Natural circulation, mixing, and stratification are important phenomena for the design and safety analysis of many advanced reactor designs with passive safety features as well as large open regions, such as pool reactor designs, spent fuel pools, and containments. Various modeling methods ranging from zero-dimensional (0-D) lumped volumes (or perfect mixing) to full three-dimensional (3-D) computational fluid dynamics (CFD) have been used. Historically, 0-D lumped volume approaches, combined with other modeling methods and assumptions, have been applied to perform so-called conservative analyses, but with the advancement of computational resources and best-estimate-plus-uncertainty methods, it is very desirable to have advanced, multidimensional modeling and simulation capabilities to improve the accuracy of reactor safety analyses, reduce modeling uncertainties, and eliminate the modeling distortions that can occur when simultaneously applying conservatisms. In the past decade there have been large investments in the pursuit of new, higher-fidelity modeling and simulation tools. However, GOTHIC TM , which has been developed and maintained by Zachry Nuclear Engineering (formerly Numerical Applications, Inc.) since the mid-1980s, already provides these capabilities. GOTHIC is an industry-trusted, computationally efficient, coarse-grid multiphase CFD tool that also includes the important attributes of traditional system-level modeling tools, such as component-level models, control system capabilities, and neutron point kinetics models.GOTHIC applies a domain decomposition approach, allowing various levels of fidelity from 0-D to full 3-D to be applied in a single model, giving the user the ability to focus computational resources in the regions of interest while still capturing the integrated system response and important feedback effects. The result is a general-purpose, multiphysics engineering design and analysis tool that can be used for both light water reactor (LWR) and non-LWR designs. This paper provides an overview of 3-D finite volume modeling in GOTHIC, including the governing equations, turbulence model, and solution methods. Additionally, a few of the verification and validation tests from GOTHIC's full test suite are presented to demonstrate fundamental capabilities, including laminar flow in a channel of parallel plates, square and rectangular cavity natural convection, natural convection through vertical and horizontal openings, and natural convection associated with a heated horizontal cylinder in a rectangular cavity. Based on the comparisons with the analytical solutions and experimental results, it is demonstrated that the multidimensional model can perform very well for a wide range of applications.
GOTHIC 8.3(QA) includes capabilities for modeling advanced, non-light water cooled reactors. Important capabilities introduced in GOTHIC 8.3(QA) include fluid property tables for various molten salts, an enhancement to the tracer tracking module to allow radioactive decay energy to be released locally in the carrier fluid and other improvements to the neutron kinetics module. With these new capabilities in place, GOTHIC is used to benchmark steady-state and transient conditions in the Molten Salt Reactor Experiment (MSRE), which operated at Oak Ridge National Laboratory from 1965 to 1969. In this experimental reactor, UF4 fuel was dissolved in molten fluoride salt, and criticality could be achieved only in the graphite moderated core. An air-cooled radiator transferred fission and decay heat to the environment. The design thermal output of the MSRE was 10 MWt, but the radiator design limited the output to 8 MWt. The original design parameters neglected the impact of decay heat on system temperatures. GOTHIC is used to benchmark system operating parameters at both the 10 MWt design condition and the 8 MWt operating condition, both with and without decay heat. The cases that include decay heat apply 7% of the nominal thermal output using the eleven decay heat precursors from ASB 9-2 as tracers. The results of the benchmark exhibit good agreement with design and operating data and demonstrate heat-up due to decay heat in the fuel salt outside the core. In the MSRE, delayed neutron precursors are not confined to the core because the fuel and fission products flow through the system. As a result, there are different values for (effective) delayed neutron fraction with and without flow, and the decay of delayed neutron precursors outside the core under full-flow conditions reduces reactivity by 0.212 % δk/k. Zero power physics testing included fuel salt pump start-up and coast-down transients with a control rod automatically moving to maintain criticality. The control rod motion calculated by GOTHIC is a reasonable match to measured data from these transients. Low power testing included a natural convection transient with no control rod motion such that reactor power was responding to heat load demand from the radiator. The reactor power and fuel salt and coolant salt temperatures calculated by GOTHIC exhibit good agreement with measured data.
A study to characterize the steam waterhammer phenomena of a low pressure cooling injection (LPCI) system for a Mark 1 boiling water reactor (BWR) has been performed using RELAP5 and GOTHIC during a transient event. The scenario of particular interest was a manual switchover from shutdown cooling mode 3 to low pressure injection due to a loss of coolant accident (LOCA). This transient was initiated by opening the isolation valves of the two trains on a LPCI system into the torus. The torus was considered to be at atmospheric pressure and 20°C. The initial condition of the problem was set up such that the liquid was stagnant in the system. The initial temperature and pressure of the liquid, which was between the torus and isolation valves, was considered to be the same as the torus conditions. On the other hand, the initial condition of the liquid upstream of the isolation valves was chosen to be at 1 MPa and near saturation temperature. The analysis showed that the liquid in the system flashed into steam and discharged into the torus after the isolation valves started to open. Discharge of steam continued until the pressure in the LPCI system reached to a hydrostatic equilibrium with the torus. Following this, the cold liquid from the torus began to reflod the LPCI piping while condensing the steam at the liquid-steam interphase. This caused a mild steam waterhammer event when all of the steam condensed in the piping segments with closed ends. A sensitivity analysis showed that, the magnitude of the steam waterhammer predicted by both codes was sensitive to the number of nodes selected to model the piping, where the steam waterhammer phenomena occurred. Technical basis was obtained from the available literature and used as a guide to choose the number of nodes for the models in both codes. Once the steam waterhammer and the hydrodynamic properties associated with this transient were predicted by both codes, the forces exerted on critical pipe components were calculated. Also, selected thermal-hydraulic properties and hydrodynamic loads were compared between both code calculations. Comparisons showed reasonable agreements.
The Molten Salt Reactor Experiment (MSRE), which operated at Oak Ridge National Laboratory from 1965 to 1969, was an experimental reactor that used UF 4 fuel dissolved in molten fluoride salt. Criticality was achieved when the fuel salt mixture passed through the graphite-moderated core region. Therefore, because the fuel and fission products flowed through the system, delayed neutron precursors were not confined to the core, and decay heat was released outside the core, which is a unique challenge relative to more traditional reactor designs with solid fuel. Therefore, research and demonstration reactors such as MSRE have become a valuable source of information for benchmarking modeling and simulation tools for advanced reactor designs. One such tool being considered is GOTHIC, which is a coarse-grid computational fluid dynamics multiphysics software package. GOTHIC includes attributes and physical phenomena needed for modeling these advanced, non-light water reactor designs. For example, GOTHIC includes fluid property tables for various molten salts; a tracer-tracking module for modeling fission products and the radioactive decay and heat release by delayed neutron precursors locally in the fluid outside the core; and other necessary capabilities for modeling molten salt reactor (MSR) designs, including the ability to model dissolved gases. GOTHIC is used to benchmark steady-state and transient conditions from the MSRE. Zero-power physics testing included fuel salt pump start-up and coast-down transients with a control rod automatically moving to maintain criticality. The control rod motion calculated by GOTHIC is a reasonable match to measured data from these transients. Further, low-power testing included a natural convection transient with no control rod motion such that reactor power was responding to heat load demand from the radiator. The reactor power and fuel salt and coolant salt temperatures calculated by GOTHIC exhibit good agreement with measured data. These results confirm GOTHIC capabilities for modeling MSR designs with circulating fuel.
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