not the semi-analytical nodal method since the polynomial expansion process does not take the special modality of SP3 equation and it’s analytical solution into consideration. There are two modality SP3 equation, so there are two SANM expansion forms. A code is developed to solve the SP3 equation under the two different forms. After the calculation of the same benchmark, the difference between the two forms of SP3 equation is found. According to the results, and in view of the special modality of the SP3 equation, advices for a strict semi-analytical method for solving SP3 equation are discussed.

Proceedings Papers

*Proc. ASME*. ICONE25, Volume 8: Computational Fluid Dynamics (CFD) and Coupled Codes; Nuclear Education, Public Acceptance and Related Issues, V008T09A014, July 2–6, 2017

Paper No: ICONE25-66497

Abstract

During hypothetical severe accidents in nuclear power plants, a large amount of hydrogen is generated rapidly as a result of Zirconium-Steam reaction and released into the containment. Hydrogen mixes with air and may come into combustion or detonation under proper conditions, which threatens the integrity of containment. Therefore, getting detailed hydrogen flow and distribution in various physical mechanisms is a key issue to resolve the hydrogen risk in containment and compartments. To study local hydrogen distribution in the containment of advanced passive PWR, an analysis model is built by 3-dimensional CFD code. Computational domain is divided by structured grid which contains over 100,000 cells. the shape and surface area of walls and obstacles of steel shell and internal structure, which have great impact on gas flow and heat transfer, are included. Hydrogen distribution in containment simulating with different turbulence models is studied, the result shows that during large amount of hydrogen release stage. In hydrogen distribution result simulating with algebraic model, hydrogen is all gathered in the dome and the peak concentration reaches 17%. When k-ε model is adopted, the peak concentration in the dome is 8%, hydrogen stratification is established in whole large space. Besides, hydrogen distribution near source also shows algebraic model cannot simulate turbulence diffusion in local compartment. It is more reasonable choosing k-ε model to study hydrogen behavior in containment. Based on adopted k-ε model, the effect of steam on hydrogen distribution is investigated. With steam injection, the hydrogen distribution is more homogeneous in upper space and average concentration is lower. In local compartment, due to diffusion enhanced by steam, the hydrogen concentration is higher in the bottom.

Proceedings Papers

*Proc. ASME*. ICONE25, Volume 8: Computational Fluid Dynamics (CFD) and Coupled Codes; Nuclear Education, Public Acceptance and Related Issues, V008T09A004, July 2–6, 2017

Paper No: ICONE25-66167

Abstract

The current paper comprises CFD-modelling and simulation of condensation and heat transfer inside horizontal pipes. Designs of future nuclear boiling water reactor concepts are equipped with emergency cooling systems which are passive systems for heat removal. The emergency cooling system consists of slightly inclined horizontal pipes which are immersed in a tank of subcooled water. At normal operation conditions, the pipes are filled with water and no heat transfer to the secondary side of the condenser occurs. In the case of an accident the water level in the core is decreasing, steam comes in the emergency pipes and due to the subcooled water around the pipe, this steam will condense. The emergency condenser acts as a strong heat sink which is responsible for a quick depressurization of the reactor core when any accident happens. The actual project is defined in order to model all these processes which happen in the emergency cooling systems. The most focus of the project is on detection of different morphologies such as annular flow, stratified flow, slug flow and plug flow. The first step is the investigation of condensation inside a horizontal tube by considering the direct contact condensation (DCC). Therefore, at the inlet of the pipe an annular flow is assumed. In this step, the Algebraic Interfacial Area Density (AIAD) model is used in order to simulate the interface. The second step is the extension of the model to consider wall condensation effect as well which is closer to the reality. In this step, the inlet is pure steam and due to the wall condensation, a liquid film occurs near the wall which leads to annular flow. The last step will be modelling of different morphologies which are occurring inside the tube during the condensation via using the Generalized Two-Phase Flow (GENTOP) model extended by heat and mass transfer. By using GENTOP the dispersed phase is able to be considered and simulated. Finally, the results of the simulations will be validated by experimental data which will be available in HZDR. In this paper the results of the first part has been presented.

