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Subchannel codes: CTF and VIPRE-01

In this chapter, two state-of-the-art and well-used subchannel codes are presented: CTF and VIPRE-01. As part of the Consortium for Advanced Simulation of Light Water Reactors, CTF is being used for single- and two-phase flow analysis under light-water reactor normal and anticipated transient operating conditions. Accurate determination of flow distribution, pressure drop, and void content is crucial for predicting margins to thermal crisis and ensuring more efficient nuclear power plant performance. In preparation for the intended applications, CTF is extensively validated against data from experimental facilities. Meanwhile, the licensed commercial code VIPRE-01 is used to generate a baseline set of simulations for the targeted tests and the solution parameters are compared to CTF results. The closure models in CTF that are in the greatest need of improvement are highlighted and discussed.

Zhao, Xingang↗

SE2-ANL Subchannel Analysis with New Heating Calculation Based on VARIANT Transport Code

The multi-assembly, steady-state sub-channel analysis code SE2-ANL has been widely used in thermal-hydraulic analysis of sodium cooled fast reactors (SFR). It is used to compute the core-wide temperature profiles for a given flow distribution and to determine the assembly flow rates yielding a desired (assembly-wise) peak temperature distribution. It is a modified version of SUPERENERGY-2 coupled with the DIF3D/GAMSOR/DIF3D procedure for coupled neutron and gamma heating calculations, developed at Argonne National Laboratory (ANL). In the current version of SE2-ANL, the neutron and gamma fluxes are calculated using the finite-difference diffusion theory option of the DIF3D code with six triangular meshes per hexagonal assembly. In addition, the pin power distributions are estimated by assuming that the power distribution within an assembly is separable in the radial and axial directions. Furthermore, the total heat generation rate in an assembly duct wall is simply determined by a user-specified fraction of the total gamma heating within that assembly. In order to determine the pin power distributions more accurately by eliminating these limitations, a new coupled heating calculation procedure has recently developed based on the neutron and gamma transport calculations with the VARIANT code. For this, the GAMSOR code has been extended to generate the intra-nodal gamma source distribution to be consistent with the trial functions of VARIANT. Using the computed neutron and gamma flux distributions, the power distribution in each fuel pin and duct wall is determined using a new utility code CURVE, which has been developed to evaluate the VARIANT flux solution at the center of each fuel pin and along the duct mid-wall. For each pin segment contained in a VARIANT node, the axial power shape is represented as a quadratic profile. The SE2-ANL code has been modified to interface with the new, coupled neutron and gamma heating calculation scheme. In addition, several improvements have been made on the computational methods and models of SE2-ANL. To eliminate the limit on the axial mesh size due to the numerical instability problem of the current explicit scheme, the numerical scheme for discretizing the energy equation in the axial direction has been changed to the {theta}-method of the SLTHEN code. An automated flow allocation scheme has also been implemented in SE2-ANL to determine assembly flow rates such that the peak cladding mid-wall temperatures of individual orifice zones are equalized over the burn cycle. The impacts of the new heating calculation scheme based on VARIANT transport solutions on the cladding and fuel temperatures have been tested against the existing method of SE2-ANL. Using the existing and new heating calculation schemes, full-core subchannel analyses were performed for the metal core design of the 1000 MWt Advanced Burner Reactor (ABR-1000), and the resulting coolant, cladding and fuel temperatures were compared. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Advances in Fuel Rod Modeling in Subchannel Thermal-Hydraulic Codes

Coolant Boiling in Rod Arrays-Two Fluid (COBRA-TF), or CTF, is a nuclear thermal hydraulic subchannel code used throughout academia and industry. It solves discretized forms of nine coupled equations for the mass, momentum, and energy equations for the liquid and vapor fields; the mass and momentum equation for the droplet field; and the energy equation for solid structures. This work focuses on improving the temperature predictions of CTF by adding new fuel thermal conductivity models that account for burnup, gadolinia content in addition to temperature. Prior to this work, CTF used a temperature dependent fuel thermal conductivity model. In reality, the fuel thermal conductivity is affected by fission product buildup and radiation damage under irradiation. This results in fuel thermal conductivity degradation, and correspondingly an increase in fuel centerline temperature. Accounting of the irradiation effects is particularly important for correct prediction of fuel temperature profile for the Doppler feedback calculation. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Implementation of a Pressure Correction Term in the CTF Subchannel Code

