W. S. Yang

Long-Lived Fission Product Transmutation Studies

Abstract A systematic study on long-lived fission products (LLFPs) transmutation has been performed with the aim of devising an optimal strategy for their transmutation in critical or subcritical reactor systems and evaluating impacts on the geologic repository. First, 99Tc and 129I were confirmed to have highest transmutation priorities in terms of transmutability and long-term radiological risk reduction. Then, the transmutation potentials of thermal and fast systems for 99Tc and 129I were evaluated by considering a typical pressurized water reactor (PWR) core and a sodium-cooled accelerator transmutation of waste system. To determine the best transmutation capabilities, various target design and loading optimization studies were performed. It was found that both 99Tc and 129I can be stabilized (i.e., zero net production) in the same PWR core under current design constraints by mixing 99Tc with fuel and by loading CaI2 target pins mixed with ZrH2 in guide tubes, but the PWR option appears to have a limited applicability as a burner of legacy LLFP. In fast systems, loading of moderated LLFP target assemblies in the core periphery (reflector region) was found to be preferable from the viewpoint of neutron economy and safety. By a simultaneous loading of 99Tc and 129I target assemblies in the reflector region, the self-generated 99Tc and 129I as well as the amount produced by several PWR cores could be consumed at a cost of ˜10% increased fuel inventory. Discharge burnups of ˜29 and ˜37% are achieved for 99Tc and 129I target assemblies with an ˜5-yr irradiation period. Based on these results, the impacts of 99Tc and 129I transmutation on the Yucca mountain repository were assessed in terms of the dose rate. The current Yucca Mountain release evaluations do not indicate a compelling need to transmute 99Tc and 129I because the resulting dose rates fall well below current regulatory limits. However, elimination of the LLFP inventory could allow significant relaxation of the waste form and container performance criteria, with associated economic benefits. Therefore, some development of either specialized waste form or transmutation target for the LLFP is prudent, especially considering the potential accumulation of large LLFP inventory with sustained use of nuclear energy into the future.

On the performance of point kinetics for the analysis of accelerator-driven systems

Abstract The ability of point kinetics to describe dynamic processes in accelerator-driven systems (ADSs) is investigated. Full three-dimensional energy-space-time-dependent calculations, coupled with thermal and hydraulic feedback effects, are performed and used as a standard of comparison. Various transient accident sequences are studied. Calculations are performed in the range of keff = 0.9594 to 0.9987 to provide insight into the dependence of the performance on the subcritical level. Numerical experiments are carried out on a minor-actinide–loaded and lead-bismuth–cooled ADS. It is shown that the point kinetics approximation is capable of providing highly accurate calculations in such systems. The results suggest better precision at lower keff levels. It is found that subcritical operation provides features that are favorable from a point kinetics view of application. For example, reduced sensitivity to system reactivity perturbations effectively mitigates any spatial distortions. If a subcritical reactor is subject to a change in the strength of the external source, or a change in reactivity within the subcritical range, the neutron population will adjust to a new stationary level. Therefore, within the normal range of operation, the power predicted by the point kinetics method and the associated error in comparison with the exact solution tends to approach an essentially bounded value. It was found that the point kinetics model is likely to underestimate the power rise following a positive reactivity insertion in an ADS, which is similar to the behavior in critical systems. However, the effect is characteristically lowered in subcritical versus critical or near-critical reactor operation.

Blanket Design Studies of a Lead-Bismuth Eutectic-Cooled Accelerator Transmutation of Waste System

Abstract The results of blanket design studies for a lead-bismuth eutectic (LBE)-cooled accelerator transmutation of waste system are presented. These studies focused primarily on achieving two important and somewhat contradictory performance objectives: First, maximizing discharge burnup, so as to minimize the number of successive recycle stages and associated recycle losses, and second, minimizing burnup reactivity loss over an operating cycle, to minimize reduction of source multiplication with burnup. The blanket is assumed to be fueled with a nonuranium metallic dispersion fuel; pyrochemical techniques are used for recycle of residual transuranic (TRU) actinides in this fuel after irradiation. The key system objective of high-discharge burnup is shown to be achievable in a configuration with comparatively high power density and relatively low burnup reactivity loss. System design and operating characteristics that satisfy these goals while meeting key thermal-hydraulic and materials-related design constraints have been preliminarily developed. Results of the performance evaluations indicate that an average discharge burnup of ~27% is achieved with a ~3.5-yr fuel residence time. Reactivity loss over the half-year cycle is 5.3%Δk. The peak fast fluence value at discharge, the TRU fraction in the charged fuel, and the peak coolant velocity are well within the assumed design limits. Owing to its use of nonuranium fuel, this proposed LBE-cooled system can consume light water reactor-discharge TRUs at the maximum rate achievable per unit of fission energy produced (~1.0 g/MWd).

