The solution of coupled neutronic/thermal hydraulic nuclear reactor calculations requires the treatment of the nonlinear feedback induced by the thermal hydraulic dependence of the neutron cross sections. As a result of these nonlinearities, current solution techniques often diverge during the iteration process. These instabilities arise due to the low level of coupling achieved by these methods between the neutronic and thermal hydraulic components. In this work, this solution method is labeled the Decoupled Iteration (DI) method, and this technique is examined in an effort to improve its efficiency and stability. An examination of the DI method also serves to provide insight into the development of more highly coupled iteration methods. After the examination of several possible iteration procedures, two techniques are developed which achieve both a higher degree of coupling and stability. One such procedure is the Outer Iteration Coupling (OIC) method, which combines the outer iteration of the multigroup diffusion calculation with the controlling iteration of the thermal hydraulic calculations. The OIC method appears to be stable for all cases, while maintaining a high level of efficiency. Another iteration procedure developed is the Modified Axial Coupling (MAC) procedure, which couples the neutronic and thermal hydraulic components at the level of the axial position within the coolant channel. While the MAC method does achieve the highest level of coupling and stability, the efficiency of this technique is less than that of the other methods examined. Several characteristics of these coupled calculation methods are examined during the investigation. All methods are shown to be relatively insensitive to thermal hydraulic operating conditions, while the dependence upon convergence criteria is quite significant. It is demonstrated that the DI method does not converge for arbitrarily small convergence criteria, which is a result of a non-asymptotic solution approximation by the DI method. This asymptotic quality is achieved in the coupled methods. Thus, not only do the OIC and MAC techniques converge for small values of the relevant convergence criteria, but the computational expense of these methods is a predictable function of these criteria. The degree of stability of the iterative techniques is enhanced by a higher level of coupling, but the efficiency of these methods tends to decrease as a higher degree of coupling is achieved. This is apparent in the diminished efficiency of the MAC procedure. Seeking an optimum balance of efficiency and stability, the OIC technique is demonstrated to be the optimum method for coupled neutronic/thermal hydraulic reactor calculations. / Graduation date: 1994

This thesis addresses the problem of representing few group, homogenised neutron cross sections as a function of state parameters (e.g. burn-up, fuel and moderator temperature, etc.) that describe the conditions in the reactor. The problem is multi-dimensional and the cross section samples, required for building the representation, are the result of expensive transport calculations. At the same time, practical applications require high accuracy. The representation method must therefore be efficient in terms of the number of samples needed for constructing the representation, storage requirements and cross section reconstruction time. Sparse grid methods are proposed for constructing such an efficient representation. Approximation through quasi-regression as well as polynomial interpolation, both based on sparse grids, were investigated. These methods have built-in error estimation capabilities and methods for optimising the representation, and scale well with the number of state parameters. An anisotropic sparse grid integrator based on Clenshaw-Curtis quadrature was implemented, verified and coupled to a pre-existing cross section representation system. Some ways to improve the integrator’s performance were also explored. The sparse grid methods were used to construct cross section representations for various Light Water Reactor fuel assemblies. These reactors have different operating conditions, enrichments and state parameters and therefore pose different challenges to a representation method. Additionally, an example where the cross sections have a different group structure, and were calculated using a different transport code, was used to test the representation method. The built-in error measures were tested on independent, uniformly distributed, quasi-random sample points. In all the cases studied, interpolation proved to be more accurate than approximation for the same number of samples. The primary source of error was found to be the Xenon transient at the beginning of an element’s life (BOL). To address this, the domain was split along the burn-up dimension into “start-up” and “operating” representations. As an alternative, the Xenon concentration was set to its equilibrium value for the whole burn-up range. The representations were also improved by applying anisotropic sampling. It was concluded that interpolation on a sparse grid shows promise as a method for building a cross section representation of sufficient accuracy to be used for practical reactor calculations with a reasonable number of samples. / Thesis (MSc Engineering Sciences (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