Proceedings Papers

*Proc. ASME*. ICONE25, Volume 1: Operations and Maintenance, Engineering, Modifications, Life Extension, Life Cycle and Balance of Plant; I&C, Digital Controls, and Influence of Human Factors, V001T04A013, July 2–6, 2017

Paper No: ICONE25-66483

Abstract

The probability that the safety I&C system fails to actuate or advertently actuates RT or ESF functions, in part, essentially determines whether a nuclear power plant could operate safely and efficiently. Since more conservative assumptions and simplifications are introduced during the analysis, this paper achieves solid results by performing the modeling and calculation based on a relatively simple approach, the reliability block diagram (RBD) method. A typical safety I&C platform structure is involved in the model presented in this paper. From the perspective of conservation and simplicity, some assumptions are adopted in this paper. A group of formulas is derived in this paper based on Boolean algebra, probability theory, basic reliability concepts and equations, to facilitate the calculations of probabilities that the safety I&C system fails to actuate or advertently actuates RT or ESF functions. All the inputs of the analysis and calculation in this paper, which includes the I&C platform structure, the constitution of the hardware modules, and reliability data, are referenced to the nuclear power plant universal database where applicable. Although the conclusion drawn in the paper doesn’t apply to the I&C platform assessment for a specific plant, the method of modeling and process of analysis provides an illustration of an alternative quantitative reliability assessment approach for a typical safety I&C system installed in the nuclear power plant.

Proceedings Papers

*Proc. ASME*. NUCLRF2017, ASME 2017 Nuclear Forum, V009T03A004, June 26–30, 2017

Paper No: NUCLRF2017-3515

Abstract

Modeling of two phase flows in nuclear power plants is very important for design, licensing, and operator training and therefore must be performed accurately. As requirements have increased, the form and accuracy of the models and computer codes have improved along with them. Early formulations for the field equations include: single phase liquid with algebraic drift flux for the gas phase, modeled with mass, momentum and energy governing equations; and two separate fields, liquid phase and gas phase, typically modeled with six governing equations. These lump bubbles and droplets into the gas and liquid phases respectively and use flow regime maps based upon available experimental data. However, the experiments do not cover the entire spectrum of reactor conditions, so that transitions and extrapolations, which are inherently inaccurate, must be employed. Further, some reactor scenarios, such as boiling and condensation, can be more accurately resolved by modeling bubbles or droplets separately from the continuous fields. Introduction of an additional field, droplet or bubble, apart from the continuous liquid and gas fields, generally uses nine governing equations. Despite the successful development of the above-mentioned methods for modeling reactor coolant flow in modern software, such as RELAP, TRAC, TRACE, CATHARE and many others, there remain reactor scenarios that require greater resolution to model. This is particularly true of conditions during reflood, where emergency spray flows dominate the cooling profile within the core. Existing system codes use a lumped approach for two phase flows that groups the fields by their phase, thereby losing track of the physical interactions between the discrete fluid fields. The accuracy of these accident analysis system codes can be improved by characterizing the interactions between additional coolant fields. To capture the effect of the various field interactions, governing equations involving six-fields have been developed. The six fields are 1) continuous liquid, 2) continuous vapor, 3) large droplets, 4) small droplets, 5) large bubbles and 6) small bubbles. The additional fields and the related governing equations introduce additional variables and source terms that require new closure relationships and primary variables. This article presents the equations and variables and develops the discrete set of 18 equations that must be solved to model the system.

Proceedings Papers

*Proc. ASME*. ICONE24, Volume 5: Student Paper Competition, V005T15A009, June 26–30, 2016

Paper No: ICONE24-60152

Abstract

HTR-10GT is a closed Brayton cycle with two-stage compression and heat recuperation. Bypass control was adopted for rapid power regulation and safety protection. A bypass valve could be set between any two positions at different pressure levels, there would be in total 21 setting possibilities, whose regulating behaviors remained to be fully clarified. The dynamic characteristics of these settings were thus analyzed by implementing numerical simulation on the integrated system model. The reactor was modeled with point-kinetics and 1D thermal-hydraulics model; compressor performance calculation was based on digitization of the performance map and Reynolds number correlation; Flügel formula was chosen to calculate turbine performance. The system was modeled with Modelica, and the DASSL code was used to solve the Differential and Algebraic Equations. The results showed that only 6 choices among the 21 remained acceptable for engineering practice. The degree and rate on power output reduction, anti-surge effect and long-term thermal effects at reactor inlet and along recuperator’s metal wall were evaluated and compared among these choices to give out proposals. This research clarified the characteristics of bypass valves at different positions to give a reference on the final design of the control methods, and proposed a combination of valves for multi-valve cooperative regulation.