Enabling high-fidelity neutron transport simulations on petascale architectures

The UNIC code is being developed as part of the DOEs Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. UNIC is an unstructured, deterministic neutron transport code that allows a highly detailed description of a nuclear reactor. The primary goal of our simulation efforts is to reduce the uncertainties and biases in reactor design calculations by progressively replacing existing multilevel averaging (homogenization) techniques with more direct solution methods based on first principles. Since the neutron transport equation is seven dimensional (three in space, two in angle, one in energy, and one in time), these simulations are among the most memory and computationally intensive in all of computational science. In order to model the complex physics of a reactor core, billions of spatial elements, hundreds of angles, and thousands of energy groups are necessary, leading to problem sizes with petascale degrees of freedom. Therefore, these calculations exhaust memory resources on current and even next-generation architectures. In this paper, we present UNIC simulation results for two important representative problems in reactor design and analysis---PHENIX and ZPR-6. In each case, UNIC shows good weak scalability on up to 163,840 cores of Blue Gene/P (Argonne) and 122,800 cores of XT5 (Oak Ridge). While our current per processor performance is less than ideal, we demonstrate a clear ability to effectively utilize the leadership computing platforms. Over the coming months, we aim to improve the per processor performance while maintaining the high parallel efficiency by employing better algorithms such as spatial p- and h-multigrid preconditioners, optimized matrix-tensor operations, and weighted partitioning for better load balancing. Combining these additional algorithmic improvements with the availability of larger parallel machines should allow us to realize our long-term goal of explicit geometry coupled multiphysics reactor simulations. In the long run, these high-fidelity simulations will be able to replace expensive mockup experiments and reduce the uncertainty in crucial reactor design and operational parameters.

Depletion perturbation theory for the constrained equilibrium cycle

Generalized perturbation theory for the coupled neutron/nuclide field is extended to the constrained equilibrium fuel cycle. A variational method is used to formulate the adjoint depletion equations for the two-point boundary value problem of the equilibrium cycle. The reactor operating constraints are treated using the methods of constrained sensitivity theory. A practical numerical algorithm is developed to solve the constrained equilibrium cycle adjoint equations and sensitivity coefficients are generated for several responses in a zero-dimensional, two-group example. In all cases, the sensitivities are in excellent agreement with the results of the direction subtraction of perturbed forward calculations.

Numerical Optimization of Computing Algorithms of the Variational Nodal Method Based on Transformation of Variables

Abstract Numerical methods based on transformation of variables are developed to improve the computational efficiency of the variational nodal method (VNM). Reordering and orthogonal transformations of the nodal unknowns are found to reduce the coefficient matrices of VNM into block-diagonal forms. These forms make it possible to reduce greatly the number of floating-point operations in matrix manipulations and hence to reduce the computational times. The red-black response matrix acceleration by transformation of interface partial-current variables has been extended to three-dimensional geometries and higher orders of spatial and angular approximations. These combined methods are incorporated within the algorithms currently used in the variational nodal code VARIANT at Argonne National Laboratory. All primary algorithms ranging from the generation of response matrices to the iterative solution method for the response matrix equations are modified to implement the new formulation. The efficiency of the new methods is tested on eigenvalue problems by comparing the computation times of the new and existing methods. Three-dimensional calculations are performed in hexagonal and Cartesian geometry for various spatial and angular approximations. The test results show that very significant gains can be obtained especially for the coupling coefficient calculations in higher angular approximations. More than an order of magnitude reduction of the total computing time is achieved in the best case.

