A detailed set of calculations was carried out for the Advanced Test Reactor (ATR) using the SN2ND solver of the UNIC code which is part of the SHARP multi-physics code being developed under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in DOE-NE. The primary motivation of this work is to assess whether high fidelity deterministic transport codes can tackle coupled dynamics simulations of the ATR. The successful use of such codes in a coupled dynamics simulation can impact what experiments are performed and what power levels are permitted during those experiments at the ATR.The advantages of the SN2ND solver over comparable neutronics tools are its superior parallel performance and demonstrated accuracy on large scale homogeneous and heterogeneous reactor geometries. However, it should be noted that virtually no effort from this project was spent constructing a proper cross section generation methodology for the ATR usable in the SN2ND solver. While attempts were made to use cross section data derived from SCALE, the minimal number of compositional cross section sets were generated to be consistent with the reference Monte Carlo input specification. The accuracy of any deterministic transport solver is impacted by such an approach and clearly it causes substantial errors in this work. The reasoning behind this decision is justified given the overall funding dedicated to the task (two months) and the real focus of the work: can modern deterministic tools actually treat complex facilities like the ATR with heterogeneous geometry modeling.SN2ND has been demonstrated to solve problems with upwards of one trillion degrees of freedom which translates to tens of millions of finite elements, hundreds of angles, and hundreds of energy groups, resulting in a very high-fidelity model of the system unachievable by most deterministic transport codes today. A space-angle convergence study was conducted to determine the meshing and angular cubature requirements for the ATR, and also to demonstrate the feasibility of performing this analysis with a deterministic transport code capable of modeling heterogeneous geometries. The work performed indicates that a minimum of 260,000 linear finite elements combined with a L3T11 cubature (96 angles on the sphere) is required for both eigenvalue and flux convergence of the ATR. A critical finding was that the fuel meat and water channels must each be meshed with at least 3 "radial zones" for accurate flux convergence. A small number of 3D calculations were also performed to show axial mesh and eigenvalue convergence for a full core problem. Finally, a brief analysis was performed with different cross sections sets generated from DRAGON and SCALE, and the findings show that more effort will be required to improve the multigroup cross section generation process.The total number of degrees of freedom for a converged 27 group, 2D ATR problem is ~340 million. This number increases to ~25 billion for a 3D ATR problem. This scoping study shows that both 2D and 3D calculati...

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Auszug aus dem Vorwort zur ersten Auflage.gleichungen braucht er nichts zu wissen. Der Apparat der Cartesischen Koordinaten in drei Dimensionen wird im Buche selbst beschrieben; ebenso werden die Lösungen der• auftretenden Differentialgleichungen erklärt. Häufig ist den analytischen Methoden gegenüber den geometrischen der Vorzug gegeben worden, da sie für die Studenten wahrscheinlich nützlicher sein werden, deren Bedürfnisse immer im Auge behalten sind.Im Anschluß an die im Text gebrachten Beispiele, die einige wohlbekannte Probleme enthalten und auf die im folgenden Bezug genommen wird, sind einigen Kapiteln größere Aufgabensammlungen beigefügt. Ich hoffe, daß sich diese ebensowohl für die Lehrer als auch für die Studenten beim Repetieren des Stoffes als nützlich erweisen. Die Beispiele sind zum größten Teil aus den Examensakten der Universität entnommen; andere, aber nur zum geringeren Teil, die ich in diesen Aktt>n nicht gefunden habe, stammen aus den wohlbekannten Sammlungen von Besant, Routh nnd Wolstenholme.Von den Werken, die mir in Prinzipienfragen recht gute Dienste geleistet haben, nenne ich Kirchhoffs Vor I es u n g e n über. Mathematische Physik (Mechanik), Pearsons Grammar of Science und Machs Mechanik. Das letztere sollte überhaupt jeder Student besitzen, der Interesse für die geschichtliche Entwicklung der dynamischen Anschauungen hat. Für die Methoden der Behandlung einzelner Fragen verdanke ich vieles den Vorlesungen des Herrn R. R. Web b, dem ich mich dadurch sehr verpflichtet fühle.