Proceedings Papers

*Proc. ASME*. ICONE24, Volume 4: Computational Fluid Dynamics (CFD) and Coupled Codes; Decontamination and Decommissioning, Radiation Protection, Shielding, and Waste Management; Workforce Development, Nuclear Education and Public Acceptance; Mitigation Strategies for Beyond Design Basis Events; Risk Management, V004T10A012, June 26–30, 2016

Paper No: ICONE24-60298

Abstract

This work proposes simulations of heat transfer under supercritical pressure conditions showing improvements with respect to previous works. This is obtained by the introduction of the Algebraic Heat Flux Model (AHFM) for evaluating the turbulent heat flux in turbulence production terms, using the in-house code THEMAT and the STAR-CCM+ code. The first code makes use of the AHFM also in the energy balance equations, while for the commercial code simplifying assumptions are considered in the implementations. Custom sets of parameters for every condition of inlet temperature and internal diameter are tuned in some cases, driven by the opinion that a single set of parameters cannot be suitable in every flow conditions, considering the complexity of the variables that concur in the heat transfer deterioration phenomenon. The AHFM model gives promising results with new sets of parameters in order to model the deterioration and the recovery phases because of its term related to the variance of temperature.

Proceedings Papers

*Proc. ASME*. ICONE21, Volume 5: Fuel Cycle, Radioactive Waste Management and Decommissioning; Reactor Physics and Transport Theory; Nuclear Education, Public Acceptance and Related Issues; Instrumentation and Controls; Fusion Engineering, V005T11A004, July 29–August 2, 2013

Paper No: ICONE21-15278

Abstract

The Matrix Method of Characteristics (MOC) is an alternative to traditional MOC, in which repeatedly characteristics sweeping is needed. In the Matrix MOC, a linear algebraic equation system, which is represented by coefficient-matrix, can be formed by sweeping only once, and then solving the linear system takes the place of repeatedly characteristics sweeping. There are many linear solvers to be use, like direct LU decomposition and widely used Krylov subspace iterative methods. In the past, 2D Matrix MOC was implemented based on the long characteristics in which tremendous memory is consumed to hold the geometrical information. Then, 2D Matrix MOC based on modular ray tracing was implemented to overcome the difficulty. Modular ray tracing just holds the geometrical information of typical modules like cells or assemblies, consequently needs less memory. In this study, Filippone-type modular ray tracing in which different azimuths own the same number of characteristics lines was used, and AutoCAD VBA programing produced the geometrical information. Also, the Matrix MOC based on modular ray tracing was implemented to solve half, fourth and eighth reactor core in which additional modules, e.g. half-module, fourth-module and eighth-module were involved and need special considerations. Numerical results demonstrate that Matrix MOC based on modular ray tracing can obtain good efficiency and accuracy.

Proceedings Papers

*Proc. ASME*. ICONE21, Volume 5: Fuel Cycle, Radioactive Waste Management and Decommissioning; Reactor Physics and Transport Theory; Nuclear Education, Public Acceptance and Related Issues; Instrumentation and Controls; Fusion Engineering, V005T14A015, July 29–August 2, 2013

Paper No: ICONE21-16157

Abstract

In this paper, we study several unsmoothed aggregation based algebraic multigrid (UA-AMG) methods with regard to different characteristics of CPUs and graphics processing units (GPUs). We propose some UA-AMG methods with lower computational complexity for CPU and CPU-GPU, and study these UA-AMG methods mixing with 4 kinds of red-black colored Gauss-Seidel smoothers for CPU-GPU since the initial mesh is structured. These UA-AMG methods are used as preconditioners for the conjugate gradient (CG) solver to solve a class of two-dimensional single-temperature radiation diffusion equations discretized by preserving symmetry finite volume element scheme. Numerical results demonstrate that, UA-NA-CG-s, which wins the best robustness and efficiency among them, is much more efficient than the default AMG preconditioned CG solvers in HYPRE, AGMG and Cusp for CPU; Under CPU-GPU, UA-W-CG-p is the most robust and efficient one, and rather more efficient than the smoothed aggregation based AMG preconditioned CG solver in Cusp.