Interface Conditions for Spherical Harmonics Methods

Abstract A set of interface conditions is derived rigorously for the general spherical harmonics solution of the Boltzmann transport equation in three-dimensional Cartesian geometry. The derivation builds upon earlier work of Davidson and Rumyantsev to arrive at sets of interface conditions applicable to both even- and odd-order N spherical harmonics approximations. The exact set of conditions is compared to the approximate set currently employed in the odd-order N variational nodal code VARIANT, and the differences in accuracy and computational effort are summarized. The exact interface conditions are necessary for first-order implementations of spherical harmonics methods.

Evaluation of Long-Life Transuranics Breakeven and Burner Cores for Waste Minimization in a PB-GCFR Fuel Cycle

Transuranics (TRU) breakeven and burner core designs have been studied for the Pebble-Bed Gas-Cooled Fast Reactor (PB-GCFR), which was developed under a 2-yr U.S. Department of Energy Nuclear Energy Research Initiative project. The issues of minimizing waste production, fuel cost, and burnup reactivity swing, and maximizing TRU burning have been investigated primarily from a neutronics viewpoint. For TRU breakeven cores, it was found that for the given core power [300 MW(thermal)] and power density (50 MW/m3), the lowest amount of radiotoxic TRU to be processed is obtained for a long-life (single-batch) core of 30-yr duration. Minimizing the TRU processed results in a minimization of the TRU losses that ultimately will have to be entombed in a geologic repository. The results show that the single-batch, long-life PB-GCFR could be designed to operate over a wide range of cycle lengths and fuel loadings. By modifying the TRU feed to have a higher minor actinide (MA) fraction than contained in light water reactor spent fuel, the burnup reactivity swing for the long-life core can be reduced significantly. With this approach, it is also possible to configure the long-life PB-GCFR core as a TRU burner using nonuranium fuel. A nonuranium fuel PB-GCFR with 24% plutonium and 76% MAs can operate for 17 full-power years and achieve 25% burnup with a reactivity swing of 3%Δk.

Preconditioned krylov solution of response matrix equations

Abstract Multigrid-preconditioned Krylov methods are applied to within-group response matrix equations of the type derived from the variational nodal method for neutron transport with interface conditions represented by orthogonal polynomials in space and spherical harmonics in angle. Since response matrix equations result in nonsymmetric coefficient matrices, the generalized minimal residual (GMRES) Krylov method is employed. Two acceleration methods are employed: response matrix aggregation and multigrid preconditioning. Without approximation, response matrix aggregation combines fine-mesh response matrices into coarse-mesh response matrices with piecewise-orthogonal polynomial interface conditions; this may also be viewed as a form of nonoverlapping domain decomposition on the coarse grid. Two-level multigrid preconditioning is also applied to the GMRES method by performing auxiliary iterations with one degree of freedom per interface that conserve neutron balance for three types of interface conditions: (a) p preconditioning is applied to orthogonal polynomial interface conditions (in conjunction with matrix aggregation), (b) h preconditioning to piecewise-constant interface conditions, and (c) h-p preconditioning to piecewise-orthogonal polynomial interface conditions. Alternately, aggregation is employed outside the GMRES algorithm to coarsen the grid, and multigrid preconditioning is then applied to the coarsened equations. The effectiveness of the combined aggregation and preconditioning techniques is demonstrated in two dimensions on a fixed-source, within-group neutron diffusion problem approximating the fast group of a pressurized water reactor configuration containing six fuel assemblies.

Scoping studies for a small modular lead-cooled fast reactor.

A scoping design study has been carried out of the feasibility of a small, 25 MWt (∼10 MWe), modular lead-cooled fast reactor coupled to an advanced power converter consisting of a gas turbine Brayton cycle that utilizes supercritical carbon dioxide as the working fluid. Major constraints of the study are an ultralong 20 year core lifetime, near zero reactivity burnup swing over the core lifetime, Pb primary coolant natural circulation heat transport, road transportability of plant modular assemblies including the reactor and guard vessels, and high Brayton cycle power conversion efficiency. It is found that the goal of a near zero reactivity burnup swing implies a low core power density that results in an unacceptably low discharge burnup.Copyright