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High-Order Homogenization Method in Diffusion Theory for Reactor Core Simulation and Design Calculation

Description: Most modern nodal methods in use by the reactor vendors and utilities are based on the generalized equivalence theory (GET) that uses homogenized cross sections and flux discontinuity factors. These homogenized parameters, referred to as infinite medium parameters, are precomputed by performing single bundle fine-mesh calculations with zero current boundary conditions. It is known that for configurations in which the node-to-node leakage (e.g., surface current-to-flux ratio) is large the use of the infinite medium parameters could lead to large errors in the nodal solution. This would be the case for highly heterogeneous core configurations, typical of modern reactor core designs.
Date: September 30, 2003
Creator: Rahnema, Farzad
Partner: UNT Libraries Government Documents Department

Review of Upscaling Methods for Describing Unsaturated Flow

Description: The representation of small-scale features can be a challenge when attempting to model unsaturated flow in large domains. Upscaling methods offer the possibility of reducing the amount of resolution required to adequately simulate such a problem. In this report, the various upscaling techniques that are discussed in the literature are reviewed. The following upscaling methods have been identified from the literature: (1) stochastic methods, (2) renormalization methods, and (3) volume averaging and homogenization methods; in addition, a final technique, full resolution numerical modeling, is also discussed. Each of these techniques has its advantages and disadvantages. The trade-off is a reduction in accuracy in favor of a method that is easier to employ. For practical applications, the most reasonable approach appears to be one in which any of the upscaling methods identified above maybe suitable for upscaling in regions where the variations in the parameter fields are small. For regions where the subsurface structure is more complex, only the homogenization and volume averaging methods are probably suitable. With the continual increases in computational capacity, fill-resolution numerical modeling may in many instances provide a tractable means of solving the flow problem in unsaturated systems.
Date: September 26, 2000
Creator: Wood, BD
Partner: UNT Libraries Government Documents Department

Nodal Diffusion Burnable Poison Treatment for Prismatic Reactor Cores

Description: The prismatic block version of the High Temperature Reactor (HTR) considered as a candidate Very High Temperature Reactor (VHTR)design may use burnable poison pins in locations at some corners of the fuel blocks (i.e., assembly equivalent structures). The presence of any highly absorbing materials, such as these burnable poisons, within fuel blocks for hexagonal geometry, graphite-moderated High Temperature Reactors (HTRs) causes a local inter-block flux depression that most nodal diffusion-based method have failed to properly model or otherwise represent. The location of these burnable poisons near vertices results in an asymmetry in the morphology of the assemblies (or blocks). Hence the resulting inadequacy of traditional homogenization methods, as these “spread” the actually local effect of the burnable poisons throughout the assembly. Furthermore, the actual effect of the burnable poison is primarily local with influence in its immediate vicinity, which happens to include a small region within the same assembly as well as similar regions in the adjacent assemblies. Traditional homogenization methods miss this artifact entirely. This paper presents a novel method for treating the local effect of the burnable poison explicitly in the context of a modern nodal method.
Date: October 1, 2010
Creator: Ougouag, A. M. & Ferrer, R. M.
Partner: UNT Libraries Government Documents Department

Whole-core neutron transport calculations without fuel-coolant homogenization

Description: The variational nodal method implemented in the VARIANT code is generalized to perform full core transport calculations without spatial homogenization of cross sections at either the fuel-pin cell or fuel assembly level. The node size is chosen to correspond to one fuel-pin cell in the radial plane. Each node is divided into triangular finite subelements, with the interior spatial flux distribution represented by piecewise linear trial functions. The step change in the cross sections at the fuel-coolant interface can thus be represented explicitly in global calculations while retaining the fill spherical harmonics capability of VARIANT. The resulting method is applied to a two-dimensional seven-group representation of a LWR containing MOX fuel assemblies. Comparisons are made of the accuracy of various space-angle approximations and of the corresponding CPU times.
Date: February 10, 2000
Creator: Smith, M. A.; Tsoulfanidis, N.; Lewis, E. E.; Palmiotti, G. & Taiwo, T. A.
Partner: UNT Libraries Government Documents Department

Criticality safety analyses of the early (unreflected) ``Jemima`` and the (reflected) ``Big Ten`` experiments: Calculated effects of fuel homogenization on reactivity