Proceedings Papers

*Proc. ASME*. ICONE20-POWER2012, Volume 3: Thermal-Hydraulics; Turbines, Generators, and Auxiliaries, 741-750, July 30–August 3, 2012

Paper No: ICONE20-POWER2012-55159

Abstract

An analytical method was proposed for the prediction of the turbulent friction factor in a circular pipe under supercritical conditions. The friction factor equation was based on the new wall function by Van Direst transformation which is widely used in compressed flow. The law of the wall of two layers was used and integrated over the entire flow area to obtain the algebraic form of the turbulent friction factor. The new turbulent friction formula was first adjusted to Colebrook equation in isothermal flow at supercritical pressures. And then it was validated in heated supercritical flow by several existing correlations. Similar trends were found between them, which confirms the physical validity of the new frictional formula. The theoretical analysis also shows that the friction factor due to the variation of fluid property at supercritical pressures is mainly caused by the density and viscosity variation. In viscous sublayer, both the viscosity play the main role, while in turbulent sublayer, only the density do.

Proceedings Papers

*Proc. ASME*. ICONE20-POWER2012, Volume 5: Fusion Engineering; Student Paper Competition; Design Basis and Beyond Design Basis Events; Simple and Combined Cycles, 507-516, July 30–August 3, 2012

Paper No: ICONE20-POWER2012-54997

Abstract

The determination of the debris transport fraction during a LOCA of a PWR is very important in the sizing of the sump screen area. In this study, the debris transport fraction during the recirculation cooling phase is evaluated with and without consideration of turbulence effect. To do this, first experiments involving tumbling velocities measurements and supplementary CFD analyses are performed to verify the turbulence effect on debris transport. From these findings, the turbulence effect on the degree of debris tumbling augmentation was found to be represented by the algebraic sum of the mean velocity and the fluctuating velocity. Then, a CFD analysis of the flooding containment floor during the recirculation cooling phase of the OPR1000 plant is performed. Based on these studies, the debris transport fraction is evaluated for NUKON. The result shows a considerable increase in the debris transport fraction when a turbulence effect is implemented compared to when it is not. Increases of 5.55 and 2.06 times are observed for large NUKON and small/fine NUKON, respectively. This result implies that the turbulence effect should be considered in the debris transport quantification for conservatism.

Proceedings Papers

*Proc. ASME*. ICONE18, 18th International Conference on Nuclear Engineering: Volume 2, 79-87, May 17–21, 2010

Paper No: ICONE18-29420

Abstract

The Generalized Minimal RESidual (GMRES) method, which is a widely-used version of Krylov subspace methods for solving large sparse non-symmetric linear systems, is adopted to accelerate the 2D arbitrary geometry characteristics solver AutoMOC. In this technique, a formulism of linear algebraic equation system for angular flux moments and boundary fluxes is derived as an alternative to traditional characteristics sweep (i.e. inner iteration) formalism, and then the GMRES method is implemented as an efficient linear system solver. Several numerical results demonstrate that the acceleration technique based on Krylov subspace methods can be applied to arbitrary geometry MOC solver successfully, and may obtain higher efficiency than the original characteristics solver does because of its spectacular effect on reducing both the number of outer iterations and the total computing time. Moreover, the results could be improved by Lyusternik-Wagner extrapolation technique in some cases.

Proceedings Papers

*Proc. ASME*. ICONE17, Volume 5: Fuel Cycle and High and Low Level Waste Management and Decommissioning; Computational Fluid Dynamics (CFD), Neutronics Methods and Coupled Codes; Instrumentation and Control, 593-598, July 12–16, 2009

Paper No: ICONE17-75731

Abstract

In this work it is applied the wavelet transform method [2] in order to reduce diverse type of noises of experimental measurement plots in transport theory. First, suppose that a problem is governed by the transport equation for neutral particles, and an unknown perturbation occurs. In this case, the perturbation can be associated to the source, or even to the flux inside the domain X . How is the behavior of the perturbed flux in relation to the flux without the perturbation? For that, we employ the wavelet transform method in order to compress the angular flux considered as a 1D, or n -th dimensional signal ψ . The compression of this signal can be performed up to some a convenient order (that depends of the length of the signal). Now, the transport signal is decomposed as [9, 11]: ψ = 〈 a m | d m | d m − 1 | d m − 2 | ⋯ | d 2 | d 1 〉 where a k represents the sub signal of k -th level generated by the low-pass filter associated to the discrete wavelet transform (DWT) chosen, and d k the sub signal of k -th level generated by the high-pass filter associated to the same DWT. It is applied basically the Haar, Daub4 and Coiflet wavelets transforms. Indeed, the sub signal am cumulates the energy, for this work of order 96% of the original signal ψ . A thresholding algorithm provides treatment for the noise, with significant reduction in the compressed signal. Then, it is established a comparison with a base of data in order to identify the perturbed signal. After the identification, it is recomposed the signal applying the inverse DWT. Many assumptions can be established: the rate signal-to-noise is properly high, the base of data must contain so many perturbed signals all with the same level of compression. The problem considered is for perturbations in the signal. For measurements the problem is similar, but in this case the unknown perturbations are generated by the apparatus of measurements, problems in experimental techniques, or simply by random noises. With the same above assumptions, the DWT is applied. For the identification, it is used a method evolving statistical and metric techniques. It is given some results obtained with an algebraic computer system.