This thesis addresses the problem of representing few group, homogenised neutron cross sections as a function of state parameters (e.g. burn-up, fuel and moderator temperature, etc.) that describe the conditions in the reactor. The problem is multi-dimensional and the cross section samples, required for building the representation, are the result of expensive transport calculations. At the same time, practical applications require high accuracy. The representation method must therefore be efficient in terms of the number of samples needed for constructing the representation, storage requirements and cross section reconstruction time. Sparse grid methods are proposed for constructing such an efficient representation. Approximation through quasi-regression as well as polynomial interpolation, both based on sparse grids, were investigated. These methods have built-in error estimation capabilities and methods for optimising the representation, and scale well with the number of state parameters. An anisotropic sparse grid integrator based on Clenshaw-Curtis quadrature was implemented, verified and coupled to a pre-existing cross section representation system. Some ways to improve the integrator’s performance were also explored. The sparse grid methods were used to construct cross section representations for various Light Water Reactor fuel assemblies. These reactors have different operating conditions, enrichments and state parameters and therefore pose different challenges to a representation method. Additionally, an example where the cross sections have a different group structure, and were calculated using a different transport code, was used to test the representation method. The built-in error measures were tested on independent, uniformly distributed, quasi-random sample points. In all the cases studied, interpolation proved to be more accurate than approximation for the same number of samples. The primary source of error was found to be the Xenon transient at the beginning of an element’s life (BOL). To address this, the domain was split along the burn-up dimension into “start-up” and “operating” representations. As an alternative, the Xenon concentration was set to its equilibrium value for the whole burn-up range. The representations were also improved by applying anisotropic sampling. It was concluded that interpolation on a sparse grid shows promise as a method for building a cross section representation of sufficient accuracy to be used for practical reactor calculations with a reasonable number of samples. / Thesis (MSc Engineering Sciences (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

Thesis (M.S. in Physics)--Naval Postgraduate School, January 1965. / Thesis Advisor(s): Handle, Harry E. "January 1965." Description based on title screen as viewed on June 2, 2010 DTIC Descriptor(s): (Neutron Cross Sections, Thermal Neutrons), (Research Reactors, Reactor Feasibility Studies), Fast Neutrons, Gold, Radioactive Isotopes, Measurement, Perturbation Theory, Neutron Capture, Indium, Standards, Errors, Materials, Neutron Flux, Mathematical Analysis, Cadmium, Reactor Shielding Materials, Computer Programming, Foils (Materials), Reactor Control, Reactor Kinetics, Reactor Start Up Sources. DTIC Identifier(s): AGN-201 Reactors Includes bibliographical references (p. 32). Also available in print.

<p>Accelerator-driven systems for transmutation of nuclear waste have been suggested as a means for dealing with spent fuel components that pose potential radiological hazard for long periods of time. While not entirely removing the need for underground waste repositories, this nuclear waste incineration technology provides a viable method for reducing both waste volumes and storage times. Potentially, the time spans could be diminished from hundreds of thousand years to merely 1.000 years or even less. A central aspect for accelerator-driven systems design is the prediction of safety parameters and fuel economy. The simulations performed rely heavily on nuclear data and especially on the precision of the neutron cross section representations of essential nuclides over a wide energy range, from the thermal to the fast energy regime. In combination with a more demanding neutron flux distribution as compared with ordinary light-water reactors, the expanded nuclear data energy regime makes exploration of the cross section sensitivity for simulations of accelerator-driven systems a necessity. This fact was observed throughout the work and a significant portion of the study is devoted to investigations of nuclear data related effects. The computer code package EA-MC, based on 3-D Monte Carlo techniques, is the main computational tool employed for the analyses presented. Directly related to the development of the code is the extensive IAEA ADS Benchmark 3.2, and an account of the results of the benchmark exercises as implemented with EA-MC is given. CERN's Energy Amplifier prototype is studied from the perspectives of neutron source types, nuclear data sensitivity and transmutation. The commissioning of the n_TOF experiment, which is a neutron cross section measurement project at CERN, is also described.</p>

Accelerator-driven systems for transmutation of nuclear waste have been suggested as a means for dealing with spent fuel components that pose potential radiological hazard for long periods of time. While not entirely removing the need for underground waste repositories, this nuclear waste incineration technology provides a viable method for reducing both waste volumes and storage times. Potentially, the time spans could be diminished from hundreds of thousand years to merely 1.000 years or even less. A central aspect for accelerator-driven systems design is the prediction of safety parameters and fuel economy. The simulations performed rely heavily on nuclear data and especially on the precision of the neutron cross section representations of essential nuclides over a wide energy range, from the thermal to the fast energy regime. In combination with a more demanding neutron flux distribution as compared with ordinary light-water reactors, the expanded nuclear data energy regime makes exploration of the cross section sensitivity for simulations of accelerator-driven systems a necessity. This fact was observed throughout the work and a significant portion of the study is devoted to investigations of nuclear data related effects. The computer code package EA-MC, based on 3-D Monte Carlo techniques, is the main computational tool employed for the analyses presented. Directly related to the development of the code is the extensive IAEA ADS Benchmark 3.2, and an account of the results of the benchmark exercises as implemented with EA-MC is given. CERN's Energy Amplifier prototype is studied from the perspectives of neutron source types, nuclear data sensitivity and transmutation. The commissioning of the n_TOF experiment, which is a neutron cross section measurement project at CERN, is also described.