Description: The early ``Jemima`` experiments (1952--1954) have been evaluated as criticality safety benchmarks. The ongoing ``Big Ten`` experiment (1971--present) is under consideration as a benchmark. These two experiments differ enormously in their overall sizes and in the absence (or presence) of an external reflector. However, they share a common characteristic: the entire core, or the majority of it, is comprised of thin, alternating layers of highly enriched uranium and natural uranium, in order to simulate fuel of uniform composition and intermediate enrichment Reference MCNP models for the experiments retain the heterogeneous compositions and include considerable structural detail. For comparison, homogenized models, which preserve overall volumes and the total mass of each isotopic species, have also been tested. Results indicate that (1) heterogeneous assemblies and their equivalent homogeneous assemblies differ significantly in k{sub eff}, and that (2) these differences occur both in the absence and in the presence of a thick external reflector composed of depleted uranium.
Date: September 1, 1995
Creator: Krohn, B.J.
Partner: UNT Libraries Government Documents Department

The Discrete Equation Method (DEM) for Fully Compressible Two-Phase Flows in Ducts of Spatially Varying Cross-Section

Description: Typically, multiphase modeling begins with an averaged (or homogenized) system of partial differential equations (traditionally ill-posed) then discretizes this system to form a numerical scheme. Assuming that the ill-posedness problem is avoided by using a well-posed formulation such as the seven-equation model, this presents problems for the numerical approximation of non-conservative terms at discontinuities (interfaces, shocks) as well as unwieldy treatment of fluxes with seven waves. To solve interface problems without conservation errors and to avoid this questionable determination of average variables and the numerical approximation of the non-conservative terms associated with 2 velocity mixture flows we employ a new homogenization method known as the Discrete Equations Method (DEM). Contrary to conventional methods, the averaged equations for the mixture are not used, and this method directly obtains a (well-posed) discrete equation system from the single-phase system to produce a numerical scheme which accurately computes fluxes for arbitrary numbers of phases and solves non-conservative products. The method effectively uses a sequence of single phase Riemann equation solves. Phase interactions are accounted for by Riemann solvers at each interface. Flow topology can change with changing expressions for the fluxes. Non-conservative terms are correctly approximated. Some of the closure relations missing from the traditional approach are automatically obtained. Lastly, we can often times identify the continuous equation system, resulting from taking the continuous limit with weak wave assumptions, of the discrete equations. This can be very useful from a theoretical standpoint. As a first step toward implict integration of the DEM method in multidimensions, in this paper we construct a DEM model for the flow of two compressible phases in 1-D ducts of spatially varying cross-section to test this approach. To relieve time step size restrictions due to stiffness and to achieve tighter coupling of equations, a fully implicit time integration method is ...
Date: July 1, 2009
Creator: Berry, Ray A.; Saurel, Richard & Grimmett, Tamara
Partner: UNT Libraries Government Documents Department

Numerical Stochastic Homogenization Method and Multiscale Stochastic Finite Element Method - A Paradigm for Multiscale Computation of Stochastic PDEs

Description: Multiscale modeling of stochastic systems, or uncertainty quantization of multiscale modeling is becoming an emerging research frontier, with rapidly growing engineering applications in nanotechnology, biotechnology, advanced materials, and geo-systems, etc. While tremendous efforts have been devoted to either stochastic methods or multiscale methods, little combined work had been done on integration of multiscale and stochastic methods, and there was no method formally available to tackle multiscale problems involving uncertainties. By developing an innovative Multiscale Stochastic Finite Element Method (MSFEM), this research has made a ground-breaking contribution to the emerging field of Multiscale Stochastic Modeling (MSM) (Fig 1). The theory of MSFEM basically decomposes a boundary value problem of random microstructure into a slow scale deterministic problem and a fast scale stochastic one. The slow scale problem corresponds to common engineering modeling practices where fine-scale microstructure is approximated by certain effective constitutive constants, which can be solved by using standard numerical solvers. The fast scale problem evaluates fluctuations of local quantities due to random microstructure, which is important for scale-coupling systems and particularly those involving failure mechanisms. The Green-function-based fast-scale solver developed in this research overcomes the curse-of-dimensionality commonly met in conventional approaches, by proposing a random field-based orthogonal expansion approach. The MSFEM formulated in this project paves the way to deliver the first computational tool/software on uncertainty quantification of multiscale systems. The applications of MSFEM on engineering problems will directly enhance our modeling capability on materials science (composite materials, nanostructures), geophysics (porous media, earthquake), biological systems (biological tissues, bones, protein folding). Continuous development of MSFEM will further contribute to the establishment of Multiscale Stochastic Modeling strategy, and thereby potentially to bring paradigm-shifting changes to simulation and modeling of complex systems cutting across multidisciplinary fields.
Date: March 30, 2010
Creator: Xu, X. Frank
Partner: UNT Libraries Government Documents Department