Proceedings Papers

*Proc. ASME*. ICONE17, Volume 5: Fuel Cycle and High and Low Level Waste Management and Decommissioning; Computational Fluid Dynamics (CFD), Neutronics Methods and Coupled Codes; Instrumentation and Control, 621-625, July 12–16, 2009

Paper No: ICONE17-75758

Abstract

The neutron transport equation has been studied from different approaches, in order to solve different situations. The number of methods and computational techniques has increased recently. In this work we present the behavior of a sequence of geometric transformations evolving different transport problems in order to obtain solve a transport problem in a truncated ellipsoid geometry and subject to known boundary conditions. This scheme was depicted in 8 , but now is solved for the different steps. First, it is considered a rectangle domain that consists of three regions, source, void and shield regions 5 . Horseshoe domain: for that it is used the complex function: f : D → C , defined as f ( z ) = 1 2 e z + 1 e z where D = z ∈ C − 0.5 ≤ Re ( z ) ≤ 0.5 , − 1 2 π ≤ Im ( z ) ≤ 1 2 π ( 0.1 ) The geometry obtained is such that the source is at the focus of an ellipse, and the target coincides with the other focus. The boundary conditions are reflective in the left boundary and vacuum in the right boundary. Indeed, if the eccentricity is a number between 0,95 and 0,99, the distance between the source and the target ranges from 20 to 100 length units. The rotation around the symmetry axis of the horseshoe domain generates a truncated ellipsoid, such that a focus coincides with the source. In this work it is analyzed the flux in each step, giving numerical results obtained in a computer algebraic system. Applications: in nuclear medicine and others.

Proceedings Papers

*Proc. ASME*. ICONE16, Volume 1: Plant Operations, Maintenance, Installations and Life Cycle; Component Reliability and Materials Issues; Advanced Applications of Nuclear Technology; Codes, Standards, Licensing and Regulatory Issues, 819-825, May 11–15, 2008

Paper No: ICONE16-48400

Abstract

In this work the hybrid methods approach is introduced in order to solve some problems in Transport Theory for different geometries. The transport equation is written as: ∂ ψ ∂ t ( x , v , t ) + v · ∇ ψ ( x , v , t ) + h ( x , μ ) ψ ( x , v , t ) = = ∫ V k ( x , v , v ′ ) ψ ( x , v ′ , t ) dv ′ + q ( x , v , t ) , in Ω T ψ ( x , v , 0 ) = φ 0 ( x , v ) , in ∂ Ω × V ψ ( x , v , t ) = φ ( x , v , t ) , in ∂ Ω × V × R ( 1 ) where x represents the spatial variable in a domain D , v an element of a compact set V , ψ is the angular flux, h ( x , v ) the collision frequency, k ( x , v , v ’) the scattering kernel function and q ( x , v ) the source function. If ψ does not depend on the time, it is said that the problem (1) is a steady transport problem. Once the problem is defined, including the boundary conditions, it is disposed a set of chained methods in order to solve the problem. Between the different alternatives, an optimal scheme for the resolution is chosen. Two illustrations are given. For two-dimensional geometries it is employed a hybrid analytical and numerical method, for transport problems: conformal mapping first, then the solution in a proper geometry (rectangular for example). Each of the following two techniques is then applied, Krylov subspaces method or spectral-LTS N method. For three-dimensional problems also it is used a hybrid analytical and numerical method, for problems with more complex geometries: a homotopy between the original boundaries (piecewise surfaces) and another (a parallelepiped for example). Then each of two techniques are applied, Krylov subspaces method or nodal-LTSN method. In this case, the design of new geometries for reactors is a straightforward task. En each case, the domain consist of three regions, one of the source, other is the void region and the third one is a shield domain. The results are obtained both with an algebraic computer system and with a language of high level. An important extension is the study and treatment of transport problems for domains with irregular geometries, between them Lipschitzian domains. One remarkable fact of this work is the combination of different modeling and resolution techniques to solve some transport problems.