CTF is a modernized and improved version of the legacy subchannel code COBRA-TF, being jointly developed and maintained by Oak Ridge National Laboratory (ORNL) and North Carolina State University. The code was adopted by ORNL for use in the Consortium for Advanced Simulation of Light Water Reactors (CASL) in 2012 to help address CASL challenge problems. Since that time, activities related to CTF have included implementing software quality assurance measures, implementing new features and models, performing validation and verification testing, establishing and supporting a CTF user group, and developing the code for use in coupled applications. CTF is applicable to single- and two-phase flows in light water reactor geometries at normal and accident operating conditions. The two-phase flow model consists of the six-equation two-phase flow model augmented by equations for the droplet field, and it also includes appropriate source terms. This work focuses on the numerical stability of the six-equation two-phase flow model and is part of a recent effort to improve CTF capabilities for simulating flows in boiling water reactors (BWRs). The six-equation two-phase flow model is not strongly hyperbolic, meaning that some of its eigenvalues are either not real or not distinct. In a Cauchy sense, and for an initial-value problem, strong hyperbolicity was found to be equivalent to well-posedness, which ensures the uniqueness of the solution in the space-time used. This concept is also of importance when designing high-order numerical methods and also when implementing boundary conditions that rely on real eigenvalues such as Riemann solvers. A tremendous amount of research is available in the literature on how to hyperbolize the six-equation two-phase flow model by adding ad hoc terms to the system of equations. Such terms are often referred to as virtual mass or interfacial pressure correction terms. From a mathematical perspective, this approach adds terms to the phasic momentum equation containing first-order partial derivatives of the unknowns to modify the Jacobian matrix, thus the imaginary part of the eigenvalues. For this work, an interfacial pressure correction (IPC) term on the same model as what was used for the CATHARE system code, is implemented in CTF. This allows for recovery of a two-pressure formulation. In the following, the six-equation two-phase flow model is recalled, along with the IPC term and its influence on the eigenvalues. Then, numerical results and convergence studies are presented for a water-faucet problem at a pressure of 10 bar. Finally, conclusions and future work are addressed.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Reactivity initiated accident uncertainty quantification for fuel assembly with subchannel code

UNIST CORE lab has developed a multiphysics coupling framework (MPCORE) consisting of Neutronics, Thermal Hydraulics and Fuel Performance modules. It can accommodate one-dimensional as well as sub-channel code Thermal Hydraulics (TH) module. Generally, running a transient requires more computational power due to the convergence of modules with each other. The difference between one-dimensional and sub-channel TH modules is studied in this research for a Reactivity Initiated Accident (RIA). Both TH modules are compared for a RIA uncertainty propagation in a single VERA fuel assembly with 2.11% enrichment. MPCORE is capable of analyzing the transient at any burnup point but for current work, only fresh fuel has been considered. The results have been obtained using dynamic gap heat conductance in FRAPTRAN. Peak centerline temperature, fuel enthalpy and DNBR are compared for both the approaches. The results indicate that the use of sub-channel code lead to greater safety margin for critical parameters. Computation time comparison is also presented for both the cases. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Comparison of subchannel and averaged channel thermal-hydraulic descriptions on coupled pin-by-pin neutronic calculations

Best-estimate transient analysis of Light Water Reactors (LWRs) requires high accuracy code systems solving neutronics (NK), thermal-hydraulics (TH) and thermal-mechanics to model the core behavior. For long time, nodal diffusion methods for solution of the transport equation using assembly size computational meshes have been applied neglecting the details within the fuel assembly, or using 'pin power reconstruction' techniques to predict those details. Moreover, the multiphysics analysis has been commonly performed coupling those neutronic diffusion methods to thermal-hydraulic system codes using a nodalization of several fuel assemblies per computational node without taking into account the effects that this type of averaging can have on the results obtained. This paper presents the work accomplished with the coupled system COBAYA4/CTF for a preliminary analysis of the effect of the different accuracy levels in the NK and TH domain. COBAYA4 is a neutronic code able to solve the diffusion equation at two resolution levels, nodal and pin by pin (PbP). CTF is a thermo-hydraulic code able to solve the coolant conservation equations also at two levels, channel (fuel assembly averaged solution) and sub-channel (real cooling channel) level. The coupled system COBAYA4/CTF is used through SALOME platform, i.e. SALOME is the software able to map conveniently the NK and TH meshes. This coupling allows combining different resolution levels for NK and TH problems. Therefore, the study of the effect of using different resolutions for the NK and TH nodalizations has been performed applying the system to a fuel assembly with selected boundary conditions. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Development of a calculation framework coupling Monte Carlo neutronics, subchannel thermal-hydraulics and 1.5D fuel thermo-mechanics

A coupled calculation system consisting of the Monte Carlo neutronic solver SERPENT and the fuel behaviour solver TRANSURANUS was extended with the sub-channel thermal-hydraulic solver SUBCHANFLOW to form a coupled calculation framework for multi-physics reactor analyses. The coupling between the 3 solvers was accomplished via a driver program written in Perl that runs the solvers, processes and transfers the output data between the solvers and monitors the convergence. While some features of the coupling are still under development, a steady-state coupled calculation resulting in convergence was performed for a single hexagonal fuel assembly to demonstrate that the base functionalities work as expected. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

ECAR-7932 Rev 0 Large Eddy Simulation of MARVEL Reactor Core Subchannel to Evaluate Model Uncertainty of Reynolds-Averaged Navier-Stokes Equation Based Computational Fluid Dynamics Analysis

In the previous work (ECAR-7210), the peak cladding temperature of the MARVEL microreactor has been evaluated by steady-state Reynolds-Averaged Navier-Stokes (RANS) based computational fluid dynamics (CFD) simulations. Although numerical uncertainties of RANS-based CFD simulations has been assessed in ECAR-7210, the model uncertainty of RANS turbulence models must be investigated to resolve the issues related to inaccurate prediction of turbulent heat flux and flow pulsation in a tight lattice rod bundle using the steady-state RANS simulations. Consequently, this ECAR conducted a high-fidelity CFD analysis utilizing Large Eddy Simulation (LES) to generate reference data and investigated the model uncertainty of RANS-based CFD simulations.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

Wire-Wrapped Fuel Pin Effect of Bundle Size on Temperature Distribution for Uniform Heat Flux

A common fuel arrangement for Sodium Fast Reactors (SFR) designs are hexagonal arrays of wire wrapped fuel pins. The helically wound wires redirect coolant to neighboring subchannels and increases mixing. The increased mixing of the coolant is beneficial to heat transfer from the fuel and prevents temperature peaking in hot channels that may occur. The purpose of this study is to observe the effect of bundle size on the temperature distribution of a coolant when a constant heat flux is implemented. Bundles of 19, 37, 61, and 91 pins were modeled. The wire-wrapping on fuel pins encourages interchannel mixing. With a constant heat flux the enhanced interchannel mixing has little observable effect. The temperature distributions of the subchannels has negligible dependence on radial or angular position. The temperature distribution additionally shows negligible dependence on the bundle size. The subchannel average temperatures further illustrate the homogeneity of the temperature across the bundles. Similarly oriented subchannels differ by less than two Kelvin. The temperature distribution within a single subchannel is fairly uniform, differing by about 15 K between the wall and the bulk flow, with the exception of two hot spots. The two hot spots, however, occur in two non-geometrically accurate locations, so little analysis can be performed. To better illustrate the effect of the enhanced mixing of the wire-wrapped fuel pins, a hot pin analysis should be performed to observe how the additional, non-uniform heat is dispersed. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Interface tracking simulations of bubbly flows in PWR relevant geometries

[en] Highlights: • Simulations were performed for turbulent bubbly flows in PWR subchannel geometry. • Liquid turbulence is fully resolved by direct numerical simulation approach. • Bubble behavior is captured using level-set interface tracking method. • Time-averaged single- and two-phase turbulent flow statistical quantities are obtained. - Abstract: The advances in high performance computing (HPC) have allowed direct numerical simulation (DNS) approach coupled with interface tracking methods (ITM) to perform high fidelity simulations of turbulent bubbly flows in various complex geometries. In this work, we have chosen the geometry of the pressurized water reactor (PWR) core subchannel to perform a set of interface tracking simulations (ITS) with fully resolved liquid turbulence. The presented research utilizes a massively parallel finite-element based code, PHASTA, for the subchannel geometry simulations of bubbly flow turbulence. The main objective for this research is to demonstrate the ITS capabilities in gaining new insight into bubble/turbulence interactions and assisting the development of improved closure laws for multiphase computational fluid dynamics (M-CFD). Both single- and two-phase turbulent flows were studied within a single PWR subchannel. The analysis of numerical results includes the mean gas and liquid velocity profiles, void fraction distribution and turbulent kinetic energy profiles. Two sets of flow rates and bubble sizes were used in the simulations. The chosen flow rates corresponded to the Reynolds numbers of 29,079 and 80,775 based on channel hydraulic diameter (D_h) and mean velocity. The finite element unstructured grids utilized for these simulations include 53.8 million and 1.11 billion elements, respectively. This has allowed to fully resolve all the turbulence scales and the deformable interfaces of individual bubbles. For the two-phase flow simulations, a 1% bubble volume fraction was used which resulted in 17 bubbles in the smaller case and 262 bubbles in the larger case. In the larger simulation case the size of the resolved bubbles is 0.65 mm in diameter, and the bulk mesh cell size is about 30 microns. Those large-scale simulations provide new level of details previously unavailable and were enabled by the excellent scaling performance of our two-phase flow solver and access to the state-of-the-art supercomputing resources. The presented simulations used up to 256 thousand processing threads on the IBM BG/Q supercomputer “Mira” (Argonne National Laboratory).

Nuclear Science & Technology↗