Proceedings Papers

#### Finding the Minimun of the Quadratic Functional in Variational Approach in Transport Theory Problems

*Proc. ASME*. ICONE16, Volume 1: Plant Operations, Maintenance, Installations and Life Cycle; Component Reliability and Materials Issues; Advanced Applications of Nuclear Technology; Codes, Standards, Licensing and Regulatory Issues, 835-840, May 11–15, 2008

Paper No: ICONE16-48479

Abstract

In this work it is reviewed the variational approach for some Transport Problems. Let X be a convex domain in R n , and V a compact set. For that, it is considered the following equation: ∂ ψ ∂ t ( x , v , t ) + v · ∇ ψ ( x , v , t ) + h ( x , μ ) ψ ( x , v , t ) = = ∫ V k ( x , v , v ′ ) ψ ( x , v ′ , t ) dv ′ + q ( x , v , t ) ( 1 ) where x represents the spatial variable in a domain D , v an element of a compact set V , Ψ is the angular flux, h ( x , v ) the collision frequency, k ( x , v , v ’) the scattering kernel function and q ( x , v ) the source function. It is put the attention in the construction of the quadratic functional J which appears in variational approaches for transport theory (for example, the Vladimirov functional). Some properties of this functional in a proper functional framework, in order to determine the minimum for J are considered. First, the general formulation is studied. Then an algorithm is given for minimizing the functional J for two remarkable problems: spherical harmonic method and spectral collocation method. A program associated to this algorithm is worked in a computer algebraic system, and also was depeloped a version in a high level language.

Proceedings Papers

*Proc. ASME*. ICONE14, Volume 3: Structural Integrity; Nuclear Engineering Advances; Next Generation Systems; Near Term Deployment and Promotion of Nuclear Energy, 435-445, July 17–20, 2006

Paper No: ICONE14-89561

Abstract

The AGENT (Arbitrary GEometry Neutron Transport) an open-architecture reactor modeling tool is deterministic neutron transport code for two or three-dimensional heterogeneous neutronic design and analysis of the whole reactor cores regardless of geometry types and material configurations. The AGENT neutron transport methodology is applicable to all generations of nuclear power and research reactors. It combines three theories: (1) the theory of R -functions used to generate real three-dimensional whole-cores of square, hexagonal or triangular cross sections, (2) the planar method of characteristics used to solve isotropic neutron transport in non-homogenized 2D) reactor slices, and (3) the one-dimensional diffusion theory used to couple the planar and axial neutron tracks through the transverse leakage and angular mesh-wise flux values. The R -function-geometrical module allows a sequential building of the layers of geometry and automatic submeshing based on the network of domain functions. The simplicity of geometry description and selection of parameters for accurate treatment of neutron propagation is achieved through the Boolean algebraic hierarchically organized simple primitives into complex domains (both being represented with corresponding domain functions). The accuracy is comparable to Monte Carlo codes and is obtained by following neutron propagation through real geometrical domains that does not require homogenization or simplifications. The efficiency is maintained through a set of acceleration techniques introduced at all important calculation levels. The flux solution incorporates power iteration with two different acceleration techniques: Coarse Mesh Rebalancing (CMR) and Coarse Mesh Finite Difference (CMFD). The stand-alone originally developed graphical user interface of the AGENT code design environment allows the user to view and verify input data by displaying the geometry and material distribution. The user can also view the output data such as three-dimensional maps of the energy-dependent mesh-wise scalar flux, reaction rate and power peaking factor. The AGENT code is in a process of an extensive and rigorous testing for various reactor types through the evaluation of its performance (ability to model any reactor geometry type), accuracy (in comparison with Monte Carlo results and other deterministic solutions or experimental data) and efficiency (computational speed that is directly determined by the mathematical and numerical solution to the iterative approach of the flux convergence). This paper outlines main aspects of the theories unified into the AGENT code formalism and demonstrates the code performance, accuracy and efficiency using few representative examples. The AGENT code is a main part of the so called virtual reactor system developed for numerical simulations of research reactors. Few illustrative examples of the web interface are briefly outlined.